There all together, 317, different equivalence classes For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 4, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [1, 2, 4, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 4, 2, 3], %2, {1}], [[1, 2, 3], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}], [[4, 3, 1, 5, 2], { [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {1}], [[2, 3, 1], {[0, 0, 0, 2]}, {1}], [[1, 3, 2], {[0, 0, 2, 0], [0, 0, 1, 1], [0, 0, 0, 2], [0, 3, 0, 0]}, {}], [[2, 1, 3], {[0, 0, 0, 2]}, {}], [[3, 2, 1, 5, 4], {[0, 1, 0, 2, 0, 0], [0, 0, 1, 2, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 2]}, {1}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {3}], [ [4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {3}], [[3, 2, 1], {[1, 0, 0, 0], [0, 3, 0, 0]}, {}], [[4, 2, 1, 3], %1, {2}], [[3, 2, 4, 1], {[0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 2]}, {}], [[1, 4, 3, 2], %3, {1}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], %2, {2}], [[4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {3}], [[4, 3, 1, 2], %3, {1}], [[4, 1, 2, 3], %2, {2}], [[3, 1, 4, 2], {[0, 3, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[1, 2], {[0, 0, 2]}, {}], [[3, 2, 5, 1, 4], {[0, 1, 0, 2, 0, 0], [0, 0, 1, 2, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 2]}, {1, 2}], [[4, 2, 3, 1], %1, {2}], [[3, 1, 2], {[0, 0, 2, 0], [0, 0, 1, 1], [0, 0, 0, 2], [0, 3, 0, 0]}, {}], [[4, 1, 3, 2], %3, {1}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [ [3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[1], {}, {}], [[3, 2, 1, 4], {[0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 2]}, {}], [ [3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[1, 3, 2, 4], %2, {1}], [[2, 4, 3, 1], %1, {1}], [[2, 1, 4, 3], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[4, 2, 1, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {1}]} %1 := {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]} %2 := {[0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} %3 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 202, 382, 396, 144, 0] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 2, 3, 4], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [4, 3, 2, 1]}, {[2, 1, 3, 4], [3, 1, 2, 4], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[3, 2, 4, 1], { [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[2, 1, 3, 4], {[0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 3, 1], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 5, 3], { [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[2, 1, 3, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 3, 0, 0], [0, 2, 1, 0]}, {}], [[4, 2, 3, 1], %2, {1}], [[1, 3, 2], {[0, 0, 2, 0]}, {}], [[1, 2], {}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 2, 4, 5, 1], {[0, 0, 1, 2, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[3, 4, 2, 5, 1], { [0, 0, 1, 2, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[2, 1], {[0, 3, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 5, 3], %1, {1}], [[3, 1, 2], {[0, 0, 2, 0], [0, 1, 0, 0]}, {}], [[2, 3, 4, 1], { [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}], [ [1, 4, 2, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[1], {}, {}], [[3, 2, 1], {[0, 1, 0, 0], [0, 0, 3, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}], [[2, 3, 1, 5, 4], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 5, 2], { [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[2, 4, 1, 3], %2, {1}], [ [4, 1, 2, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [1, 4, 3, 5, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [ [3, 4, 1, 5, 2], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[2, 4, 3, 1], %2, {2}], [[4, 2, 3, 5, 1], %1, {1}], [[2, 4, 3, 5, 1], %1, {1}]} %1 := {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]} %2 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 222, 563, 1226, 2376, 4213] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 1, 4, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 1, 2], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 1, 4, 3], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {1}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {}], [[1, 3, 2], {}, {2}], [[2, 4, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 3, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 3, 5, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1], {}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 5, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {}], [[1], {}, {}], [ [4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[0, 0, 1, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 239, 734, 2134, 5934, 15918] For the equivalence class of patterns, { {[1, 4, 3, 2], [3, 4, 1, 2], [4, 3, 2, 1]}, {[3, 2, 1, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [2, 3, 4, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [4, 1, 2, 3]}} the member , {[1, 4, 3, 2], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[1, 2, 3], {[0, 2, 0, 0], [3, 0, 0, 0], [2, 1, 0, 0]}, {}], [[], {}, {}], [[1, 2], {[3, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[2, 0, 0, 0], [0, 1, 0, 0]}, {3}], [[3, 1, 2], {[2, 0, 0, 0]}, {}], [[2, 1, 3], {[2, 0, 0, 0], [0, 2, 0, 0]}, {}], [[3, 1, 2, 4], { [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[4, 1, 2, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {3}], [[2, 1], {}, {}], [[2, 1, 3, 4], {[2, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {3}], [ [1, 2, 3, 4], {[2, 1, 0, 0, 0], [2, 0, 1, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [3, 0, 0, 0, 0]}, {2}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 1, 4, 3], %1, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], %1, {1}], [[1, 2, 4, 3], %1, {1}], [[1, 3, 4, 2], %1, {1}], [[2, 3, 4, 1], %1, {1}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 236, 745, 2286, 6866, 20285] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 1, 3, 4], [2, 3, 4, 1]}, {[1, 4, 3, 2], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [4, 1, 2, 3]}, {[1, 3, 4, 2], [2, 1, 3, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [3, 1, 2, 4]}, {[2, 4, 3, 1], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 4, 3, 2], [3, 4, 2, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 1, 3, 4], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 1]}, {1}], [[4, 3, 2, 1], {}, {2}], [[4, 3, 1, 5, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 2, 1, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[4, 3, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[1, 3, 2], {[0, 1, 1, 1]}, {}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {2}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {1}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1]}, {1}], [[3, 2, 1], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [ [4, 2, 5, 3, 1], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0]}, {1}], [ [3, 1, 5, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 1]}, {1}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[1, 4, 3, 2], {[0, 1, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 0, 1, 1]}, {3}], [ [4, 2, 1, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[3, 2, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 254, 858, 2889, 9775, 33371] For the equivalence class of patterns, { {[2, 3, 4, 1], [3, 2, 4, 1], [4, 1, 2, 3]}, {[2, 3, 4, 1], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [3, 2, 1, 4]}, {[1, 4, 3, 2], [3, 1, 2, 4], [3, 2, 1, 4]}, {[1, 3, 4, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, {[2, 3, 4, 1], [4, 1, 2, 3], [4, 2, 1, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [4, 1, 2, 3], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [1, 4, 3, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {[0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {4}], [[1, 3, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 2], {[0, 2, 0]}, {}], [[1, 2, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {2}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [ [3, 1, 2, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {4}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[3, 4, 1, 2], {[0, 2, 0, 0, 0], [0, 0, 0, 2, 0]}, {}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {3}], [ [2, 3, 1, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [ [3, 4, 1, 2, 5], {[0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 249, 804, 2540, 7977, 25106] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 2, 1, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 4, 1, 2], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 4, 1], [3, 4, 1, 2]}, {[2, 3, 4, 1], [3, 2, 1, 4], [3, 4, 1, 2]}, {[3, 2, 1, 4], [3, 4, 1, 2], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 1, 4, 3], [4, 1, 2, 3]}, {[2, 1, 4, 3], [2, 3, 4, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 1, 4, 3], [2, 3, 4, 1]}} the member , {[2, 3, 4, 1], [3, 2, 1, 4], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 4, 3, 2], {[2, 0, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {2}], [[2, 1, 3], {[1, 0, 0, 1], [0, 2, 0, 1]}, {}], [[3, 1, 2, 4], {[0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1]}, {}], [[1, 2, 3], {[1, 0, 0, 0], [0, 2, 0, 1]}, {1}], [[2, 3, 1, 4], {[0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}], [ [2, 1, 4, 3], {[0, 2, 0, 1, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 2, 0, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}], [ [3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[4, 1, 3, 2], {[2, 0, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [ [3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 5, 4, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0]}, {2}], [ [2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[3, 2, 5, 4, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3, 5], { [0, 0, 0, 2, 0, 1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {2}], [[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 2, 0, 1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {1}], [ [3, 5, 2, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 1], [0, 1, 0, 0]}, {}], [[2, 1], {}, {}], [[3, 1, 2], {[1, 0, 0, 1], [2, 0, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {1}], [[1], {}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {2}], [[1, 2], {[2, 0, 1]}, {}], [[4, 1, 2, 3], {[0, 2, 0, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}], [[1, 3, 2], {[1, 0, 0, 1], [2, 0, 1, 0]}, {}], [[2, 5, 1, 4, 3], { [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0]}, {2}], [[2, 1, 5, 4, 3], {[0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 237, 761, 2415, 7626, 24034] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[2, 1, 3, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [3, 4, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {[2, 0, 0, 0]}, {}], [[2, 4, 3, 1], %1, {4}], [[4, 3, 1, 2], %1, {1}], [[3, 2, 1, 4], {[0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 2], {[3, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[1, 4, 3, 2], %1, {2}], [[1, 2, 3], {[0, 0, 1, 0], [3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {1} ], [[1, 4, 2, 3], %2, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 3, 2, 4], { [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {}], [[4, 1, 3, 2], %1, {1}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], %2, {1}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[3, 1, 4, 2], %2, {1}], [[3, 1, 2], {[2, 0, 0, 0]}, {}], [[2, 1, 3, 4], { [0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {3}], [[4, 2, 3, 1], %1, {4}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} %2 := {[0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 69, 181, 375, 651, 1009, 1449] For the equivalence class of patterns, { {[4, 1, 3, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 1, 4], [3, 1, 2, 4]}, {[2, 4, 3, 1], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 3, 4, 2], [1, 4, 2, 3]}} the member , {[4, 1, 3, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1, 2}], [[2, 1, 3], {}, {}], [[2, 1, 3, 4], {}, {3}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1, 2}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[3, 2, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0]}, {1, 2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 310, 1251, 5151, 21536, 91137] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 1, 2, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2]}, {[3, 2, 1, 4], [3, 4, 1, 2], [4, 2, 1, 3]}, {[1, 4, 3, 2], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 4, 3], [2, 3, 4, 1]}, {[1, 4, 3, 2], [2, 4, 3, 1], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [4, 1, 2, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1]}} the member , {[3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 3, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}], [[2, 1], {[1, 0, 1]}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[2, 3, 1], {[1, 0, 1, 0], [1, 0, 0, 1], [0, 1, 0, 0]}, {3}], [[1, 2], {}, {}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 1, 0], [0, 0, 0, 1]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {1}], [[2, 1, 3], {[1, 0, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {1}], [ [4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[4, 1, 2, 3], {[1, 0, 0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {2}], [[3, 1, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155] For the equivalence class of patterns, { {[2, 3, 1, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 4, 2, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [2, 4, 3, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [3, 2, 4, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [4, 1, 3, 2]}, {[1, 2, 3, 4], [2, 1, 4, 3], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 3, 4, 2], [3, 4, 1, 2], [4, 3, 2, 1]}} the member , {[2, 3, 1, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [1, 2, 3, 4], {[0, 0, 3, 0, 0], [2, 0, 0, 1, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [2, 1, 0, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [2, 0, 1, 0, 0], [3, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[3, 1, 2], {[2, 0, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {}], [[1, 2], {[3, 0, 0]}, {}], [[1, 3, 2], {[2, 0, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {}], [[3, 1, 2, 4], {[0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[3, 1, 2, 5, 4], { [0, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {2}], [[1, 3, 2, 5, 4], { [0, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 3, 0, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [2, 0, 0, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 2, 3], %1, {2}], [[4, 1, 2, 5, 3], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[1, 2, 4, 3], %1, {1}], [[3, 1, 2, 4, 5], {[0, 1, 0, 2, 0, 0], [0, 0, 1, 2, 0, 0], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [1, 0, 2, 0, 0, 0], [0, 1, 2, 0, 0, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {2}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1]}, {1}], [ [2, 1, 4, 3], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [1, 0, 1, 0, 1], [0, 1, 1, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [2, 0, 1, 0]}, {}] , [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0]}, {1}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 4, 2, 3], %1, {1}], [[1, 4, 2, 5, 3], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[2, 4, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4, 5], { [0, 1, 0, 2, 0, 0], [0, 0, 1, 2, 0, 0], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [1, 0, 2, 0, 0, 0], [0, 1, 2, 0, 0, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}]} %1 := {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 220, 646, 1835, 5095, 13924] For the equivalence class of patterns, { {[2, 4, 3, 1], [3, 2, 4, 1], [4, 3, 1, 2]}, {[3, 4, 2, 1], [4, 1, 3, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [1, 4, 2, 3], [2, 1, 3, 4]}, {[1, 2, 4, 3], [2, 3, 1, 4], [3, 1, 2, 4]}} the member , {[3, 4, 2, 1], [4, 1, 3, 2], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}], [[], {}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {2}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 290, 1118, 4398, 17595, 71385] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 4, 3, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 4, 3, 1], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 1, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 1, 4], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 3, 4, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 3, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [4, 1, 2, 3], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [1, 4, 3, 2], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], %1, {3}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[3, 1, 2, 4], %1, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {}, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[2, 4, 3, 1], %1, {2}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], %1, {1}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 242, 772, 2409, 7439, 22872] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 3, 1, 4], [2, 4, 3, 1]}, {[2, 3, 1, 4], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 2, 4], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 3, 1, 4], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [2, 4, 3, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[4, 5, 1, 2, 3], {[1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[], {}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0], [0, 1, 1, 0]}, {1}], [[1, 2], {}, {}], [ [3, 1, 2, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {2}], [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[4, 1, 2, 3], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[1], {}, {}], [[3, 1, 2], {[1, 1, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 1, 0, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [2, 3, 1, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 4, 1, 2, 5], { [1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 243, 777, 2408, 7288, 21661] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 3, 4], [2, 3, 4, 1]}, {[1, 2, 4, 3], [2, 1, 3, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, {[3, 2, 1, 4], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 1, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {[1, 0, 2]}, {}], [[2, 3, 1], {[0, 0, 0, 2], [0, 1, 1, 1]}, {}], [[3, 2, 1], {}, {1}], [ [2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[4, 5, 1, 3, 2], {[1, 0, 1, 0, 0, 1], [1, 0, 1, 1, 0, 0], [1, 0, 2, 0, 0, 0], [1, 0, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {4}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [ [1, 2, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 5, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 0, 2], [1, 0, 2, 0], [1, 0, 1, 1]}, {2}], [[2, 4, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 4, 2, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 2], {[0, 0, 0, 2], [1, 0, 2, 0], [1, 0, 1, 1]}, {1}], [[2, 1], {}, {}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {3}], [[1], {}, {}], [[3, 4, 2, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 4, 2, 1], {[0, 1, 0, 1, 1], [0, 0, 1, 0, 1], [0, 0, 0, 0, 2]}, {}], [[3, 5, 2, 1, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {5}], [ [4, 5, 2, 1, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {5}], [ [4, 5, 2, 3, 1], {[0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {1, 2}], [[4, 5, 3, 2, 1], {[0, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {3}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 2]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 1, 1, 0], [1, 0, 2, 0, 0], [1, 0, 1, 0, 1], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {}], [[4, 5, 1, 2, 3], {[0, 1, 0, 1, 0, 1], [0, 1, 0, 2, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 2]}, {1, 2}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 2]}, {}], [ [1, 4, 5, 2, 3], {[0, 1, 0, 1, 0, 1], [0, 1, 0, 2, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 2]}, {2, 3}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [ [4, 5, 3, 1, 2], {[1, 0, 1, 0, 0, 1], [1, 0, 1, 1, 0, 0], [1, 0, 2, 0, 0, 0], [1, 0, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {3}], [[1, 4, 5, 3, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 255, 866, 2927, 9923, 33898] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[2, 3, 4, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 4, 3, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [3, 2, 1, 4]}, {[1, 2, 3, 4], [1, 4, 2, 3], [3, 2, 1, 4]}, {[1, 2, 3, 4], [1, 4, 3, 2], [2, 3, 1, 4]}, {[1, 2, 3, 4], [1, 4, 3, 2], [3, 1, 2, 4]}, {[2, 3, 4, 1], [4, 1, 3, 2], [4, 3, 2, 1]}} the member , {[2, 3, 4, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[4, 1, 2, 3], {[0, 0, 1, 2, 0], [1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {2}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[], {}, {}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 2, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {[1, 2, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 1, 2, 0], [1, 1, 0, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[2, 3, 1], {[1, 2, 0, 0], [1, 0, 2, 0], [1, 1, 1, 0]}, {}], [[2, 4, 1, 3], {[0, 0, 1, 2, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0]}, {2}], [ [1, 4, 2, 3], {[0, 0, 1, 2, 0], [1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0], [0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], { [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[2, 1, 3], {[1, 2, 0, 0], [1, 1, 1, 0]}, {}], [[3, 1, 2], {[1, 1, 0, 0], [1, 0, 1, 0], [0, 1, 2, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 233, 739, 2343, 7458, 23801] For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 4, 3, 1], [3, 1, 2, 4]}, {[1, 4, 2, 3], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [3, 2, 4, 1]}, {[2, 4, 3, 1], [3, 1, 2, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 4, 3], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 4, 1, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 1, 4, 3], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {4}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {4}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 2, 4, 1], %1, {1}], [[3, 4, 1, 2], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[1, 2], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 1, 0]}, {}], [[2, 3, 1], {}, {}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0]}, {2}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {4}], [[2, 5, 1, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[4, 2, 3, 1], %1, {1}], [[3, 4, 2, 1], %1, {1}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[2, 3, 1, 4], %1, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [ [3, 4, 1, 2, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {2}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 244, 794, 2553, 8179, 26192] For the equivalence class of patterns, { {[1, 3, 4, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [2, 4, 3, 1]}, {[1, 4, 2, 3], [3, 4, 2, 1], [4, 3, 1, 2]}, {[3, 1, 2, 4], [3, 4, 2, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 4, 2, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [3, 2, 4, 1]}} the member , {[1, 3, 4, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2], {[2, 0, 0, 0]}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[2, 1, 3], {[2, 0, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 2], {[2, 0, 0, 0]}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [2, 0, 0, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [2, 0, 0, 0, 0]}, {2}], [[2, 1], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {3}], [[1], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {1}], [ [2, 5, 1, 4, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {4}], [ [2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 4, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [2, 0, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[2, 1, 4, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 233, 719, 2146, 6260, 17968] For the equivalence class of patterns, { {[1, 4, 2, 3], [1, 4, 3, 2], [2, 4, 1, 3]}, {[1, 3, 4, 2], [1, 4, 3, 2], [3, 1, 4, 2]}, {[2, 4, 1, 3], [4, 1, 2, 3], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4]}, {[2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 1, 4, 2], [3, 2, 4, 1]}, {[3, 1, 4, 2], [4, 1, 2, 3], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [1, 4, 3, 2], [2, 4, 1, 3]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[2, 1], {}, {1}], [[1, 3, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 2], {[0, 2, 0]}, {}], [[1, 2, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {2}], [[1], {}, {}] } Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299, 37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946, 353224531663] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 3, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 2, 4, 1], [4, 2, 1, 3]}, {[1, 3, 2, 4], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 1, 2, 4], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [2, 4, 3, 1], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 1, 1, 0]}, {1}], [[3, 4, 2, 1], {}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 1], {}, {}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 0, 1]}, {}], [[2, 1], {}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[3, 2, 4, 1], {}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 267, 951, 3407, 12309, 44867] For the equivalence class of patterns, { {[2, 3, 4, 1], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [4, 1, 2, 3], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {3}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 2, 5, 4, 1], {[0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[2, 1, 3], {}, {}], [[2, 1, 4, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [[3, 1, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {3}], [[3, 1, 5, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 1, 4, 3], {[1, 1, 0, 1, 0]}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 2, 4, 1], {[0, 1, 1, 0, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[2, 1, 5, 4, 3], {[1, 1, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0]}, {3}], [[3, 2, 1], {[0, 1, 1, 0]}, {2}], [ [3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[2, 4, 3, 1], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 259, 862, 2808, 9090, 29489] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 3, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 1, 3, 4], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 4, 3, 2], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 0, 1, 0, 1], [0, 1, 1, 0, 1], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {3}], [[3, 4, 1, 2], %1, {1}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 1, 3, 2], %1, {3}], [[1, 2], {}, {}], [[3, 2, 5, 1, 4], { [1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [ [4, 3, 2, 5, 1], {[0, 1, 0, 2, 0, 0], [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [ [2, 4, 3, 1], {[1, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {}], [[3, 1, 2], {[1, 0, 0, 0], [0, 0, 0, 2], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 5, 4, 1, 2], {[0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[3, 4, 2, 1], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 2]}, {1}], [[3, 2, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [ [4, 3, 5, 1, 2], {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[3, 2, 1, 4], {[0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [ [3, 5, 4, 2, 1], {[0, 1, 0, 2, 0, 0], [0, 1, 1, 1, 0, 0], [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [1, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 2]}, {1}], [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 0, 2]}, {}], [[3, 2, 1], {[0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 4, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [ [4, 3, 5, 2, 1], {[0, 1, 0, 2, 0, 0], [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0]}, {1}], [[2, 5, 3, 1, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {4}], [[2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[1, 3, 2], {[0, 0, 0, 2], [1, 0, 2, 0], [0, 1, 2, 0], [1, 0, 1, 1], [0, 1, 1, 1]}, {}] , [[4, 3, 1, 2], %1, {2}], [[4, 3, 1, 5, 2], {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [ [4, 3, 2, 1], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [ [3, 2, 1, 5, 4], {[1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 1, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}]} %1 := {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [0, 1, 1, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 205, 536, 1264, 2722, 5424] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 1, 4, 3], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 1, 4, 3], [2, 3, 1, 4]}, {[2, 4, 3, 1], [3, 4, 1, 2], [4, 2, 1, 3]}, {[3, 2, 4, 1], [3, 4, 1, 2], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [2, 1, 4, 3], [3, 1, 2, 4]}, has a scheme of depth , 4 here it is: {[[1, 4, 3, 2], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}], [[], {}, {}], [[2, 1, 3], {[0, 1, 0, 1], [0, 0, 1, 0]}, {3}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 2, 0], [0, 1, 2, 0, 0], [0, 1, 0, 0, 2], [0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 1, 1], [0, 1, 2, 0], [0, 1, 0, 2]}, {2}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 0, 0, 1]}, {1}], [[2, 1], {[0, 1, 2]}, {}], [[3, 2, 1], {[0, 0, 1, 1], [0, 1, 2, 0], [0, 1, 0, 2]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 257, 883, 3019, 10306, 35174] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 3, 1], [3, 2, 1, 4]}, {[2, 3, 1, 4], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 4, 2, 3], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [4, 1, 3, 2]}, {[1, 4, 3, 2], [3, 1, 2, 4], [3, 2, 4, 1]}, {[2, 3, 4, 1], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 4, 3, 2], [2, 3, 1, 4], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [2, 4, 3, 1], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [ [1, 3, 2, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [[3, 1, 2], {}, {}], [[2, 1, 3, 4], {[1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 3, 2, 5, 4], %1, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1, 3], {[1, 0, 1, 0], [0, 1, 1, 0]}, {}], [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 5, 1, 2, 4], %1, {1}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}], [[4, 2, 3, 5, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [4, 5, 1, 2, 3], {[0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[4, 1, 3, 5, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 5, 4], %1, {2}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {1}], [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 4, 1, 2, 5], {[0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 1, 2, 4, 5], {[0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[2, 3, 1, 4], {[1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 0, 0]}, {3}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 228, 670, 1864, 5000, 13099] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 3, 1, 4], [4, 3, 1, 2]}, {[1, 4, 2, 3], [3, 1, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [3, 2, 4, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 3, 1, 4], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {3}], [[2, 3, 1], {[0, 0, 0, 1]}, {}], [[2, 1], {}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 3, 1], %1, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1]}, {}], [[1, 2, 4, 3], {[0, 1, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4, 5], %2, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2], {}, {}], [[2, 4, 3, 5, 1], %1, {1}], [[1, 4, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[3, 2, 4, 5, 1], %1, {1}], [[2, 1, 3, 4, 5], %2, {3}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4, 5], %2, {2}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {3}], [[4, 2, 3, 5, 1], %1, {1}], [[3, 1, 2, 5, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 0, 1]}, {}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [ [3, 1, 5, 2, 4], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[4, 2, 5, 3, 1], %1, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %2 := {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 219, 626, 1698, 4452, 11428] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 4, 3], [2, 3, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [3, 4, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 4, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], %4, {1}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 0], [0, 3, 0, 0]}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[4, 2, 3, 5, 1], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {2}], [[3, 1, 2], {[0, 0, 2, 1]}, {}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 5, 2], %3, {1}], [[1, 4, 3, 2], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1]}, {2}], [[4, 2, 3, 1], {[0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 1, 3], {[0, 3, 0, 0]}, {}], [[3, 4, 1, 2], {[0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[1, 4, 2, 3], %4, {2}], [[2, 3, 1, 4], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [ [2, 1, 5, 4, 3], {[0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 1, 0], [1, 0, 1, 0, 1, 0], [1, 0, 0, 1, 1, 0]}, {3}], [[2, 4, 5, 1, 3], %2, {1}], [[3, 1, 2, 4], {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}], [[3, 1, 4, 2], {[0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 3, 0, 0, 0], [0, 0, 0, 2, 1], [1, 0, 0, 0, 0]}, {}], [ [2, 1, 4, 3], {[0, 3, 0, 0, 0], [0, 0, 0, 2, 1], [1, 0, 1, 0, 1], [1, 0, 0, 1, 1]}, {}], [[3, 2, 4, 1], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 4, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], { [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {3}], [[2, 5, 1, 3, 4], %1, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1]}, {1}], [[1, 2, 3], {[0, 0, 0, 1], [0, 3, 0, 0]}, {}], [[1, 2, 4, 3], %4, {3}], [ [4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 3, 5, 1, 4], %1, {3}], [[1, 3, 2, 5, 4], {[0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {4}], [[1, 3, 2], {[0, 0, 2, 1]}, {}], [[2, 5, 1, 4, 3], {[1, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 1, 0]}, {2}], [ [2, 4, 3, 5, 1], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {1}], [ [1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[1, 4, 2, 5, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 1, 4, 5, 3], %2, {1}], [[2, 3, 4, 1], { [0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 4, 1, 3, 5], { [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 1, 3, 5, 4], {[0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {4}], [ [3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[3, 1, 4, 5, 2], %3, {1}], [[1, 3, 2, 4], {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}], [[3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[3, 4, 5, 1, 2], %3, {1}], [[2, 1, 4, 3, 5], { [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 4, 1, 5, 3], %2, {1}], [[3, 1, 2, 5, 4], {[0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {4}], [[2, 3, 1, 5, 4], %1, {4}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]} %4 := {[0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 204, 479, 951, 1687, 2764] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 1, 3, 4], [2, 3, 4, 1]}, {[3, 2, 1, 4], [3, 2, 4, 1], [4, 3, 1, 2]}, {[3, 2, 1, 4], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 4, 3, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 4, 2, 3], [2, 1, 3, 4], [4, 1, 2, 3]}, {[1, 2, 4, 3], [3, 1, 2, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 4, 3, 1], [4, 3, 1, 2]}} the member , {[1, 4, 3, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 1, 3, 4], {}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 2, 3, 4], {}, {2}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 2, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 0]}, {3}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 989, 3541, 12660, 45316] For the equivalence class of patterns, { {[1, 4, 3, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 4, 1], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 1, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [2, 3, 4, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 4, 1], [4, 3, 2, 1]}} the member , {[1, 4, 3, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1], {[3, 0, 0], [0, 3, 0]}, {}], [[3, 1, 2, 4], {[0, 1, 0, 2, 0], [0, 0, 0, 3, 0], [1, 1, 0, 1, 0], [2, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 2, 0], [0, 1, 0, 0], [3, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 2, 0, 0], [3, 0, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0], [0, 0, 1, 0], [3, 0, 0, 0], [2, 1, 0, 0]}, {}], [[3, 1, 2, 4, 5], {[0, 1, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0], [1, 1, 0, 1, 0, 0], [2, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 2, 1, 0], [1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0], [3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {4}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [3, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [3, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 3, 5, 1], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 2, 0]}, {2}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {2}], [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {2}], [ [3, 1, 2, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {2}], [[2, 3, 1], {[0, 0, 2, 0], [3, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0]}, {1}], [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[3, 2, 1], {[0, 2, 0, 0], [1, 0, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[2, 1, 3, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 232, 717, 2157, 6370, 18557] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 3, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 3, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 1, 2, 4], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[4, 1, 2, 3], %1, {2}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {2}], [[2, 4, 3, 1], %1, {2}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], %1, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 2, 3, 1], %1, {1}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 255, 813, 2443, 6985, 19175] For the equivalence class of patterns, { {[3, 4, 2, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, {[4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4]}, {[1, 2, 3, 4], [1, 3, 2, 4], [2, 1, 3, 4]}} the member , {[3, 4, 2, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}], [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[2, 1, 3], {}, {2}], [[1, 3, 2], {}, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 80, 322, 1346, 5783, 25372, 113174, 511649, 2338988, 10793251, 50205607, 235156609, 1108120540, 5249646137, 24987770893, 119443412277, 573125649031] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 2, 1, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 4, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 3, 2], [2, 3, 4, 1]}, {[1, 4, 3, 2], [2, 3, 4, 1], [3, 4, 2, 1]}} the member , {[2, 1, 3, 4], [2, 3, 4, 1], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[1, 0, 0, 1]}, {}], [[2, 3, 1], {[1, 0, 0, 1]}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], %1, {1}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {2}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[1, 3, 2], {[1, 0, 0, 1]}, {}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[1, 4, 3, 2], %1, {2}], [[4, 1, 3, 2], %1, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[2, 4, 3, 1], %1, {2}]} %1 := {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 256, 876, 2987, 10182, 34726] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 1, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 4, 2, 3], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 3, 4, 2], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [3, 2, 4, 1]}, {[2, 3, 4, 1], [3, 1, 2, 4], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 4, 3, 1], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 1, 0, 1]}, {}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], %1, {3}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 1], [1, 0, 0, 0]}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {2}], [[2, 3, 1, 4], {[1, 1, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 1, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 1, 0]}, {2}], [[2, 1, 4, 3], %1, {1}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [ [3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[4, 1, 5, 3, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [ [4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {3}], [[3, 5, 1, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {3}], [[2, 1, 3], {[1, 0, 1, 0], [1, 1, 0, 1]}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [[2, 4, 1, 3], %1, {3}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {4}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 232, 712, 2116, 6155, 17629] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 1, 4, 3], [4, 2, 3, 1]}, {[2, 1, 4, 3], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 4, 3, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [4, 2, 3, 1]}, {[1, 4, 2, 3], [2, 1, 4, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 2, 4], [3, 4, 1, 2], [4, 2, 1, 3]}, {[1, 3, 2, 4], [3, 2, 4, 1], [3, 4, 1, 2]}} the member , {[1, 4, 2, 3], [2, 1, 4, 3], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 3, 2, 1], {}, {2}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {}], [ [5, 1, 3, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[5, 4, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {2}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0]}, {}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {}, {2}], [[5, 1, 4, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[5, 1, 4, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {}], [[5, 4, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[5, 3, 1, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [[5, 4, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [ [4, 3, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {3}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 2, 0]}, {}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[3, 2, 1, 4], %1, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {3}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[4, 1, 3, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 3], {[0, 0, 1, 0], [1, 2, 0, 0]}, {}], [[2, 3, 1, 4], %1, {1}], [[2, 1, 3, 4], %1, {3}], [[5, 2, 4, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}]} %1 := {[1, 2, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 239, 740, 2194, 6298, 17653] For the equivalence class of patterns, { {[3, 2, 1, 4], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 4, 3, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 2, 1, 4], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 1, 2, 4], [3, 2, 1, 4]}, {[1, 3, 4, 2], [1, 4, 3, 2], [4, 1, 2, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [2, 3, 4, 1]}, {[2, 3, 4, 1], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 3, 4, 1], [3, 2, 4, 1]}} the member , {[1, 4, 3, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1], {[0, 3, 0]}, {}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[1], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [0, 2, 0, 0, 0]}, {3}], [[3, 2, 1], {[0, 0, 1, 0], [0, 3, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [ [3, 2, 4, 1], {[0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[2, 3, 1], {[0, 0, 2, 0], [0, 3, 0, 0], [0, 2, 1, 0]}, {1}], [[3, 1, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {3}], [[1, 3, 2], {[0, 0, 2, 0], [0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 260, 913, 3206, 11258, 39533] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 1, 4, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 4, 1, 3], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 1, 4, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[3, 4, 5, 2, 1], {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {3}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 4, 1], {[0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 1]}, {}], [ [3, 1, 2, 4], {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 1], [0, 3, 0, 0], [0, 0, 3, 0]}, {}], [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 5, 1, 2], { [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 1, 0, 1, 1], [0, 0, 1, 1, 1], [0, 1, 1, 0, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0]}, {}], [[3, 4, 2, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}], [[1, 3, 2, 4], {[0, 0, 0, 3, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1], [0, 1, 1, 1]}, {}] , [[3, 1, 2], {[0, 0, 1, 1], [0, 3, 0, 0], [0, 0, 3, 0], [0, 2, 0, 1]}, {}], [[1, 2, 3], {[0, 0, 0, 1], [0, 0, 3, 0]}, {}], [[2, 4, 1, 3], { [0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 0, 2, 0, 1], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}], [[4, 2, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}], [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], { [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 1, 1]}, {}], [[2, 1, 3, 4], {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [ [3, 2, 4, 1], {[0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 1, 0, 1, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[2, 4, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}], [ [1, 3, 2, 5, 4], {[0, 2, 0, 1, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 2, 4, 3], %3, {1}], [[2, 1, 4, 5, 3], {[0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 5, 1, 2, 4], %1, {1}], [[1, 3, 4, 2], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {2}], [[2, 3, 1], {[0, 1, 1, 1]}, {}], [[1, 4, 3, 2], %4, {2}], [[3, 2, 5, 1, 4], {[0, 0, 0, 2, 0, 1], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 1, 1]}, {1}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 5, 1, 4], %1, {1}], [[3, 4, 2, 1, 5], %2, {3}], [[1, 4, 2, 3], %3, {1}], [[3, 1, 2, 5, 4], %1, {1}], [[3, 4, 1, 2], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 2, 0, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {}], [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[4, 2, 3, 1, 5], %2, {1}], [[3, 4, 1, 2, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]}, {1}], [[4, 5, 2, 1, 3], {[0, 0, 2, 0, 0, 1], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {2}], [ [5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [ [4, 5, 2, 3, 1], {[0, 2, 0, 0, 0, 1], [0, 1, 1, 0, 0, 1], [0, 0, 2, 0, 0, 1], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[4, 3, 1, 2], %4, {1}], [ [2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[4, 1, 3, 2], %4, {1}], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [ [4, 2, 1, 3], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {2}], [[3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], { [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {1}], [ [2, 1, 3, 5, 4], {[0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 5, 2, 1, 4], {[0, 0, 0, 2, 0, 1], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 1, 1]}, {1}], [ [4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1]}, {1}], [[4, 1, 2, 3], %3, {2}], [[3, 2, 4, 1, 5], %2, {1}], [[4, 5, 3, 1, 2], { [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 4, 3, 1, 5], %2, {2}], [[2, 4, 5, 1, 3], {[0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 5, 3, 1, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 2, 4, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 3, 1, 5, 4], %1, {1}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {2}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 1, 1]}, {}], [ [2, 1, 4, 3], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}], [[3, 2, 4, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]} %3 := {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]} %4 := {[0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 69, 164, 252, 221, 85, 0] For the equivalence class of patterns, { {[2, 4, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[2, 4, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[3, 1, 4, 2], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [3, 1, 4, 2]}, {[1, 2, 4, 3], [2, 1, 4, 3], [2, 4, 1, 3]}, {[2, 1, 3, 4], [2, 1, 4, 3], [2, 4, 1, 3]}, {[3, 1, 4, 2], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 4, 3], [3, 1, 4, 2]}} the member , {[2, 4, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {2}], [[1, 4, 2, 3], {}, {3}], [[2, 3, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 310, 1251, 5151, 21536, 91137] For the equivalence class of patterns, { {[1, 2, 4, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 3, 4, 1], [3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 0, 2, 0]}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[1, 4, 2, 3], %1, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}], [[3, 4, 1, 2], %1, {1}], [[4, 1, 3, 2], %1, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], %1, {2}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 2, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], %1, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 246, 763, 2227, 6191, 16567] For the equivalence class of patterns, { {[2, 4, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[3, 1, 4, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [2, 4, 1, 3]}, {[1, 2, 3, 4], [1, 2, 4, 3], [3, 1, 4, 2]}, {[1, 2, 3, 4], [2, 1, 3, 4], [2, 4, 1, 3]}, {[1, 2, 3, 4], [2, 1, 3, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, {[2, 4, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[3, 1, 4, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 1, 2], {}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 4, 1, 2], %1, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], %1, {2}], [[4, 3, 1, 2], %1, {3}], [[1, 3, 2], {}, {1}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}], [[4, 2, 1, 3], %1, {2}], [[2, 4, 1, 3], %1, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {}, {3}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {2}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 265, 925, 3201, 11017, 37793] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 1, 4, 3], [2, 3, 1, 4]}, {[1, 4, 2, 3], [2, 1, 4, 3], [3, 1, 2, 4]}, {[3, 2, 4, 1], [3, 4, 1, 2], [4, 2, 1, 3]}, {[2, 4, 3, 1], [3, 4, 1, 2], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [2, 1, 4, 3], [2, 3, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [ [1, 2, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 2, 4, 3], {[0, 1, 0, 0, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 5, 4, 1], %2, {1}], [[1, 3, 2], {}, {}], [[1, 2, 5, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[5, 1, 2, 4, 3], {[0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], %1, {1}], [[1, 3, 5, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3, 5], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 5, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 5, 3, 4, 1], %2, {1}], [[3, 1, 4, 2], %1, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {}], [[5, 1, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 1, 0, 1], [0, 0, 1, 0]}, {}], [[3, 2, 4, 1], %1, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {}], [[1, 2, 4, 3], {[0, 1, 0, 0, 0]}, {}], [[5, 2, 3, 4, 1], %2, {1}], [[4, 1, 3, 2], {}, {1}], [[1, 2, 5, 4, 3], {[0, 1, 0, 0, 0, 0]}, {3}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {4}], [ [4, 1, 2, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {2}], [[1, 4, 3, 2], {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {2}], [[2, 4, 3, 1], %1, {2}], [[5, 1, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} %2 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 255, 863, 2891, 9638, 32068] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 4, 2, 3], [3, 1, 2, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 2, 4, 1], [4, 2, 1, 3]}} the member , {[1, 4, 3, 2], [2, 4, 3, 1], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 4, 2, 1], {}, {3}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 2, 3], {}, {2}], [[2, 1, 3], {}, {1}], [[1, 3, 2], {[1, 0, 0, 0], [0, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 309, 1237, 5026, 20626, 85242] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [4, 1, 3, 2]}, {[3, 1, 2, 4], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [2, 4, 3, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [4, 2, 1, 3]}, {[2, 3, 1, 4], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 4, 2], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [3, 2, 4, 1]}} the member , {[1, 3, 2, 4], [1, 4, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 1, 2], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[4, 5, 1, 2, 3], {}, {4}], [[2, 1, 3, 4], {}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 4, 1, 2, 5], {}, {1}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {}, {3}], [[3, 4, 1, 2], {}, {}], [[2, 3, 1, 4], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 271, 938, 3146, 10252, 32583] For the equivalence class of patterns, { {[2, 3, 4, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, {[4, 1, 2, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [1, 4, 3, 2]}, {[1, 2, 3, 4], [1, 3, 2, 4], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 1, 4], %1, {1}], [[2, 1, 3, 4], %1, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}], [[1, 4, 3, 2], %1, {1}], [[1, 3, 2], {}, {}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0]}, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {4}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {4}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {4}], [[2, 1, 4, 3], {}, {2}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {3}], [[1, 4, 2, 3], %1, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0]}, {2}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 278, 1019, 3734, 13678, 50100] For the equivalence class of patterns, { {[2, 3, 1, 4], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [2, 4, 3, 1]}, {[3, 1, 2, 4], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 4, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[1, 2, 3], {}, {2}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 287, 1079, 4082, 15522, 59280] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 3, 4, 2], [2, 1, 3, 4], [4, 2, 1, 3]}, {[2, 4, 3, 1], [3, 1, 2, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 1, 3, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 2, 4, 3], [2, 4, 3, 1], [3, 1, 2, 4]}} the member , {[1, 4, 2, 3], [3, 2, 4, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 4, 1, 2], {}, {3}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {}, {2}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 1, 2], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {1}], [[4, 3, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {}], [[4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 5, 3, 2, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 5, 3, 1, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 244, 787, 2468, 7570, 22809] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 4, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [4, 1, 2, 3], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0]}, {1}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}], [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 3, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}], [ [4, 2, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [5, 2, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 248, 735, 1952, 4697, 10378] For the equivalence class of patterns, { {[2, 3, 4, 1], [2, 4, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 4, 1, 3], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 1, 3, 4], [3, 1, 4, 2]}, {[1, 4, 3, 2], [2, 1, 3, 4], [2, 4, 1, 3]}, {[3, 1, 4, 2], [3, 4, 2, 1], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 4, 2], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [2, 4, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[3, 4, 1, 2], {[0, 0, 0, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}], [[1, 3, 2], {[1, 0, 1, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0]}, {2}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {4}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 245, 804, 2617, 8511, 27709] For the equivalence class of patterns, { {[2, 3, 4, 1], [3, 4, 2, 1], [4, 1, 2, 3]}, {[2, 3, 4, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 1, 3, 4], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {2}], [[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[2, 1, 4, 3], {}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {3}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [ [3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [4, 2, 5, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0]}, {}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 241, 766, 2399, 7514, 23648] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 1, 4, 2], [4, 3, 2, 1]}, {[2, 3, 4, 1], [2, 4, 1, 3], [4, 3, 2, 1]}, {[2, 4, 1, 3], [4, 1, 2, 3], [4, 3, 2, 1]}, {[3, 1, 4, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [2, 4, 1, 3]}, {[1, 2, 3, 4], [1, 4, 3, 2], [3, 1, 4, 2]}, {[1, 2, 3, 4], [3, 1, 4, 2], [3, 2, 1, 4]}} the member , {[1, 2, 3, 4], [2, 4, 1, 3], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 4, 3, 1], %2, {1}], [[3, 4, 1, 2], {[0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], %2, {1}], [[1, 3, 4, 2], %1, {2}], [[1, 2, 4, 3], %1, {3}], [[2, 1, 3, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 5, 2], %3, {1}], [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[3, 2, 4, 5, 1], %4, {1}], [[3, 1, 5, 4, 2], %3, {1}], [[3, 2, 5, 4, 1], %4, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[3, 4, 2, 5, 1], %4, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[3, 4, 1, 5, 2], %3, {1}], [[2, 3, 1, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], %1, {2}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 4, 1], %2, {1}], [[3, 4, 2, 1], %1, {1}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {2}], [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], %1, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1]}, {2}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 1]}, {3}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 1]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 3, 1], {[0, 0, 1, 0]}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1]}, {1}], [[2, 1, 4, 3], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} %3 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} %4 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 229, 726, 2299, 7296, 23180] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 3, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [3, 2, 1, 4]}, {[1, 2, 4, 3], [1, 4, 3, 2], [2, 1, 4, 3]}} the member , {[3, 4, 1, 2], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3], {}, {2}], [[1, 3, 2], {}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {1}], [[3, 1, 2], {[0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 313, 1290, 5475, 23764, 105001, 470738, 2136022, 9791501, 45275765, 210931962, 989153896, 4665405537, 22117490066, 105333232395, 503705307121] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [3, 1, 4, 2]}, {[1, 3, 4, 2], [1, 4, 2, 3], [2, 4, 1, 3]}, {[2, 4, 3, 1], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 4, 1, 3], [4, 1, 3, 2], [4, 2, 1, 3]}, {[3, 1, 4, 2], [4, 1, 3, 2], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 1, 2, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [3, 1, 2, 4]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [2, 4, 1, 3]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {1}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299, 37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946, 353224531663] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 3, 4, 2], [2, 3, 4, 1]}, {[2, 1, 3, 4], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 4, 3, 2], [4, 1, 3, 2], [4, 3, 1, 2]}, {[3, 2, 1, 4], [4, 2, 1, 3], [4, 3, 1, 2]}, {[3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 2, 3], [4, 1, 2, 3]}, {[2, 1, 3, 4], [3, 1, 2, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 4, 3, 1], [3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [1, 3, 4, 2], [2, 3, 4, 1]}, has a scheme of depth , 4 here it is: {[[3, 4, 1, 2], {}, {1, 2}], [[], {}, {}], [[1, 3, 2], {}, {2}], [[3, 4, 2, 1], {}, {3}], [[1, 2], {}, {}], [[2, 1], {}, {1}], [ [2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 3, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {}, {1, 2}], [[1, 2, 3], {[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, {[3, 4, 1, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [2, 1, 4, 3]}, {[1, 2, 3, 4], [1, 4, 2, 3], [2, 1, 4, 3]}, {[2, 4, 3, 1], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4]}, {[1, 2, 3, 4], [2, 1, 4, 3], [3, 1, 2, 4]}, {[3, 2, 4, 1], [3, 4, 1, 2], [4, 3, 2, 1]}} the member , {[3, 4, 1, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {[3, 0, 0]}, {}], [[1, 3, 2], {[2, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {2}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [0, 2, 0, 0]}, {2}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {1}], [[3, 1, 2], {[2, 0, 0, 0], [0, 1, 0, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 74, 259, 905, 3163, 11058, 38664, 135193, 472724, 1652965, 5779907, 20210571, 70670238, 247112450, 864077593, 3021418466, 10564988371] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 3, 4, 2], [3, 1, 2, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 4, 3, 1], [4, 2, 1, 3]}, {[3, 2, 1, 4], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 3, 1, 4], [4, 1, 2, 3]}, {[2, 4, 3, 1], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 4, 3, 2], [3, 2, 4, 1], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [3, 1, 2, 4], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {1}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 1, 1]}, {1}], [ [2, 1, 5, 4, 3], {[0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {4}], [[3, 1, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {3}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[3, 2, 5, 4, 1], { [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 1, 5, 3, 4], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 0, 1, 1]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 265, 926, 3216, 11152, 38741] For the equivalence class of patterns, { {[2, 1, 4, 3], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 2, 1, 4], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [2, 3, 4, 1], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 3, 2, 1], {}, {2}], [[1, 5, 4, 3, 2], {}, {3}], [[1, 2], {}, {}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 5, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[4, 2, 5, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {3}], [[3, 4, 2, 1], {}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0]}, {3}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 5, 4, 3, 1], {}, {2}], [[1, 5, 3, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [1, 4, 3, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 5, 4, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {}, {2}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {}, {}], [[4, 5, 3, 1, 2], {[1, 0, 0, 0, 0, 0]}, {4}], [ [3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0]}, {}], [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {4}], [[4, 5, 3, 2, 1], {}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 232, 707, 2066, 5858, 16257] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 4, 1, 3], [4, 2, 1, 3]}, {[1, 2, 3, 4], [2, 4, 1, 3], [2, 4, 3, 1]}, {[3, 1, 2, 4], [3, 1, 4, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 4, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 4, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [4, 3, 2, 1]}} the member , {[1, 4, 2, 3], [2, 4, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 3, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 0, 1, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {[1, 2, 0], [0, 3, 0]}, {}], [[2, 1, 3], {[1, 2, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [1, 0, 2, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 0, 3, 0]}, {}], [[2, 1, 3, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [1, 0, 0, 2, 0], [0, 0, 3, 0, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0]}, {3}], [[3, 2, 1, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[1, 2, 3], { [1, 2, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [1, 0, 2, 0], [0, 1, 2, 0], [1, 1, 1, 0], [0, 0, 3, 0]}, {2}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[3, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 240, 746, 2217, 6371, 17864] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 3, 2], [3, 4, 2, 1]}, {[1, 4, 2, 3], [1, 4, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 4, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, {[3, 1, 2, 4], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [2, 4, 3, 1]}, {[1, 2, 4, 3], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 1, 3, 4], [4, 1, 2, 3], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [1, 4, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 3, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 2], {[0, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 2, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {4}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {3}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 3, 1], {[0, 0, 2, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 270, 930, 3114, 10196, 32820] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 3, 1, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [4, 2, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 1, 2, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 3, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 2, 4, 1], [3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [4, 2, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], %2, {1}], [[3, 4, 1, 2], {}, {1}], [[4, 2, 3, 1], %1, {1}], [[3, 1, 2, 4], %2, {2}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {}, {1}], [[3, 2, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], %1, {3}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], %2, {1}], [[1, 4, 3, 2], %2, {2}], [[2, 4, 3, 1], %1, {2}], [[3, 1, 4, 2], {}, {1}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} %2 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 234, 691, 1910, 5019, 12690] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [3, 2, 1, 4]}, {[2, 4, 3, 1], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [3, 1, 2, 4]}, {[2, 3, 4, 1], [4, 1, 3, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 2, 1, 0, 0], [0, 0, 0, 2, 1], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 1], [0, 0, 1, 0]}, {}], [[2, 3, 1], {[0, 0, 2, 1]}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[0, 1, 0, 0], [0, 0, 2, 1]}, {1}], [[2, 1, 3], {[0, 2, 0, 1], [0, 1, 1, 1], [0, 0, 2, 1]}, {}], [[1, 2], {[0, 2, 1]}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [ [2, 3, 1, 4], {[0, 1, 0, 1, 1], [0, 0, 0, 2, 1], [0, 2, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 0, 2, 1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {2}], [ [3, 1, 2, 4], {[0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [0, 0, 2, 0, 1], [0, 1, 0, 0, 0]}, {2}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 2, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {3}], [[3, 1, 2], {[0, 1, 0, 1], [0, 2, 1, 0]}, {}], [[1, 3, 2, 4], {[0, 0, 0, 2, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {2}], [[3, 4, 1, 2, 5], { [0, 0, 2, 0, 0, 1], [0, 0, 1, 0, 1, 1], [0, 0, 0, 0, 2, 1], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], { [0, 0, 0, 0, 2, 1], [0, 0, 2, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {3}], [[4, 2, 3, 1], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 1, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 2, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 240, 759, 2365, 7369, 23069] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 4, 3, 1], [3, 1, 2, 4]}, {[1, 3, 4, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 4, 3, 1], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [4, 2, 1, 3]}, {[2, 3, 1, 4], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 2, 3], [3, 2, 4, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [3, 2, 4, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 2], {[0, 3, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 3, 1], {[0, 0, 3, 0]}, {}], [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 3, 0], [0, 2, 0, 0, 0]}, {}], [[4, 5, 2, 3, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0]}, {3}], [ [4, 5, 1, 2, 3], {[0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {4}], [[4, 5, 2, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 3, 0], [1, 0, 0, 0, 0]}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {1} ], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[3, 2, 1, 4], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], { [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [ [3, 1, 2, 4], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 5, 1, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]}, {3}], [[3, 4, 1, 2, 5], { [0, 0, 1, 2, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 2, 0], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 3, 0]}, {1}], [ [4, 5, 3, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]}, {4}], [ [3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 4, 2, 1, 5], {[0, 0, 1, 2, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 2, 0], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 3, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 228, 678, 1929, 5307, 14203] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 1, 3, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [2, 4, 3, 1], [4, 3, 1, 2]}, {[3, 1, 2, 4], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 1, 3, 4], [2, 4, 3, 1]}, {[1, 3, 4, 2], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 4, 2, 3], [3, 4, 2, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 1, 3, 4], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[4, 3, 2, 1], {[0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [0, 1, 1, 0, 1], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1]}, {3}], [[4, 2, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 2, 0]}, {3}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 4, 3, 1], { [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [ [3, 2, 1, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {4}], [ [4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[4, 2, 1, 5, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 3, 1, 5, 2], { [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1], {[0, 0, 2, 0], [0, 0, 1, 1]}, {1}], [[3, 2, 1], {[0, 0, 2, 0]}, {}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 241, 759, 2305, 6806, 19652] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 3, 1, 4], [4, 2, 1, 3]}, {[3, 1, 2, 4], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 3, 4, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 3, 4, 2], [4, 1, 3, 2]}, {[1, 4, 2, 3], [4, 2, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 2, 4, 3], [1, 4, 2, 3], [2, 4, 3, 1]}, {[2, 3, 1, 4], [2, 4, 3, 1], [3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [1, 3, 4, 2], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[1, 2, 3], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], %1, {1}], [[2, 1, 3, 4], %1, {1}], [[2, 1, 4, 3, 5], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], {}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {}, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[3, 1, 5, 4, 2], {[0, 1, 0, 0, 0, 0]}, {1}], [[5, 2, 3, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 4, 3, 1], {}, {3}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 3, 2, 4], %1, {1}], [[3, 2, 4, 1], {}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {}], [[5, 3, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}], [[1, 4, 3, 2], {}, {3}], [[2, 1, 5, 4, 3], {}, {4}], [[5, 3, 4, 1, 2], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2, 3}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 286, 1067, 3992, 14976, 56338] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 1, 3], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 3, 4, 2], [2, 4, 3, 1], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 1, 2, 4], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 1, 4, 2], [4, 2, 1, 3]}, {[1, 4, 2, 3], [3, 1, 4, 2], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [2, 4, 1, 3], [4, 1, 3, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 2, 3], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 1, 3], {[0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 3, 4, 1], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 4, 2], [4, 1, 2, 3]}, {[1, 2, 3, 4], [2, 3, 4, 1], [2, 4, 1, 3]}, {[1, 2, 3, 4], [2, 4, 1, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 4, 1, 3], [4, 3, 2, 1]}, {[2, 4, 1, 3], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 4, 3, 2], [3, 1, 4, 2], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 1, 4, 2], [4, 1, 2, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 1, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {3}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {2}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}], [ [2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 1, 1]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 251, 817, 2570, 7872, 23621] For the equivalence class of patterns, { {[1, 3, 4, 2], [3, 1, 4, 2], [3, 4, 2, 1]}, {[3, 1, 2, 4], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 4, 2, 3], [2, 4, 1, 3], [4, 3, 1, 2]}, {[2, 3, 1, 4], [2, 4, 1, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 1, 3, 4], [2, 4, 1, 3], [4, 2, 1, 3]}, {[1, 2, 4, 3], [3, 1, 4, 2], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [2, 4, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 3, 4], {}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {}, {2}], [[3, 1, 2], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 287, 1079, 4082, 15522, 59280] For the equivalence class of patterns, { {[2, 4, 1, 3], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 3, 4], [2, 4, 1, 3]}, {[2, 4, 3, 1], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 1, 3, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 4, 2, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 1, 3, 4], [2, 4, 1, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 1], {}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[1, 3, 2], {[0, 1, 1, 1]}, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 0, 0, 1, 1]}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[2, 4, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {1}], [[2, 5, 4, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [1, 5, 3, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 4, 3, 2, 5], { [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 5, 4, 3, 2], {[0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {3}], [[1, 5, 4, 2, 3], { [0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1]}, {4}], [[1, 4, 2, 3], {[0, 0, 1, 1, 1], [0, 1, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 274, 978, 3463, 12201, 42869] For the equivalence class of patterns, { {[2, 3, 1, 4], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 1, 4], [4, 1, 3, 2]}, {[1, 2, 3, 4], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 3, 4, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, {[2, 3, 4, 1], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [3, 2, 4, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 3, 4, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 2, 1, 4], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 2, 0]}, {}], [[1, 2], {}, {}], [[2, 1], {[0, 3, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[3, 1, 2], {[0, 0, 2, 0], [0, 1, 0, 0]}, {}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 5, 3], { [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {4}], [[2, 1, 3], {[0, 3, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 3, 0, 0, 0], [0, 0, 0, 2, 0]}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {4}], [[4, 3, 1, 2], { [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[4, 3, 2, 1], %3, {1}], [[3, 2, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 4, 2, 1], %3, {1}], [[4, 2, 3, 1], {[0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 1, 5, 4, 3], {[0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {3}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], %3, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 1, 3, 5, 4], {[0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {4}], [[3, 2, 4, 5, 1], %2, {1}], [[2, 1, 4, 3, 5], {[0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {5}], [[3, 1, 4, 5, 2], %1, {2}], [[3, 1, 5, 4, 2], %1, {2}], [[2, 1, 5, 3, 4], { [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[3, 2, 5, 4, 1], %2, {1}], [[2, 3, 1, 5, 4], { [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 4, 2, 5, 1], %2, {1}], [[3, 4, 1, 5, 2], %1, {2}], [[2, 4, 1, 5, 3], { [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {2}], [ [3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}], [ [3, 2, 1], {[0, 0, 0, 1], [0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}] , [[2, 3, 4, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {2}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {3}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 3, 1, 4], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 1, 3, 4], {[0, 3, 0, 0, 0], [0, 0, 0, 0, 1]}, {}]} %1 := {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]} %2 := {[0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} %3 := {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 199, 502, 1232, 2962, 6970] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 3, 2, 4], [2, 1, 3, 4]}, {[3, 4, 2, 1], [4, 2, 3, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4], [2, 1, 3, 4]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {[0, 0, 0, 2]}, {2}], [[3, 1, 2], {[0, 0, 0, 2]}, {1}], [[1, 3, 2], {[0, 0, 0, 1]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 3, 4, 2], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 4, 2, 3], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 2, 3, 4], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 2, 3, 4], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 2, 4, 3], [3, 1, 2, 4], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [2, 4, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 5, 1], %4, {5}], [[], {}, {}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 4, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 5, 2], %1, {3}], [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {4}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0], [0, 0, 0, 0, 1]}, {}], [[3, 4, 1, 2], {[0, 0, 1, 0, 2], [0, 0, 0, 1, 2], [1, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {5}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 1, 2]}, {}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {}], [[3, 1, 2], {[1, 1, 0, 0], [0, 0, 1, 2]}, {}], [[3, 4, 1, 5, 2], %1, {2}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0], [0, 0, 0, 0, 1]}, {}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0], [0, 0, 0, 0, 1]}, {}], [[3, 4, 5, 1, 2], { [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[3, 5, 1, 2, 4], %2, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 2], [0, 0, 0, 1, 2], [1, 0, 0, 0, 0], [0, 0, 1, 1, 0]}, {}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {}], [[3, 4, 2, 5, 1], %4, {5}], [[1, 4, 3, 2], {[0, 0, 0, 1, 2], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [ [1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 0, 1, 2], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [ [4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 1, 2], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [ [4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[2, 1, 4, 3], {[0, 0, 0, 1, 2], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {4}], [ [1, 2, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 5, 2], %3, {2}], [[1, 4, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0]}, {1}], [[1, 3, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 5, 4], %2, {1}], [[1, 3, 5, 2, 4], %2, {1}], [[1, 4, 5, 3, 2], %3, {4}], [[2, 1, 3, 5, 4], %2, {1}], [[2, 1, 4, 5, 3], %5, {1}], [[2, 4, 5, 1, 3], %5, {1}], [[2, 4, 1, 5, 3], %5, {1}], [[2, 3, 1, 5, 4], %2, {1}], [[3, 4, 5, 2, 1], %4, {4}], [[2, 3, 5, 1, 4], %2, {1}], [[3, 4, 1, 2, 5], { [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[4, 5, 1, 2, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [ [4, 2, 3, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[4, 1, 3, 5, 2], %3, {1}], [[3, 1, 2, 5, 4], %2, {1}], [[4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 1, 2], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 5, 2, 4], %2, {1}], [[3, 1, 4, 2, 5], %1, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 1, 0]} %4 := {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0]} %5 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 200, 465, 929, 1667, 2766] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 1, 2, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 4, 1, 3], [4, 2, 1, 3], [4, 3, 1, 2]}, {[3, 1, 4, 2], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 3, 1, 4], [2, 4, 1, 3]}, {[1, 2, 4, 3], [1, 3, 4, 2], [3, 1, 4, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [2, 4, 1, 3]}} the member , {[3, 1, 4, 2], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1, 2}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0]}, {1, 2}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 299, 1172, 4677, 18947, 77746] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 4, 2, 3], [3, 4, 2, 1], [4, 1, 2, 3]}, {[3, 1, 2, 4], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 1, 3, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 4, 3, 2], [2, 1, 3, 4], [2, 4, 3, 1]}, {[1, 2, 4, 3], [3, 2, 1, 4], [3, 2, 4, 1]}, {[1, 2, 4, 3], [3, 2, 1, 4], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 3, 4, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], %1, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[2, 3, 1, 4], %1, {1}], [[3, 4, 1, 2], {}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0]}, {4}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 4, 1, 3], {}, {3}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[1, 2, 3], {[1, 0, 0, 0], [0, 1, 0, 0]}, {1}], [[2, 1, 3, 4], %1, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 241, 756, 2276, 6640, 18915] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [2, 3, 1, 4]}, {[2, 3, 4, 1], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 3, 4], [3, 2, 1, 4]}, {[1, 2, 4, 3], [1, 4, 3, 2], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 1, 3, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 4, 2, 1], [4, 1, 3, 2]}, {[2, 4, 3, 1], [4, 1, 2, 3], [4, 3, 1, 2]}} the member , {[2, 3, 4, 1], [3, 4, 2, 1], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0]}, {2}], [[], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[1, 3, 2], {[1, 0, 1, 0]}, {}], [[3, 1, 2], {[1, 0, 1, 0]}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 257, 886, 3050, 10505, 36206] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 2, 4], [2, 1, 4, 3]}, {[3, 4, 1, 2], [4, 2, 3, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [1, 3, 2, 4], [2, 1, 4, 3]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 0, 0, 2]}, {1}], [[1, 3, 2], {[0, 0, 0, 1]}, {2}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[3, 2, 1], {[0, 0, 3, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 0, 3]}, {1}], [[2, 1, 3], {[0, 0, 1, 0], [0, 0, 0, 2]}, {1}], [[2, 3, 1], {[0, 0, 1, 1], [0, 0, 0, 2], [0, 0, 3, 0]}, {2}], [[2, 1], {[0, 0, 3]}, {}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 75, 268, 958, 3425, 12245, 43778, 156514, 559565, 2000543, 7152292, 25570698, 91419729, 326841561, 1168515890, 4177649198, 14935828405 ] For the equivalence class of patterns, { {[2, 3, 1, 4], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 2, 1, 4], [4, 1, 3, 2]}, {[2, 4, 3, 1], [3, 1, 2, 4], [3, 2, 1, 4]}, {[1, 3, 4, 2], [1, 4, 3, 2], [4, 2, 1, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [3, 2, 4, 1]}, {[1, 4, 2, 3], [2, 3, 4, 1], [3, 2, 4, 1]}, {[2, 3, 4, 1], [2, 4, 3, 1], [3, 1, 2, 4]}, {[1, 3, 4, 2], [4, 1, 2, 3], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [1, 4, 3, 2], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0]}, {}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], %1, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[3, 5, 1, 2, 4], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [ [4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[2, 1, 3, 4], %1, {1}], [[1, 3, 2, 4], %1, {1}], [[2, 4, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], %1, {3}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [ [2, 5, 1, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [ [2, 4, 1, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 5, 1, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 256, 880, 3025, 10406, 35805] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 2, 3, 4], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 2, 4, 3], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 4, 3, 2], [2, 1, 3, 4], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [2, 3, 4, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {2}], [[], {}, {}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 0, 1, 0, 1]}, {}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {2}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[3, 1, 4, 2], {[0, 0, 1, 0, 1]}, {}], [[2, 4, 1, 3], {}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {3}], [[1, 4, 2, 3], %3, {1}], [[4, 1, 2, 3], %3, {2}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[1, 2, 4, 3], %3, {1}], [[1, 3, 2, 5, 4], %2, {1}], [[1, 4, 2, 5, 3], %1, {1}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[4, 2, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 5, 3], %1, {1}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {4}], [[3, 1, 2, 5, 4], %2, {1}], [[4, 1, 5, 2, 3], %1, {1}], [[4, 2, 5, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[3, 1, 5, 2, 4], %2, {1}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {4}], [ [3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[3, 5, 1, 2, 4], %2, {1}], [[4, 5, 1, 2, 3], %1, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]} %3 := {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 216, 555, 1252, 2549, 4787] For the equivalence class of patterns, { {[2, 4, 1, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, {[3, 1, 4, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, {[2, 4, 1, 3], [2, 4, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 2, 4], [3, 1, 4, 2]}, {[1, 2, 3, 4], [1, 3, 4, 2], [3, 1, 4, 2]}, {[1, 2, 3, 4], [1, 4, 2, 3], [2, 4, 1, 3]}, {[3, 1, 4, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [2, 4, 1, 3]}} the member , {[3, 1, 4, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {2}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0]}, {1, 2}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1, 2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 274, 978, 3463, 12201, 42869] For the equivalence class of patterns, { {[2, 3, 4, 1], [3, 1, 4, 2], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 1, 4, 2], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [2, 4, 1, 3], [4, 1, 2, 3]}} the member , {[2, 3, 4, 1], [3, 1, 4, 2], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0]}, {3}], [[3, 2, 1], {[0, 1, 1, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [ [2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[3, 5, 4, 1, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [2, 5, 4, 1, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [ [2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}], [ [3, 5, 4, 2, 1], {[0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[2, 4, 3, 1], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 253, 843, 2772, 9080, 29759] For the equivalence class of patterns, { {[2, 3, 4, 1], [3, 2, 1, 4], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 2, 1, 4], [4, 1, 2, 3]}, {[2, 3, 1, 4], [2, 3, 4, 1], [3, 2, 1, 4]}, {[1, 3, 4, 2], [1, 4, 3, 2], [2, 3, 4, 1]}, {[3, 2, 1, 4], [4, 1, 2, 3], [4, 2, 1, 3]}, {[1, 4, 3, 2], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 4, 3, 2], [2, 3, 4, 1], [2, 4, 3, 1]}, {[1, 4, 2, 3], [1, 4, 3, 2], [4, 1, 2, 3]}} the member , {[2, 3, 4, 1], [3, 2, 1, 4], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}], [[2, 1], {[1, 0, 1]}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[1, 2], {}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 1, 0], [0, 0, 0, 1]}, {1}], [[2, 1, 3], {[1, 0, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}], [[2, 3, 1], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[1, 4, 2, 3], %1, {1}], [[4, 1, 2, 3], %1, {2}], [[3, 5, 1, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {3}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], %1, {3}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {2}], [ [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 286, 1066, 3977, 14841, 55386] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 1, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 1, 4, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 4, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 2, 4, 3], [2, 4, 1, 3], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [4, 3, 1, 2]}} the member , {[1, 3, 4, 2], [3, 1, 4, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3, 4], %1, {3}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[3, 2, 4, 1], %1, {1}], [[1, 3, 2], {}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[3, 4, 1, 2], {}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], %1, {2}], [[1, 3, 2, 4], %1, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 3, 1], %1, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0]}, {1}], [[2, 3, 1, 4], %1, {1}], [[3, 1, 2, 4], %1, {2}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0]}, {3}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0]}, {4}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155] For the equivalence class of patterns, { {[2, 3, 1, 4], [4, 1, 2, 3], [4, 2, 1, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 3, 4, 1], [2, 4, 3, 1]}, {[2, 3, 4, 1], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 3, 1, 4], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 3, 4, 2], [1, 4, 3, 2], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 2, 1, 4], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [1, 4, 3, 2], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [ [2, 1, 3, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[1, 3, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 2], {[0, 2, 0]}, {}], [[1, 2, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {2}], [[4, 1, 3, 2], %1, {1}], [[3, 1, 4, 2], %1, {1}], [[2, 1, 4, 3], %1, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 0, 2, 0]}, {1}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {}], [[3, 1, 2, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 265, 929, 3249, 11362, 39746] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 3, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 4, 2, 3], [3, 2, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 3, 2, 4], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 4, 3, 2], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[2, 3, 1], {[1, 0, 1, 1]}, {}], [[], {}, {}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[2, 1], {}, {}], [[1], {}, {}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {3}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2], {[1, 0, 1, 0], [0, 0, 0, 1]}, {2}], [[3, 4, 1, 2], {[1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [ [2, 5, 1, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {4}], [[3, 1, 2, 5, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {2}], [[1, 2, 4, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {3}], [[4, 2, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [[3, 1, 2], {[1, 0, 1, 0], [1, 1, 0, 1]}, {}], [[4, 1, 2, 5, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[0, 1, 0, 1], [1, 0, 0, 0]}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [ [3, 1, 2, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[1, 2, 3, 4], %1, {1}], [ [2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {2}], [ [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {3}], [[2, 3, 1, 4], %1, {3}], [[2, 1, 3, 4], %1, {1}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {2}], [[3, 2, 4, 1], {[1, 0, 0, 1, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 229, 686, 1972, 5514, 15131] For the equivalence class of patterns, { {[2, 1, 3, 4], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 2, 4, 3], [4, 1, 2, 3], [4, 2, 1, 3]}, {[2, 1, 3, 4], [2, 3, 4, 1], [2, 4, 3, 1]}, {[1, 4, 2, 3], [1, 4, 3, 2], [3, 4, 2, 1]}, {[3, 1, 2, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 3, 4, 2], [1, 4, 3, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 2, 1, 4], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [4, 1, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 4, 2, 1], %2, {3}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}], [[4, 1, 3, 2], %2, {3}], [[1, 3, 2], {[0, 0, 2, 0]}, {}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], %2, {3}], [[2, 3, 1], {}, {}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0]}, {2}], [[2, 1], {}, {}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], %2, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[4, 2, 3, 1], %2, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 3, 2, 4], %2, {2}], [[1, 4, 2, 3], %2, {2}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {3}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {3}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0]}, {3}], [[3, 1, 4, 2, 5], %1, {3}], [[4, 1, 5, 3, 2], %1, {3}], [[3, 1, 5, 2, 4], %1, {3}], [[4, 2, 5, 3, 1], %1, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 2, 0]}, {}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]} %2 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 262, 890, 2949, 9575, 30590] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [2, 1, 4, 3]}} the member , {[3, 4, 1, 2], [4, 1, 2, 3], [4, 2, 3, 1]}, has a scheme of depth , 4 here it is: {[[2, 1, 3], {[1, 1, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0]}, {3}], [[3, 2, 1], {[0, 1, 1, 0]}, {2}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {3}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 289, 1103, 4261, 16603, 65100] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 4, 2, 1], [4, 3, 2, 1]}, {[2, 1, 3, 4], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 4, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [3, 4, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [4, 3, 1, 2]}, {[1, 2, 3, 4], [2, 1, 3, 4], [3, 4, 2, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0], [2, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 4, 1, 3], { [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[1, 2], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3], {[2, 0, 0, 0]}, {1}], [[1, 3, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {2}], [[2, 3, 1], {[2, 0, 0, 0]}, {}], [[2, 1], {[2, 0, 0]}, {}], [[3, 1, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 223, 587, 1356, 2820, 5395] For the equivalence class of patterns, { {[2, 3, 4, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 1], {[3, 0, 0], [0, 3, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 4, 2], { [0, 0, 0, 3, 0], [2, 0, 0, 1, 0], [2, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], { [0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0], [0, 0, 1, 0], [3, 0, 0, 0], [2, 1, 0, 0]}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 3, 1], {[3, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}] , [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [2, 0, 1, 0], [0, 0, 3, 0]}, {}], [[4, 2, 1, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [ [3, 2, 1, 4], {[0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 4, 3, 1, 5], {[0, 0, 1, 2, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[4, 2, 5, 3, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 2, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 4, 3, 1], { [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[2, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {3}], [[3, 2, 1, 5, 4], { [0, 1, 0, 2, 0, 0], [0, 0, 1, 2, 0, 0], [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {2}], [[2, 4, 1, 3], { [2, 1, 0, 0, 0], [2, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [3, 0, 0, 0, 0]}, {3}], [[3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 4, 2, 1], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {3}], [[2, 1, 3], {[3, 0, 0, 0], [0, 3, 0, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {1}], [ [2, 1, 4, 3], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [2, 0, 0, 1, 0], [1, 1, 0, 1, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [2, 1, 0, 0, 0], [2, 0, 1, 0, 0], [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 3, 1, 5, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]}, {1}], [[3, 5, 4, 1, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 3, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0]}, {1}], [ [3, 1, 4, 2, 5], {[0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 5, 4, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 2, 0, 0], [1, 0, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[4, 1, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 204, 560, 1617, 4796, 14249] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 1, 4, 3], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 4, 2, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 4, 3], [4, 1, 3, 2]}, {[2, 1, 3, 4], [2, 1, 4, 3], [3, 2, 4, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [2, 4, 3, 1]}, {[1, 3, 4, 2], [3, 4, 1, 2], [3, 4, 2, 1]}, {[3, 1, 2, 4], [3, 4, 1, 2], [4, 3, 1, 2]}} the member , {[1, 4, 2, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1, 3, 4], {}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3, 4], {}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[3, 1, 2, 4], {}, {3}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {}, {3}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 1], {[0, 1, 0, 0]}, {3}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0]}, {2}], [[1, 2, 4, 3], {[0, 0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 287, 1080, 4094, 15611, 59811] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 3, 4, 1], [4, 1, 2, 3]}, {[1, 4, 2, 3], [2, 3, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 3, 4, 1], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 1, 2, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 3, 2], [3, 2, 1, 4], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [2, 3, 4, 1], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 4, 2, 1], {}, {3}], [[3, 1, 5, 4, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[2, 1, 5, 3, 4], %3, {1}], [[3, 1, 5, 2, 4], %3, {1}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0]}, {1}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], %2, {1}], [[3, 1, 4, 2, 5], %1, {1}], [[2, 4, 3, 1], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0]}, {3}], [[2, 3, 1, 4], %2, {1}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0]}, {}], [[2, 1, 4, 3], {}, {}], [[3, 1, 2, 4], %2, {1}], [[2, 4, 3, 1, 5], %1, {2}], [[4, 2, 5, 3, 1], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {1}], [ [3, 5, 4, 1, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[2, 5, 3, 1, 4], %3, {3}], [[3, 5, 4, 2, 1], {[0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[1, 2, 3], {[1, 0, 0, 0], [0, 1, 0, 0]}, {1}], [[2, 1, 3, 4], %2, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 1, 1, 0]}, {4}], [[2, 1, 4, 3, 5], %1, {1}], [ [3, 2, 5, 4, 1], {[0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {2}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 262, 895, 3022, 10188, 34524] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 2, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 3, 2, 4], [2, 3, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [4, 2, 3, 1]}} the member , {[1, 2, 3, 4], [3, 2, 1, 4], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 2, 1, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {4}], [ [2, 1, 4, 3, 5], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {5}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {}], [[3, 2, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [1, 0, 0, 1, 0]}, {}], [[4, 2, 1, 3], {[0, 0, 2, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[1, 3, 2], {[0, 2, 1, 0]}, {}], [[4, 3, 1, 2], {[0, 2, 1, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {2}], [[4, 3, 2, 1], %1, {1}], [[3, 4, 2, 1], %1, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 4, 1, 2], {[0, 2, 1, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {1}], [ [4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 2, 1, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 2, 1, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {1}], [ [1, 3, 4, 2], {[0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[3, 2, 4, 5, 1], %4, {3}], [[3, 1, 4, 5, 2], %5, {1}], [[2, 1, 4, 5, 3], { [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[3, 1, 5, 4, 2], %3, {1}], [[3, 2, 5, 4, 1], %4, {3}], [[2, 1, 5, 4, 3], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {3}], [[2, 1, 5, 3, 4], %2, {1}], [[3, 4, 1, 5, 2], %5, {1}], [[2, 4, 1, 5, 3], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {2}], [[3, 4, 2, 5, 1], %4, {1}], [[3, 4, 5, 2, 1], %4, {1}], [[2, 3, 1, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {4}], [[3, 4, 5, 1, 2], %5, {1}], [[2, 4, 5, 1, 3], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {}], [[2, 3, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 5, 1, 3, 4], %2, {1}], [[3, 5, 1, 4, 2], %3, {1}], [[2, 5, 1, 4, 3], { [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[1, 3, 2, 4], {[0, 2, 1, 0, 0], [0, 0, 0, 0, 1]}, {4}], [[2, 4, 3, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], %4, {1}], [ [2, 5, 4, 1, 3], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[3, 5, 4, 1, 2], %3, {1}], [[2, 5, 3, 1, 4], %2, {2}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [1, 0, 0, 0, 0]}, {}], [[2, 4, 1, 3, 5], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {5}], [[3, 2, 1], {[1, 0, 1, 0], [0, 0, 0, 1], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[3, 1, 2], {[1, 0, 0, 0], [0, 2, 1, 0]}, {}], [[3, 2, 4, 1], %1, {3}]} %1 := {[0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]} %4 := {[0, 2, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]} %5 := {[1, 0, 0, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 200, 481, 1004, 1886, 3270] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 3, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [4, 1, 2, 3], [4, 3, 2, 1]}, {[3, 1, 2, 4], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 3, 4, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 2, 1, 4], [3, 2, 4, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1], {[1, 0, 1]}, {}], [[1, 2], {}, {}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 1, 0], [0, 0, 0, 1]}, {1}], [[2, 3, 1], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[1, 3, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {2}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {2}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {4}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {3}], [[3, 2, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[1, 0, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 241, 756, 2276, 6640, 18915] For the equivalence class of patterns, { {[3, 2, 4, 1], [3, 4, 2, 1], [4, 1, 3, 2]}, {[3, 2, 4, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 3, 4, 2], [2, 1, 3, 4], [3, 1, 2, 4]}, {[2, 4, 3, 1], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 1, 3, 4], [2, 3, 1, 4]}, {[2, 4, 3, 1], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 2, 4, 3], [1, 4, 2, 3], [2, 3, 1, 4]}} the member , {[1, 3, 4, 2], [2, 1, 3, 4], [3, 1, 2, 4]}, has a scheme of depth , 4 here it is: {[[1, 4, 3, 2], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}], [[], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 0, 0, 1]}, {1}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {[0, 0, 1, 1]}, {2}], [[2, 4, 3, 1], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 277, 1016, 3756, 13994, 52491] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 4, 2, 3], [2, 1, 4, 3], [2, 4, 3, 1]}, {[1, 3, 4, 2], [3, 2, 4, 1], [3, 4, 1, 2]}, {[2, 3, 1, 4], [2, 4, 3, 1], [3, 4, 1, 2]}, {[3, 1, 2, 4], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 4, 3], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 1, 2], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[2, 1, 3, 4], {}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3, 4], {}, {2}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {}, {3}], [[4, 1, 2, 3], {}, {3}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2, 4, 3], {[0, 0, 0, 1, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[1, 3, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 268, 961, 3467, 12591, 46012] For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 3, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 1, 4], [3, 4, 1, 2]}, {[1, 2, 3, 4], [1, 4, 3, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [4, 1, 2, 3], [4, 3, 2, 1]}} the member , {[2, 1, 4, 3], [2, 3, 4, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[3, 4, 1, 2, 5], %2, {1}], [[3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[4, 5, 3, 1, 2], %1, {4}], [[], {}, {}], [[4, 2, 1, 3, 5], %2, {1}], [[5, 2, 1, 3, 4], %3, {1}], [[5, 3, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[5, 3, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 2, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 2, 3, 1, 4], %3, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {}], [[5, 3, 4, 1, 2], %1, {4}], [[4, 2, 3, 1, 5], %2, {1}], [[3, 1, 2], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 5, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 4, 1, 2], {}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 2, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1, 5], %2, {1}], [[3, 4, 2, 1, 5], %2, {1}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0]}, {}], [[3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 4, 1, 3, 5], %2, {1}], [[2, 5, 1, 3, 4], %3, {2}], [[3, 5, 2, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[2, 5, 3, 1, 4], %3, {1}], [[2, 4, 3, 1, 5], %2, {1}], [[3, 5, 4, 1, 2], %1, {4}], [[4, 1, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0]}, {3}], [[3, 1, 5, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 3, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2, 5], %2, {1}], [[4, 5, 1, 3, 2], %1, {3}], [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {4}], [ [4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[1, 0, 0, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 69, 198, 498, 1121, 2305, 4402] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 3, 1, 4], [2, 4, 3, 1]}, {[1, 3, 4, 2], [2, 4, 3, 1], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 2, 4, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 3, 1, 4], [3, 2, 4, 1]}, {[1, 4, 2, 3], [3, 1, 2, 4], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 2, 4, 1], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [2, 4, 3, 1], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {2}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 2], {[1, 2, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {3}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 2, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0], [1, 2, 0, 0], [1, 0, 2, 0]}, {2}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 1, 0], [1, 0, 2, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 267, 948, 3367, 11988, 42842] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 1, 4, 3], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [2, 4, 3, 1]}, {[1, 4, 2, 3], [2, 4, 3, 1], [3, 4, 1, 2]}, {[3, 1, 2, 4], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 3, 4, 2], [3, 4, 1, 2], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 4, 1, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 4, 3], [3, 2, 4, 1]}, {[2, 1, 4, 3], [3, 1, 2, 4], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [2, 1, 4, 3], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[4, 5, 1, 2, 3], {[0, 0, 0, 0, 2, 0]}, {4}], [[3, 1, 2], {}, {}], [[3, 2, 4, 1], %1, {1}], [[4, 1, 3, 2], %1, {3}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[4, 2, 3, 1], %1, {1}], [[3, 4, 2, 1], %1, {1}], [[2, 3, 1, 4], %1, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[1, 3, 2, 4], %1, {4}], [[4, 1, 2, 3], {}, {3}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 4, 3, 2], %1, {2}], [[3, 1, 4, 2], %1, {3}], [[3, 4, 1, 2], {[0, 0, 0, 2, 0]}, {}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], %1, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], %1, {3}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155] For the equivalence class of patterns, { {[3, 4, 2, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [2, 1, 3, 4]}, {[1, 2, 4, 3], [2, 1, 3, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[3, 4, 2, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {[3, 0, 0]}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 3, 2], {[2, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3], {[2, 0, 0, 0], [0, 2, 0, 0]}, {2}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {1}], [[3, 1, 2], {[2, 0, 0, 0], [0, 0, 1, 0]}, {2}], [[2, 3, 1], {[0, 2, 0, 0], [1, 0, 0, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 73, 250, 853, 2911, 9938, 33931, 115849, 395534, 1350437, 4610679, 15741842, 53746011, 183500361, 626509422, 2139036965, 7303129015] For the equivalence class of patterns, { {[2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2]}, {[1, 4, 2, 3], [2, 4, 1, 3], [3, 2, 4, 1]}, {[1, 4, 2, 3], [3, 1, 4, 2], [3, 2, 4, 1]}, {[1, 3, 4, 2], [2, 4, 1, 3], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 1, 4, 2], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 1, 4, 2], [4, 1, 3, 2]}, {[2, 3, 1, 4], [2, 4, 1, 3], [4, 1, 3, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4]}} the member , {[1, 3, 4, 2], [2, 4, 1, 3], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {4}], [[1], {}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 991, 3563, 12800, 45976] For the equivalence class of patterns, { {[1, 3, 2, 4], [3, 4, 1, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 1, 4, 3], [4, 2, 3, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 1, 2], [3, 4, 2, 1]}} the member , {[1, 3, 2, 4], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1, 3, 4], {}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1]}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 0, 1]}, {}], [[1, 2, 3, 4], {}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {}, {3}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1]}, {3}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[1, 4, 3, 2], %1, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], %1, {1}], [[1, 3, 4, 2], %1, {1}], [[3, 1, 2, 4, 5], {}, {1}], [[4, 2, 3, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 5, 4], {[0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 5, 3], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 1, 3, 5, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {3}], [[3, 1, 2, 4], {}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1]}, {2}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 240, 744, 2192, 6192, 16896] For the equivalence class of patterns, { {[2, 3, 4, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [3, 2, 1, 4]}, {[3, 4, 2, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [2, 1, 3, 4]}} the member , {[2, 3, 4, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[3, 4, 2, 1], %2, {3}], [[2, 1, 3], {[2, 0, 0, 0]}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2, 5], %1, {1}], [[2, 3, 1, 4], %2, {1}], [[2, 1, 3, 4], %2, {1}], [[1], {}, {}], [[4, 2, 3, 1], %3, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {2}], [[4, 1, 3, 2], %3, {2}], [[2, 3, 1], {[2, 0, 0, 0]}, {}], [[2, 1], {[2, 0, 0]}, {}], [[3, 4, 1, 2, 5], %1, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[3, 1, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {}], [[4, 1, 5, 3, 2], %1, {2}], [[1, 3, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [[2, 4, 3, 1], %3, {1}], [ [2, 4, 1, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[3, 4, 1, 2], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[1, 4, 3, 2], %3, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[2, 1, 4, 3], { [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {3}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {2}], [[3, 1, 4, 2], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[4, 5, 1, 3, 2], %1, {3}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 5, 2, 3, 1], %1, {3}], [[3, 2, 4, 1], %2, {2}], [[4, 2, 5, 3, 1], %1, {2}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 250, 861, 2967, 10220, 35203] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [2, 3, 4, 1]}, {[2, 4, 3, 1], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 2, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [4, 1, 3, 2], [4, 2, 1, 3]}, {[1, 4, 3, 2], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 3, 4, 2], [1, 4, 2, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [4, 1, 3, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [4, 1, 2, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 4, 2, 1], {}, {3}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 1, 2, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 2, 4, 1], [4, 3, 2, 1]}, {[4, 1, 2, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 3, 4, 1], [2, 4, 3, 1], [4, 3, 2, 1]}, {[4, 1, 2, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [1, 4, 3, 2]}, {[1, 2, 3, 4], [1, 4, 2, 3], [1, 4, 3, 2]}, {[1, 2, 3, 4], [2, 3, 1, 4], [3, 2, 1, 4]}} the member , {[1, 2, 3, 4], [3, 1, 2, 4], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], %1, {2}], [[3, 1, 2], {[0, 0, 0, 1]}, {1}], [[3, 4, 2, 1], %1, {1}], [[1, 3, 2], {}, {}], [[3, 1, 4, 2], %1, {1}], [[3, 2, 4, 1], %1, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1]}, {2}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 1]}, {3}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 1, 4, 3], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1]}, {2}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[3, 4, 1, 2], %1, {1}], [ [3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1]}, {2}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 277, 1012, 3702, 13553, 49642] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 2, 3, 4], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 3, 4, 2], [3, 1, 2, 4], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [2, 4, 3, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[2, 1, 4, 5, 3], %2, {1}], [[3, 2, 1], {[0, 0, 1, 0]}, {1}], [ [3, 1, 4, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [ [3, 2, 4, 5, 1], {[0, 2, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 1, 0], [0, 0, 0, 2, 1, 0], [0, 2, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0]}, {1}], [ [3, 4, 1, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[], {}, {}], [[2, 4, 1, 5, 3], %2, {1}], [[2, 3, 1, 5, 4], %1, {3}], [[2, 4, 5, 1, 3], %2, {1}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [3, 4, 5, 1, 2], {[1, 0, 2, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 3, 5, 1, 4], %1, {3}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 4, 2, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0], [1, 0, 0, 0, 1, 0]}, {3}], [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], { [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [1, 1, 0, 0, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], { [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {}], [[2, 1, 3, 5, 4], %1, {1}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[1, 3, 2, 4], {[0, 2, 0, 1, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 1, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[2, 3, 1], {[1, 0, 1, 0], [0, 2, 1, 0]}, {}], [[3, 1, 2], {[1, 1, 0, 0], [1, 0, 2, 0], [0, 1, 2, 0], [1, 0, 1, 1], [0, 1, 1, 1], [0, 0, 1, 2]}, {}], [[2, 1, 3], {[1, 1, 0, 0], [0, 2, 1, 0]}, {}], [[1, 3, 2], {[1, 0, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {}], [[3, 1, 2, 4], {[0, 2, 0, 1, 0], [0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 1, 1, 0]}, {1}], [[1, 2, 3], {[0, 0, 0, 1], [0, 2, 1, 0]}, {}], [[4, 1, 2, 3], { [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 2, 0, 0], [0, 0, 1, 0, 2], [0, 1, 1, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 4, 3], { [0, 0, 1, 2, 0], [0, 0, 0, 1, 2], [0, 0, 1, 1, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 2, 0, 0], [0, 0, 1, 0, 2], [0, 0, 0, 1, 2], [0, 1, 1, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 2, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [ [1, 3, 4, 2], {[0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {2}], [[1, 2, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {2}], [[1, 4, 3, 2], {[0, 1, 2, 0, 0], [0, 0, 1, 0, 2], [0, 1, 1, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[0, 0, 1, 2, 0], [0, 0, 0, 1, 2], [0, 0, 1, 1, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [0, 0, 1, 0, 2], [0, 0, 0, 1, 2], [1, 0, 1, 0, 1], [0, 1, 1, 0, 1], [1, 1, 0, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %2 := {[0, 0, 1, 2, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 192, 441, 929, 1870, 3670] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {[2, 0, 0, 0]}, {}], [[1, 2], {[3, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[2, 0, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], %1, {2}], [[4, 3, 1, 2], %1, {3}], [[1, 4, 3, 2], %1, {1}], [[1, 4, 2, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [0, 0, 1, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {}], [[4, 1, 2, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [ [3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {1}], [ [1, 3, 2, 4], {[0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 4, 3, 1], %1, {2}], [[3, 1, 2, 4], {[0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[4, 2, 3, 1], %1, {1}], [[3, 1, 4, 2], { [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0]}, {3}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {2}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 69, 194, 470, 1009, 1969, 3562] For the equivalence class of patterns, { {[3, 1, 4, 2], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [2, 4, 1, 3]}, {[1, 3, 4, 2], [2, 1, 4, 3], [3, 1, 4, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [2, 4, 1, 3]}, {[2, 4, 1, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, {[3, 1, 4, 2], [3, 4, 1, 2], [4, 1, 3, 2]}, {[2, 1, 4, 3], [3, 1, 2, 4], [3, 1, 4, 2]}} the member , {[1, 4, 2, 3], [2, 1, 4, 3], [2, 4, 1, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 4, 1], %1, {1}], [[3, 2, 1], {}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[1, 3, 2, 4], %1, {4}], [[4, 1, 2, 3], {}, {3}], [[1, 4, 3, 2], %1, {2}], [[2, 4, 3, 1], %1, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], %1, {1}], [[3, 1, 2, 4], {[0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], %1, {3}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {1}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 299, 1172, 4677, 18947, 77746] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 4, 3], [1, 4, 3, 2]}, {[2, 3, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [3, 2, 1, 4]}, {[4, 1, 2, 3], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [1, 2, 4, 3], [1, 4, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1], {}, {1}], [[1], {}, {}], [[3, 4, 2, 1], {[0, 0, 0, 3, 0], [0, 0, 0, 0, 2]}, {3}], [[3, 4, 1, 2], { [0, 3, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1, 2}], [[1, 2], {[0, 3, 0], [0, 0, 2]}, {}], [[2, 3, 1], {[0, 0, 0, 2], [0, 0, 3, 0]}, {}], [[1, 2, 3], {[0, 0, 1, 0], [0, 0, 0, 1], [0, 3, 0, 0]}, {2}], [[1, 3, 2], {[0, 0, 2, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 0, 0, 2]}, {1}], [[2, 4, 1, 3], {[0, 3, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1, 2}], [[2, 3, 1, 4], { [0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1, 2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 278, 1021, 3756, 13827, 50916] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 3, 2], [2, 4, 3, 1]}, {[3, 1, 2, 4], [4, 1, 2, 3], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 3, 4, 1], [2, 4, 3, 1]}, {[2, 3, 1, 4], [2, 3, 4, 1], [3, 2, 4, 1]}, {[1, 4, 2, 3], [4, 1, 2, 3], [4, 1, 3, 2]}, {[3, 1, 2, 4], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 2, 1, 4], [3, 2, 4, 1]}} the member , {[1, 4, 2, 3], [4, 1, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[3, 1, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[1], {}, {}], [[1, 2, 3], {}, {2}], [[2, 3, 1], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 1], {[0, 2, 0]}, {}], [[2, 1, 3], {[0, 2, 0, 0]}, {1}], [[3, 2, 1], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 3, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 2, 1], [4, 1, 3, 2]}, {[2, 1, 3, 4], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 1, 3, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 3, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 2, 4, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [3, 4, 2, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}], [[], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0], [1, 1, 0, 0, 0]}, {}], [[4, 1, 3, 2], {[1, 1, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 5, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [ [1, 4, 2, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [1, 5, 3, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[2, 5, 3, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 5, 2, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0]}, {1}], [ [3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0]}, {3}], [ [3, 2, 5, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 5, 1, 4, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {2}], [[5, 1, 2, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 1, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0]}, {3}], [ [5, 2, 3, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[5, 1, 3, 4, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0]}, {}], [[2, 1, 3], {[1, 1, 0, 0]}, {}], [[2, 1, 4, 3], {[1, 1, 0, 0, 0]}, {}], [[3, 1, 2], {[1, 1, 1, 0]}, {}], [[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 213, 564, 1340, 2909, 5860] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 4, 1], [4, 1, 3, 2]}, {[2, 4, 3, 1], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 4, 3, 1], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 3, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 3, 1, 4], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [3, 2, 4, 1], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 2, 0, 0], [1, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[5, 3, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {}], [[2, 5, 4, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 2, 1], {}, {}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0]}, {1}], [ [2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 3, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 5, 4, 1, 2], {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {4}], [ [5, 4, 2, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 3, 1, 2], {[0, 1, 0, 0, 0]}, {3}], [[5, 4, 3, 2, 1], {}, {3}], [[5, 4, 3, 1, 2], {[0, 1, 0, 0, 0, 0]}, {4}], [[2, 4, 3, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 5, 3, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 236, 745, 2286, 6866, 20285] For the equivalence class of patterns, { {[3, 2, 1, 4], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 4, 3, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 4, 3, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [4, 1, 2, 3]}, {[1, 2, 3, 4], [1, 4, 2, 3], [2, 3, 4, 1]}, {[2, 4, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [4, 1, 2, 3]}} the member , {[1, 4, 3, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {}, {3}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[4, 1, 2, 3], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[1], {}, {}], [[3, 1, 2], {[1, 1, 0, 0]}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {}, {1}], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 1, 0, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 4, 2, 1], %1, {1}], [[4, 2, 3, 1], %1, {2}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [2, 5, 1, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0]}, {4}], [ [2, 4, 1, 3, 5], {[0, 0, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [ [3, 5, 2, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 5, 1, 4, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [3, 4, 1, 2, 5], {[1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [ [4, 5, 2, 3, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 5, 1, 2, 4], { [0, 0, 0, 1, 0, 0], [1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0]}, {4}], [[2, 4, 3, 1], %1, {1}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0], [1, 1, 0, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}], [[4, 5, 1, 2, 3], {[1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0]}, {4}], [[3, 4, 1, 2], {[1, 1, 0, 0, 0]}, {}]} %1 := {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 991, 3566, 12850, 46458] For the equivalence class of patterns, { {[3, 2, 4, 1], [3, 4, 2, 1], [4, 3, 1, 2]}, {[3, 4, 2, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 4, 3, 1], [3, 4, 2, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [3, 1, 2, 4]}, {[1, 2, 4, 3], [1, 4, 2, 3], [2, 1, 3, 4]}, {[1, 2, 4, 3], [2, 1, 3, 4], [2, 3, 1, 4]}, {[1, 2, 4, 3], [1, 3, 4, 2], [2, 1, 3, 4]}, {[3, 4, 2, 1], [4, 2, 1, 3], [4, 3, 1, 2]}} the member , {[3, 2, 4, 1], [3, 4, 2, 1], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[1, 3, 2], {[2, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3], {[1, 0, 0, 0]}, {2}], [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[4, 3, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 3, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {}], [[3, 1, 2], {[2, 0, 0, 0]}, {2}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 278, 1026, 3818, 14308, 53932] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {[2, 0, 0, 0], [0, 3, 0, 0], [0, 0, 3, 0]}, {}], [ [3, 2, 1, 4], {[0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 2], {[3, 0, 0]}, {}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 3, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [ [3, 1, 2, 4], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [0, 0, 0, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[4, 3, 1, 2], %3, {1}], [[1, 4, 2, 3], %2, {1}], [[1, 4, 3, 2], %3, {2}], [[4, 1, 3, 2], %3, {1}], [[4, 1, 2, 3], %2, {2}], [[2, 1, 3, 4], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [2, 0, 0, 0, 0]}, {1}], [[1, 2, 4, 3], %2, {1}], [[1, 3, 4, 2], {[0, 0, 0, 3, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 4, 3, 5, 2], %1, {2}], [[1, 3, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 4, 3, 5, 1], %1, {2}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[4, 1, 2, 5, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [ [3, 1, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[4, 2, 3, 5, 1], %1, {1}], [[4, 1, 3, 5, 2], %1, {1}], [[3, 1, 4, 2], {[0, 0, 0, 3, 0], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [0, 0, 0, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[1, 3, 2], {[2, 0, 0, 0], [0, 3, 0, 0], [0, 0, 3, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[2, 3, 4, 1], {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {4}], [[2, 4, 3, 1], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[4, 2, 1, 3], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 2, 3], {[0, 0, 0, 1], [3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [0, 0, 3, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]} %2 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [0, 0, 2, 0, 0]} %3 := {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 69, 162, 240, 199, 73, 0] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [1, 4, 2, 3], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 4, 3, 1], [3, 1, 2, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [4, 1, 3, 2], [4, 2, 1, 3]}, {[2, 3, 1, 4], [2, 4, 3, 1], [3, 1, 2, 4]}, {[1, 3, 4, 2], [4, 1, 3, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[2, 1, 3], {}, {}], [[4, 1, 3, 2], %1, {3}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0]}, {}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], %1, {1}], [[3, 4, 2, 1], %1, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], %1, {3}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 265, 929, 3249, 11362, 39746] For the equivalence class of patterns, { {[2, 4, 3, 1], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 3, 1, 4], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [2, 3, 1, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 4, 3, 1], [3, 1, 2, 4]}, {[2, 3, 1, 4], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 2, 4, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 2, 4, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 3, 1, 4], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {4}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 1, 0, 0, 1]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {}], [[2, 1], {}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {}], [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {4}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {2}], [[1, 2, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {4}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [ [4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[4, 2, 5, 3, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {1}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}], [[4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0]}, {3}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {1}], [ [2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 0, 1]}, {3}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {3}], [[3, 1, 5, 2, 4], { [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 241, 757, 2288, 6724, 19365] For the equivalence class of patterns, { {[1, 3, 2, 4], [1, 4, 3, 2], [2, 1, 3, 4]}, {[1, 2, 4, 3], [1, 3, 2, 4], [3, 2, 1, 4]}, {[3, 4, 2, 1], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 4, 1], [4, 2, 3, 1], [4, 3, 1, 2]}} the member , {[1, 3, 2, 4], [1, 4, 3, 2], [2, 1, 3, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {[0, 1, 0, 0], [0, 0, 0, 1]}, {3}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 2], {}, {}], [[1], {}, {}], [[2, 1, 3], {[0, 0, 2, 0], [0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 2], [0, 1, 0, 0, 2], [0, 0, 0, 0, 3], [0, 1, 1, 0, 0]}, {3}], [[2, 3, 1], {[0, 0, 2, 0], [0, 0, 1, 2], [0, 0, 0, 3]}, {2}], [[3, 2, 1], {[0, 0, 3, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 0, 3]}, {1}], [[2, 1], {[0, 0, 3]}, {}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [3, 1, 2, 4], {[0, 0, 0, 0, 1], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 2], [0, 0, 0, 3]}, {}], [[4, 2, 3, 1], { [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 0, 1, 2], [0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [0, 0, 0, 0, 3], [0, 0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 991, 3563, 12800, 45976] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 3, 1, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [2, 4, 3, 1], [3, 4, 2, 1]}, {[4, 1, 2, 3], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 1, 2, 4], [3, 2, 1, 4]}, {[4, 1, 2, 3], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [1, 4, 3, 2]}, {[2, 3, 4, 1], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 2, 3], [1, 4, 3, 2]}} the member , {[4, 1, 2, 3], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[2, 1, 3], {[0, 2, 0, 0]}, {}], [[], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[2, 1], {[0, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {2}], [[3, 2, 1], {[0, 0, 2, 0], [0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {3}], [ [3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0], [0, 0, 0, 2, 0]}, {1, 2}], [[2, 1, 3, 4], {[0, 2, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 3, 1, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 3, 4, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [3, 2, 4, 1]}, {[1, 2, 4, 3], [1, 3, 4, 2], [4, 2, 1, 3]}, {[2, 4, 3, 1], [3, 1, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [3, 1, 2, 4]}} the member , {[1, 3, 4, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], %1, {1}], [[3, 1, 2], {[0, 1, 1, 0]}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 2, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[3, 4, 2, 1], %1, {1}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [3, 5, 1, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [3, 5, 2, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 5, 1, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {3}], [ [3, 5, 1, 2, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {3}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], %1, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 240, 754, 2309, 6987, 21036] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 3, 4, 1], [2, 4, 1, 3]}, {[2, 1, 3, 4], [3, 1, 4, 2], [4, 1, 2, 3]}, {[3, 1, 4, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 4, 3, 2], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [4, 1, 2, 3]}, {[2, 4, 1, 3], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [3, 1, 4, 2]}, {[1, 4, 3, 2], [2, 4, 1, 3], [3, 4, 2, 1]}} the member , {[1, 4, 3, 2], [3, 1, 4, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[2, 1, 4, 3], %1, {1}], [[3, 2, 4, 1], %1, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], %1, {2}], [[4, 1, 3, 2], %1, {2}], [[1, 3, 2, 4], %1, {1}], [[2, 4, 3, 1], %1, {3}], [[2, 4, 1, 3], %1, {3}], [[1, 4, 2, 3], %1, {3}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [ [3, 5, 1, 2, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0]}, {3}], [[2, 3, 1, 4], %1, {1}], [[3, 1, 2, 4], %1, {2}], [[3, 4, 1, 2, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [ [4, 5, 1, 2, 3], {[0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {4}], [[3, 4, 1, 2], {[0, 2, 0, 0, 0]}, {}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155] For the equivalence class of patterns, { {[3, 1, 4, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [2, 4, 1, 3]}, {[1, 2, 4, 3], [2, 1, 3, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[3, 1, 4, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 2], {[2, 0, 0, 0]}, {}], [[1, 3, 2], {[2, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[4, 1, 2, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {3}], [[2, 1], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {3}], [[1], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 257, 883, 3015, 10258, 34826] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 1, 2, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [1, 4, 2, 3], [2, 4, 3, 1]}, {[2, 3, 1, 4], [2, 4, 3, 1], [3, 2, 4, 1]}, {[3, 1, 2, 4], [4, 1, 3, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 1, 3], {[0, 2, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {3}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 288, 1091, 4172, 16069, 62240] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 3, 4, 1], [3, 1, 4, 2]}, {[2, 3, 4, 1], [3, 1, 4, 2], [3, 2, 1, 4]}, {[2, 4, 1, 3], [3, 2, 1, 4], [4, 1, 2, 3]}, {[3, 1, 4, 2], [3, 2, 1, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 1, 4, 2], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 4, 1], [2, 4, 1, 3]}, {[2, 3, 4, 1], [2, 4, 1, 3], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 4, 1, 3], [4, 1, 2, 3]}} the member , {[2, 3, 4, 1], [3, 1, 4, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[], {}, {}], [[1, 2], {}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}], [[2, 1], {[1, 1, 1]}, {}], [ [3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[1, 0, 0, 1], [0, 1, 0, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 1], {[0, 0, 0, 1], [1, 1, 1, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 1], [1, 1, 1, 0]}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {2}], [[1, 3, 2], {[1, 0, 0, 1], [0, 1, 1, 1]}, {}], [[4, 5, 1, 2, 3], { [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[3, 5, 2, 4, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 1, 4, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[4, 2, 3, 1], {[1, 1, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {1}], [ [2, 4, 1, 3], {[0, 1, 0, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0]}, {3}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[1, 1, 1, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {2}], [ [4, 5, 2, 3, 1], {[1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}], [[2, 5, 1, 4, 3], { [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0]}, {2}], [[4, 5, 1, 3, 2], { [0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[3, 4, 2, 1], {[1, 1, 1, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [2, 1, 4, 3], {[0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1]}, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 250, 853, 2911, 9938, 33931] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 4, 3], [2, 4, 3, 1]}, {[2, 1, 4, 3], [3, 1, 2, 4], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 4, 1, 2], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [2, 4, 3, 1], [3, 4, 1, 2]}, {[2, 3, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [4, 1, 3, 2]}} the member , {[1, 4, 2, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[2, 1, 3], {[0, 2, 0, 0]}, {}], [[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 2, 3, 4], {}, {2}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[1, 2, 4, 3], {[0, 0, 0, 1, 0]}, {3}], [[1, 3, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[2, 1, 3, 4], {[0, 2, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 2, 0], [0, 1, 0, 0]}, {3}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 939, 3315, 11737, 41732] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [3, 4, 2, 1]}} the member , {[2, 1, 3, 4], [3, 4, 1, 2], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 2], {}, {}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {2}], [ [1, 5, 4, 3, 2], {[1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {3}], [[4, 3, 2, 1], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 0]}, {2}], [ [3, 2, 1, 4], {[0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {3}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0], [1, 0, 0, 0, 0]}, {3}], [[3, 2, 1], {[1, 1, 1, 0]}, {}], [[2, 5, 4, 3, 1], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {2}], [ [2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 5, 3, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [ [1, 5, 4, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0]}, {1}], [ [1, 4, 3, 2, 5], {[0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {3}], [[2, 1, 3], {[1, 1, 0, 0], [0, 0, 0, 1]}, {}], [[1, 4, 3, 2], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 218, 610, 1585, 3895, 9186] For the equivalence class of patterns, { {[4, 1, 3, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 4, 3, 1], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [1, 4, 2, 3]}, {[1, 2, 3, 4], [2, 3, 1, 4], [3, 1, 2, 4]}} the member , {[4, 1, 3, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[2, 1, 3, 4], {}, {3}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1, 2}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1, 2}], [[2, 1, 4, 3], {[1, 1, 0, 0, 0]}, {1, 2}], [[3, 2, 1], {[1, 0, 0, 0], [0, 0, 1, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 310, 1251, 5151, 21536, 91137] For the equivalence class of patterns, { {[3, 4, 1, 2], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [2, 1, 4, 3]}, {[3, 4, 1, 2], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [2, 1, 4, 3]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4], [2, 1, 4, 3]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[3, 1, 2], {}, {1}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 1]}, {2}], [[2, 3, 1], {[0, 0, 1, 1]}, {2}], [[2, 1, 3], {[0, 0, 1, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 3, 2, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[1, 2], {[3, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[3, 1, 2, 4], {[0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {}], [[2, 1, 3], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {3}], [[4, 1, 2, 5, 3], { [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [2, 0, 0, 0, 0]}, {1}], [ [2, 1, 3, 4], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [2, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 2, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 5, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 1, 1, 1, 0], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [ [3, 1, 2, 4, 5], {[0, 1, 0, 2, 0, 0], [0, 0, 1, 2, 0, 0], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [1, 0, 2, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 2, 1, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [1, 0, 0, 1, 1, 0], [2, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [ [4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [2, 1, 0, 0, 0], [1, 2, 0, 0, 0], [0, 3, 0, 0, 0], [2, 0, 1, 0, 0], [3, 0, 0, 0, 0]}, {2}], [[1, 2, 4, 3], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0]}, {2}], [[1, 3, 2], {[2, 0, 0, 0], [0, 0, 0, 1], [0, 2, 1, 0]}, {}], [[1, 4, 2, 3], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[2, 4, 3, 1], {[0, 0, 2, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[3, 1, 2], {[2, 0, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {}], [[1, 2, 3], { [3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [1, 1, 1, 0]}, {}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 0, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 2, 1, 0], [0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[4, 1, 2, 3], {[0, 0, 2, 1, 0], [0, 0, 2, 0, 1], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 69, 190, 446, 927, 1745, 3036] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 1, 4, 3], [3, 1, 2, 4]}, {[3, 4, 1, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [2, 1, 4, 3]}, {[2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4]}, {[3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 2, 3], [2, 1, 4, 3]}, {[2, 4, 3, 1], [3, 4, 1, 2], [3, 4, 2, 1]}} the member , {[3, 4, 1, 2], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 3, 2], {}, {1}], [[2, 1, 3], {[0, 2, 0, 0]}, {2}], [[2, 3, 1], {[0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299, 37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946, 353224531663] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [3, 4, 2, 1]}, {[1, 4, 2, 3], [2, 1, 3, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 2, 4, 1], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 3, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [3, 4, 2, 1], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[0, 0, 1, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 5, 3, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [1, 5, 3, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[3, 2, 5, 4, 1], {[1, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {2}], [ [2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [ [2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 2, 3, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[1, 4, 3, 2], {}, {3}], [[2, 1, 5, 4, 3], {}, {4}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 5, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [ [1, 4, 2, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[1, 5, 2, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 236, 705, 1970, 5224, 13307] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 3, 4], [4, 2, 3, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1]}, {1}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 0, 1]}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[2, 4, 3, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0]}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1, 5, 4], %1, {1}], [[3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {4}], [[4, 2, 1, 5, 3], %1, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 5, 1, 3], %1, {1}], [[3, 2, 5, 1, 4], %1, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0]}, {2}], [[4, 3, 5, 1, 2], { [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[4, 5, 3, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1]}, {1}], [ [2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 1, 4], %1, {1}], [[4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1]}, {1}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}], [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[5, 2, 4, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1]}, {1}], [[3, 5, 4, 1, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 1, 1]}, {1}], [ [4, 3, 1, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 228, 616, 1460, 3110, 6082] For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 1, 4, 2], [3, 4, 1, 2]}, {[1, 4, 3, 2], [2, 1, 4, 3], [2, 4, 1, 3]}, {[2, 4, 1, 3], [3, 4, 1, 2], [4, 1, 2, 3]}, {[2, 3, 4, 1], [2, 4, 1, 3], [3, 4, 1, 2]}, {[1, 4, 3, 2], [2, 1, 4, 3], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 4, 1, 2], [4, 1, 2, 3]}, {[2, 1, 4, 3], [3, 1, 4, 2], [3, 2, 1, 4]}} the member , {[1, 4, 3, 2], [2, 1, 4, 3], [2, 4, 1, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[3, 2, 1], {}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {3}], [[4, 1, 2, 3], {[0, 1, 1, 0, 0]}, {3}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 289, 1107, 4322, 17162, 69137] For the equivalence class of patterns, { {[2, 3, 4, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[3, 2, 4, 1], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 1, 3, 4], [3, 1, 2, 4]}, {[1, 2, 4, 3], [1, 3, 4, 2], [3, 2, 1, 4]}, {[2, 4, 3, 1], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 2, 4, 3], [1, 4, 2, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 4, 3, 2], [2, 1, 3, 4], [2, 3, 1, 4]}} the member , {[2, 3, 4, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {2}], [[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 4, 2, 5], %1, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[4, 2, 5, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0]}, {2}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[3, 4, 1, 2, 5], %1, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {}], [[4, 5, 1, 2, 3], %1, {3}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 5, 3, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {}], [[4, 1, 5, 2, 3], %1, {2}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 241, 768, 2415, 7587, 23905] For the equivalence class of patterns, { {[2, 4, 3, 1], [4, 2, 3, 1], [4, 3, 1, 2]}, {[3, 2, 4, 1], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 2, 4], [2, 3, 1, 4]}, {[1, 2, 4, 3], [1, 3, 2, 4], [3, 1, 2, 4]}, {[1, 3, 2, 4], [1, 4, 2, 3], [2, 1, 3, 4]}, {[3, 4, 2, 1], [4, 1, 3, 2], [4, 2, 3, 1]}, {[3, 4, 2, 1], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [2, 1, 3, 4]}} the member , {[3, 2, 4, 1], [4, 2, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299, 37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946, 353224531663] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 4, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 1, 2], [4, 1, 3, 2]}, {[2, 1, 4, 3], [3, 1, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [3, 4, 2, 1]}, {[2, 1, 4, 3], [2, 3, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 2, 4, 1], [3, 4, 1, 2]}} the member , {[1, 2, 4, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}], [[], {}, {}], [[3, 1, 2], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0]}, {}], [[2, 1, 4, 3], {}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {3}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0]}, {3}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[3, 1, 5, 2, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [3, 1, 4, 2, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0]}, {3}], [[4, 2, 5, 3, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 220, 630, 1697, 4365, 10842] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 1, 3, 4], [4, 2, 1, 3]}, {[2, 3, 4, 1], [3, 1, 2, 4], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 4, 3, 2], [2, 1, 3, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 2, 4, 3], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 2, 4, 3], [3, 2, 1, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 4, 2, 1], [4, 1, 2, 3]}} the member , {[2, 3, 4, 1], [3, 1, 2, 4], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {3}], [[3, 1, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 2], {[0, 0, 0, 1]}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 1]}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {4}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 1]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 229, 683, 1954, 5452, 14974] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 3, 4, 2], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 4, 3, 2], [2, 3, 1, 4], [2, 4, 3, 1]}, {[1, 4, 2, 3], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 3, 2], [3, 1, 2, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 2, 4, 1], [4, 1, 2, 3]}} the member , {[2, 3, 1, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 1, 2], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[2, 3, 1], {[0, 0, 0, 1]}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 1, 3], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {2}], [[2, 3, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {2}], [[1, 2], {[1, 0, 1]}, {}], [[2, 5, 1, 4, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {4}], [[3, 4, 1, 2], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [ [2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {1}], [ [3, 5, 1, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {2}], [[3, 5, 2, 4, 1], %1, {1}], [[4, 2, 5, 3, 1], %1, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0], [1, 0, 0, 0, 1]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0], [1, 0, 0, 0, 1]}, {3}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 1], [1, 0, 0, 0]}, {1}], [[3, 1, 5, 4, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {3}], [[2, 1, 4, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [ [2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[2, 1, 5, 4, 3], { [0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1]}, {3}], [[4, 1, 5, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {3}], [[2, 1, 4, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[1, 3, 2], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[4, 5, 2, 3, 1], %1, {1}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {2}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 261, 877, 2852, 9020, 27877] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [2, 1, 4, 3]}, {[1, 2, 3, 4], [2, 1, 4, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 4, 1, 2], [4, 3, 2, 1]}} the member , {[3, 4, 1, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {[3, 0, 0]}, {}], [[2, 1], {[3, 0, 0], [0, 3, 0]}, {}], [[1], {}, {}], [[3, 2, 1], {[0, 2, 0, 0], [1, 0, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {1}], [[3, 1, 2], {[2, 0, 0, 0], [0, 2, 0, 0], [0, 0, 1, 0]}, {2}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 3, 0]}, {1}], [[2, 1, 3], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {2}], [[1, 3, 2], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [0, 0, 3, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 72, 246, 845, 2901, 9955, 34165, 117254, 402409, 1381046, 4739681, 16266344, 55825262, 191589456, 657525254, 2256593172, 7744512803] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 1, 3], [3, 2, 4, 1]}, {[1, 2, 3, 4], [3, 1, 4, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 4, 1, 3], [4, 3, 2, 1]}, {[2, 3, 1, 4], [3, 1, 4, 2], [4, 3, 2, 1]}, {[2, 4, 1, 3], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 4, 2, 3], [3, 1, 4, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 4, 3, 1], [3, 1, 4, 2]}, {[1, 2, 3, 4], [2, 4, 1, 3], [4, 1, 3, 2]}} the member , {[1, 2, 3, 4], [3, 1, 4, 2], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 4, 5, 2, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 5, 1, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {5}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {3}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {2}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {2}], [[2, 3, 4, 1], { [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {4}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {2}], [[2, 4, 3, 1], {[0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {4}], [[2, 4, 5, 1, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 4, 5, 1, 2], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 1, 2], {[0, 0, 1, 1]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 4, 1, 2], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 230, 689, 1970, 5460, 14833] For the equivalence class of patterns, { {[1, 3, 2, 4], [1, 4, 2, 3], [2, 3, 4, 1]}, {[2, 4, 3, 1], [3, 2, 1, 4], [4, 2, 3, 1]}, {[1, 4, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 4, 1], [3, 1, 2, 4]}, {[3, 2, 1, 4], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 4, 3, 2], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [4, 1, 2, 3]}, {[1, 3, 2, 4], [1, 3, 4, 2], [4, 1, 2, 3]}} the member , {[1, 4, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[1, 2, 3], {}, {2}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 0, 0]}, {3}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {}], [[2, 3, 1, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [ [2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 265, 926, 3216, 11152, 38741] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 1, 2, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [2, 3, 4, 1]}, {[3, 2, 1, 4], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 2, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 4, 3, 2], [2, 4, 3, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 1, 2, 4], [4, 1, 2, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {}, {2}], [[3, 4, 2, 1], {}, {3}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 2, 4, 1], {}, {1}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 4, 1, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3], {}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 297, 1144, 4433, 17238, 67184] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 3, 4, 2], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 4, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 3, 1, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[2, 3, 1], {[0, 0, 0, 1]}, {}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[1, 2, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4, 5], %5, {1}], [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], %1, {5}], [[1, 4, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[2, 1, 3, 4, 5], %5, {3}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4, 5], %5, {2}], [[3, 4, 1, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {4}], [[3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[4, 1, 5, 3, 2], %1, {5}], [[1, 3, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {}], [[4, 5, 2, 1, 3], %3, {3}], [[3, 4, 1, 2], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [[3, 1, 4, 2], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [[3, 4, 2, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {2}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {2}], [[2, 4, 1, 3], {[1, 0, 1, 1, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [ [2, 1, 4, 3], {[1, 0, 1, 1, 0], [1, 0, 1, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [ [1, 3, 2, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [[1, 2, 4, 3], {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}], [[2, 4, 3, 5, 1], %4, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {3}], [[2, 1, 3, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [[3, 2, 4, 5, 1], %4, {3}], [[3, 1, 2, 5, 4], {[0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[4, 2, 3, 5, 1], %4, {2}], [[4, 1, 2, 5, 3], %2, {2}], [[4, 2, 5, 3, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [3, 1, 5, 2, 4], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[4, 1, 5, 2, 3], %2, {2}], [[3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 2, 1, 5, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {1}], [[3, 1, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {}], [[4, 2, 1, 5, 3], %3, {2}], [[4, 3, 1, 5, 2], %1, {3}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[4, 2, 5, 1, 3], %3, {2}], [[4, 3, 5, 1, 2], %1, {4}], [[4, 5, 2, 3, 1], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 5, 1, 2, 3], %2, {3}], [[3, 5, 1, 2, 4], { [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [[4, 5, 3, 1, 2], %1, {4}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %2 := {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]} %4 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} %5 := {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 209, 545, 1348, 3270, 7908] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [3, 1, 2, 4]}, {[1, 2, 4, 3], [1, 3, 4, 2], [2, 3, 1, 4]}, {[1, 3, 4, 2], [2, 1, 3, 4], [2, 3, 1, 4]}, {[1, 4, 2, 3], [2, 1, 3, 4], [3, 1, 2, 4]}, {[2, 4, 3, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 4, 3, 1], [3, 4, 2, 1], [4, 1, 3, 2]}, {[3, 2, 4, 1], [3, 4, 2, 1], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 1, 3, 4], [2, 3, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[1, 3, 2], {[0, 1, 1, 1]}, {}], [[2, 1], {}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 5, 4, 1], %1, {1}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 5, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 5, 3, 4, 1], %1, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {}], [[5, 1, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 2, 3, 4, 1], %1, {1}], [[2, 3, 1], {[0, 0, 0, 1]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[5, 1, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [ [1, 2, 5, 3, 4], {[0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [1, 2, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 2, 3, 4], {[0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[1, 4, 2, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 1, 1, 1], [0, 1, 0, 0, 0]}, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}], [ [1, 5, 2, 4, 3], {[0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1]}, {2}], [[5, 1, 2, 4, 3], {[0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {4}], [[1, 2, 5, 4, 3], {[0, 0, 1, 1, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 1, 1]}, {3}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {4}], [[1, 2, 4, 3], {[0, 0, 1, 1, 1], [0, 1, 0, 0, 0]}, {}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 286, 1067, 3993, 14992, 56488] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 3, 1, 4], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [2, 4, 3, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[4, 5, 1, 2, 3], {[1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[], {}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {2}], [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[4, 1, 2, 3], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[1], {}, {}], [[3, 1, 2], {[1, 1, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 1, 0, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[2, 1, 3, 4], {[1, 1, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0]}, {}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {3}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [3, 4, 1, 2, 5], {[1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 251, 817, 2570, 7872, 23621] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 1, 2, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 2, 3], [4, 2, 1, 3]}, {[1, 2, 4, 3], [1, 3, 4, 2], [3, 2, 4, 1]}, {[1, 3, 4, 2], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 1, 4], [2, 4, 3, 1]}, {[3, 1, 2, 4], [3, 2, 4, 1], [3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [1, 4, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 4, 2, 1], %1, {3}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[4, 1, 3, 2], %1, {3}], [[1, 2], {}, {}], [[3, 1, 2, 4], %1, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[4, 2, 3, 1], %1, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], %1, {3}], [[3, 4, 1, 2], {[0, 0, 0, 2, 0]}, {1}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 262, 891, 2964, 9700, 31374] For the equivalence class of patterns, { {[3, 2, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]}, {[4, 2, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 4, 2]}, {[1, 2, 3, 4], [1, 2, 4, 3], [1, 4, 2, 3]}, {[1, 2, 3, 4], [2, 1, 3, 4], [2, 3, 1, 4]}, {[2, 4, 3, 1], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [3, 1, 2, 4]}, {[4, 1, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[3, 2, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3], {[1, 0, 0, 0]}, {2}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}], [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[1, 3, 2], {}, {1}], [[3, 1, 2], {}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 309, 1237, 5026, 20626, 85242, 354080, 1476368, 6173634, 25873744, 108628550, 456710589, 1922354351, 8098984433, 34147706833, 144068881455] For the equivalence class of patterns, { {[2, 3, 1, 4], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 3, 4, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, {[3, 1, 2, 4], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [2, 4, 3, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [3, 2, 4, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [4, 1, 3, 2]}, {[1, 2, 3, 4], [1, 3, 2, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [4, 2, 3, 1], [4, 3, 2, 1]}} the member , {[1, 3, 4, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[4, 5, 3, 1, 2], %1, {4}], [[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 5, 1, 3, 2], %1, {5}], [[2, 1, 3], {}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 5, 1, 4, 2], %1, {5}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 5, 1, 3, 4], %3, {3}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 1, 2], %2, {3}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[3, 1, 2], {[1, 0, 0, 0]}, {}], [[2, 5, 1, 4, 3], %3, {3}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 5, 3, 1, 4], %3, {3}], [[2, 5, 4, 1, 3], %3, {4}], [[4, 2, 1, 5, 3], %1, {1}], [[3, 2, 1, 5, 4], {[1, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 1, 2], %1, {4}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 1, 3], %1, {1}], [ [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 5, 2, 1, 4], %1, {3}], [[4, 2, 1, 3], %2, {2}], [[4, 1, 2, 3], %2, {2}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 1, 3], %1, {3}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], %2, {4}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], %2, {3}], [[3, 5, 1, 2, 4], %1, {3}], [[4, 5, 1, 2, 3], %1, {3}], [[3, 1, 2, 4], %2, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0]}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[3, 5, 4, 1, 2], %1, {4}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0]}, {}], [[4, 1, 3, 2], %2, {4}], [[4, 3, 1, 5, 2], %1, {5}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {}], [ [3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 258, 842, 2614, 7787, 22466] For the equivalence class of patterns, { {[2, 3, 4, 1], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 3, 2], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 4, 3, 2], [3, 1, 2, 4], [4, 1, 2, 3]}, {[1, 4, 2, 3], [3, 2, 1, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 3, 4, 2], [2, 3, 4, 1], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [3, 2, 1, 4], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[3, 4, 1, 2], {[1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[1, 2], {}, {}], [[3, 2, 4, 1], %2, {1}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], %1, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[2, 3, 1], {[1, 0, 0, 1]}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}], [[3, 2, 1], {[0, 0, 1, 0], [0, 0, 0, 1]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}], [ [2, 1, 4, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {3}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {2}], [ [2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {1}], [ [2, 4, 1, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {2}], [ [4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [[3, 5, 1, 4, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {2}], [[3, 5, 2, 4, 1], %1, {1}], [[4, 2, 5, 3, 1], %1, {1}], [[4, 2, 3, 1], %2, {1}], [[3, 4, 2, 1], %2, {1}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {3}], [ [2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}], [[4, 1, 5, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {3}], [[2, 1, 4, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[1, 3, 2], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[4, 5, 2, 3, 1], %1, {1}], [[2, 1, 3], {[1, 0, 0, 1]}, {}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {2}], [[3, 1, 4, 2], {[1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} %2 := {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 245, 795, 2508, 7732, 23393] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 1, 4, 3], [2, 3, 1, 4]}, {[2, 3, 4, 1], [3, 4, 1, 2], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 1, 4, 3], [3, 2, 1, 4]}, {[2, 4, 3, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, {[1, 3, 4, 2], [2, 1, 4, 3], [3, 2, 1, 4]}, {[3, 2, 4, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 4, 3, 2], [2, 1, 4, 3], [3, 1, 2, 4]}} the member , {[2, 3, 4, 1], [3, 4, 1, 2], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[2, 1, 4, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {[1, 0, 1, 0]}, {}], [[3, 1, 2], {[1, 0, 1, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {3}], [ [2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {2}], [[2, 1, 4, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [1, 0, 0, 1, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 253, 845, 2791, 9188, 30246] For the equivalence class of patterns, { {[3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 4, 3], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3]}} the member , {[2, 3, 4, 1], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[2, 1, 4, 3], {}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0]}, {2}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [ [4, 2, 5, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0]}, {}], [[2, 3, 1], {[0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 273, 971, 3439, 12172, 43098] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 3, 4, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, {[2, 3, 1, 4], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [3, 2, 4, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [4, 2, 1, 3]}, {[1, 2, 3, 4], [2, 1, 3, 4], [2, 4, 3, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [4, 1, 3, 2]}, {[3, 1, 2, 4], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[1, 4, 2, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 2], {[0, 3, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[1, 3, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {}], [[3, 2, 4, 1], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 0, 2, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[1, 2, 3], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[2, 3, 1], {[1, 0, 0, 0], [0, 0, 3, 0]}, {}], [[1, 2, 3, 4], %2, {2}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [ [1, 2, 4, 3], {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[2, 3, 4, 1], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 0, 2, 0, 0]}, {}], [[2, 1, 3, 4], %2, {1}], [[2, 3, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[1, 4, 3, 2], %1, {1}], [[2, 4, 5, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], %2, {3}], [ [2, 3, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 2, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 0, 2, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 1, 4, 2], %1, {1}], [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 2, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 2, 0, 0]}, {4}], [[1, 3, 2, 4], {[0, 1, 0, 2, 0], [0, 0, 0, 3, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {2}], [[4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [ [3, 2, 1, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[1, 3, 4, 2], %1, {1}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 2, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 0, 2, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[3, 4, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 2, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 2, 0, 0]}, {4}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} %2 := {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 238, 724, 2078, 5706, 15161] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 1, 3, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 2, 4, 3], [2, 3, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 3, 2, 4], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 4, 2, 3], [2, 1, 3, 4], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [2, 4, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 0, 1]}, {}], [[2, 1], {}, {}], [[4, 1, 2, 3], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[3, 1, 2], {[1, 1, 0, 0]}, {}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[2, 1, 3, 4], {[0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {4}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 3, 1, 4], {[0, 0, 1, 1, 0]}, {2}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 4, 1, 2], {[1, 1, 0, 0, 0], [0, 1, 0, 1, 0]}, {}], [[4, 1, 5, 3, 2], %2, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[3, 5, 1, 2, 4], %1, {1}], [[3, 1, 2, 4, 5], {[1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[4, 5, 1, 2, 3], { [1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[4, 5, 1, 3, 2], %2, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 1, 0, 0]}, {3}], [ [4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[3, 1, 2, 5, 4], %1, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {}], [ [4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[3, 1, 2, 4], {[1, 1, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[4, 1, 3, 5, 2], %2, {2}], [[4, 2, 3, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[3, 1, 5, 2, 4], %1, {1}], [[4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {2}], [ [1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 239, 734, 2131, 5900, 15697] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 2, 4, 3], [1, 4, 3, 2], [4, 1, 3, 2]}, {[1, 4, 2, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 3, 1, 4], [2, 3, 4, 1], [3, 4, 2, 1]}, {[3, 1, 2, 4], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 3, 4, 2], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 1, 4], [3, 2, 4, 1]}} the member , {[1, 2, 4, 3], [1, 4, 3, 2], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {}, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[5, 2, 3, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}], [[2, 4, 3, 1], {[0, 0, 1, 0, 0]}, {}], [[5, 3, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}], [[5, 3, 4, 1, 2], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2, 3}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {2}], [[2, 4, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [2, 5, 3, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 5, 4, 1, 2], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 287, 1079, 4082, 15522, 59280] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[3, 4, 2, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, {[3, 4, 2, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [2, 3, 1, 4]}, {[1, 2, 3, 4], [1, 2, 4, 3], [3, 1, 2, 4]}, {[1, 2, 3, 4], [1, 3, 4, 2], [2, 1, 3, 4]}, {[1, 2, 3, 4], [1, 4, 2, 3], [2, 1, 3, 4]}, {[2, 4, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[3, 4, 2, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: {[[2, 1, 3], {[1, 1, 0, 0]}, {2}], [[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 0, 1, 0]}, {3}], [[3, 1, 2], {[1, 1, 0, 0]}, {2}], [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[1, 3, 2], {}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 301, 1197, 4875, 20235, 85294, 364131, 1571212, 6841633, 30025137, 132668839, 589726354, 2635305193, 11832046239, 53348943586, 241461778944] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 4, 1, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 1, 4, 2], [4, 2, 1, 3]}, {[2, 4, 1, 3], [3, 2, 1, 4], [4, 1, 3, 2]}, {[1, 4, 3, 2], [2, 4, 1, 3], [3, 2, 4, 1]}, {[2, 4, 3, 1], [3, 1, 4, 2], [3, 2, 1, 4]}, {[1, 4, 2, 3], [2, 3, 4, 1], [3, 1, 4, 2]}, {[2, 3, 4, 1], [2, 4, 1, 3], [3, 1, 2, 4]}, {[2, 3, 1, 4], [3, 1, 4, 2], [4, 1, 2, 3]}} the member , {[1, 3, 4, 2], [2, 4, 1, 3], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 2, 4, 1], %1, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}], [[4, 1, 3, 2], %1, {3}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 3, 2], {}, {}], [[4, 2, 3, 1], %1, {1}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0]}, {}], [[1, 4, 3, 2], {[0, 0, 1, 1, 0]}, {3}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], %1, {3}], [[2, 4, 3, 1], %1, {1}], [[2, 1, 5, 4, 3], {[0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [ [2, 1, 5, 3, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 939, 3311, 11676, 41183] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [2, 4, 3, 1]}, {[1, 2, 3, 4], [1, 4, 2, 3], [4, 1, 3, 2]}, {[3, 1, 2, 4], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [2, 4, 3, 1], [4, 3, 2, 1]}, {[2, 3, 1, 4], [3, 2, 4, 1], [4, 3, 2, 1]}} the member , {[1, 4, 2, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [0, 2, 0, 0, 0]}, {3}], [[3, 2, 1], {[1, 0, 0, 0]}, {2}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[2, 3, 1], {[0, 0, 2, 0]}, {1}], [[1, 3, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 4, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [ [1, 3, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {2, 3}], [ [1, 3, 2, 4], {[0, 1, 0, 2, 0], [0, 0, 0, 3, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [ [1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4, 5], {[0, 1, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 0, 3, 0], [0, 2, 0, 0, 0, 0]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 248, 787, 2389, 7013, 20079] For the equivalence class of patterns, { {[4, 1, 2, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, {[2, 3, 4, 1], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [1, 4, 3, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [3, 2, 1, 4]}} the member , {[4, 1, 2, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1, 3, 4], {}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1, 2}], [[2, 1, 4, 3], {[1, 1, 0, 0, 0]}, {1, 2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1, 2}], [[3, 1, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 310, 1251, 5150, 21517, 90921] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [2, 3, 1, 4]}, {[1, 3, 2, 4], [1, 4, 2, 3], [3, 1, 2, 4]}, {[2, 4, 3, 1], [4, 1, 3, 2], [4, 2, 3, 1]}} the member , {[3, 2, 4, 1], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {3}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 3, 1, 4], [2, 4, 1, 3]}, {[1, 4, 3, 2], [3, 1, 2, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 3, 4, 2], [3, 1, 4, 2], [3, 2, 1, 4]}, {[2, 3, 4, 1], [2, 4, 1, 3], [4, 2, 1, 3]}, {[2, 3, 4, 1], [3, 1, 4, 2], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 4, 1, 3], [2, 4, 3, 1], [4, 1, 2, 3]}} the member , {[1, 3, 4, 2], [3, 1, 4, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 1, 0, 1]}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[2, 1, 3, 4], %4, {3}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {2}], [[4, 1, 2, 3], %1, {2}], [[1, 4, 2, 3], %1, {1}], [[3, 5, 1, 2, 4], %2, {3}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0]}, {1}], [ [4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {3}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], %4, {1}], [[2, 1, 4, 3, 5], %3, {1}], [[1, 3, 2], {[0, 1, 0, 1]}, {}], [[2, 5, 1, 3, 4], %2, {4}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {2}], [[3, 4, 1, 2], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [[2, 4, 1, 3, 5], %3, {1}], [[2, 3, 1, 4], %4, {1}], [[3, 1, 2, 4], %4, {2}], [[3, 4, 1, 2, 5], %3, {1}], [[3, 5, 2, 4, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1]}, {2}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[2, 4, 1, 3], %1, {}], [[2, 1, 5, 3, 4], %2, {4}], [[2, 1, 4, 3], %1, {}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]} %2 := {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]} %3 := {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %4 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 263, 904, 3066, 10324, 34652] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 1, 3, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 3, 2], {[0, 0, 0, 2], [1, 2, 0, 0]}, {}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[3, 2, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], { [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], { [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 2]}, {1}], [[3, 1, 2], {[0, 0, 0, 2], [1, 2, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 0, 3, 0]}, {}], [[2, 3, 1], {[0, 0, 0, 2], [0, 0, 3, 0]}, {}], [[4, 3, 1, 2], %2, {1}], [ [4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 4, 2, 3], {[1, 2, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {3}], [[1, 4, 3, 2], %2, {2}], [[1, 3, 2, 4], {[1, 2, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 3, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 2, 0, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[4, 1, 2, 3], {[1, 2, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {3}], [ [3, 1, 2, 4], {[1, 2, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 1, 3, 2], %2, {1}], [[3, 1, 4, 2], {[1, 2, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [ [2, 1, 4, 3], {[1, 1, 1, 0, 0], [1, 2, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 5, 3, 1, 4], %1, {1}], [[2, 4, 3, 1, 5], %1, {1}], [[3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {1}], [[2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 1, 5, 3], %1, {1}], [[3, 2, 1, 5, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[4, 3, 1, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[4, 3, 5, 1, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}], [ [3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[4, 2, 5, 1, 3], %1, {1}], [[5, 2, 3, 1, 4], %1, {2}], [[5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1, 5], %1, {2}], [[5, 2, 4, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {}], [[2, 1, 3], {[0, 0, 0, 1], [0, 0, 3, 0]}, {}], [[2, 4, 3, 1], { [1, 0, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {}], [[3, 2, 4, 1], {[0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 177, 333, 538, 792, 1095] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 1, 3, 4], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 4, 2, 1], [4, 2, 3, 1]}, {[3, 1, 2, 4], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 2, 4], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [2, 4, 3, 1]}, {[1, 4, 2, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [3, 2, 4, 1]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {}, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[5, 2, 3, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 0, 1]}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {}, {1}], [[5, 3, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}], [[5, 3, 4, 1, 2], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2, 3}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1]}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [ [3, 2, 5, 4, 1], {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 283, 1032, 3740, 13522, 48930] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 4, 3], [3, 4, 2, 1]}, {[2, 1, 4, 3], [3, 1, 2, 4], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 1, 2], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 2, 4, 3], [2, 4, 3, 1], [3, 4, 1, 2]}} the member , {[1, 2, 4, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[2, 1, 3], {[0, 2, 0, 0]}, {}], [[], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[3, 2, 4, 1], %2, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 1, 3], %2, {1}], [[1, 4, 3, 2], {}, {3}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[3, 4, 2, 1], %2, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0]}, {}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], %1, {1}], [[3, 1, 5, 4, 2], %1, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 2, 0, 0, 0, 0]}, {4}], [[3, 5, 4, 2, 1], %1, {4}], [ [2, 5, 3, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[3, 1, 4, 2], %2, {1}], [[3, 5, 4, 1, 2], {[0, 0, 0, 0, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [ [2, 4, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {2}], [[2, 5, 4, 1, 3], %1, {2}]} %1 := {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 240, 748, 2240, 6525, 18653] For the equivalence class of patterns, { {[1, 4, 3, 2], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 4, 3, 2], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 2, 4], [4, 1, 2, 3]}, {[1, 2, 4, 3], [1, 3, 2, 4], [2, 3, 4, 1]}, {[3, 2, 1, 4], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 3, 4], [2, 3, 4, 1]}, {[3, 2, 1, 4], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [4, 1, 2, 3]}} the member , {[1, 4, 3, 2], [4, 2, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[2, 1, 3, 4], {}, {3}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 1], {}, {}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [[1], {}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0]}, {1}], [[3, 5, 1, 4, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2], {[0, 2, 0, 0], [1, 0, 0, 0]}, {}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 989, 3544, 12696, 45578] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 4, 3], [3, 1, 2, 4]}, {[3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 3, 4], [2, 1, 4, 3]}, {[1, 2, 4, 3], [2, 1, 4, 3], [2, 3, 1, 4]}, {[3, 4, 1, 2], [3, 4, 2, 1], [4, 2, 1, 3]}, {[2, 4, 3, 1], [3, 4, 1, 2], [4, 3, 1, 2]}, {[3, 2, 4, 1], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 1, 3, 4], [2, 1, 4, 3]}} the member , {[1, 2, 4, 3], [2, 1, 4, 3], [3, 1, 2, 4]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[3, 1, 2], {[0, 0, 0, 1]}, {1}], [[2, 1, 3], {[0, 0, 1, 0]}, {3}], [[2, 3, 1], {[0, 0, 1, 1]}, {2}], [[3, 2, 1], {[0, 0, 1, 1]}, {1}], [[1, 3, 2], {[0, 0, 1, 1]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 76, 276, 1001, 3626, 13126, 47501, 171876, 621876, 2250001, 8140626, 29453126, 106562501, 385546876, 1394921876, 5046875001, 18259765626] This enumerating sequence seems to have the 2 3 -1 + 5 x - 6 x + x rational generating function, ----------------------- 2 3 -1 + 6 x - 10 x + 5 x For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 2, 1, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 3, 2], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [2, 3, 4, 1], [3, 4, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 2, 1], {}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {}, {1}], [[1, 4, 3, 2], {}, {2}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}], [ [2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 232, 707, 2066, 5858, 16257] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 1, 3, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 2, 4, 3], [3, 2, 1, 4], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [2, 3, 4, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 4, 1, 2], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [0, 1, 0, 0, 1]}, {}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[4, 5, 1, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {2}], [[4, 2, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [ [4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[0, 1, 0, 1], [1, 0, 0, 0]}, {}], [[4, 2, 5, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {5}], [ [3, 1, 2, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[1, 2, 3, 4], %2, {1}], [ [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {3}], [[2, 3, 1, 4], %2, {3}], [[2, 1, 3, 4], %2, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[2, 1, 4, 3], {[1, 0, 1, 1, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 4, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[3, 1, 2, 5, 4], %1, {1}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 1, 5, 2, 4], %1, {1}], [[4, 1, 5, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 5, 1, 2, 4], %1, {1}], [[1, 3, 2], {[0, 0, 0, 1], [1, 1, 1, 0]}, {}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {2}], [[3, 1, 4, 2], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 4, 1, 3], {[1, 0, 1, 1, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[3, 1, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {4}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 203, 517, 1187, 2504, 4921] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 4, 3, 1], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [4, 3, 2, 1]}, {[2, 1, 4, 3], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 2, 3, 4], [3, 4, 1, 2], [4, 1, 3, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 3, 4, 2], [2, 1, 4, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 4, 1, 2], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [2, 1, 4, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 4, 1, 3], %1, {1}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 2], {[0, 3, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [ [4, 5, 1, 2, 3], {[0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {4}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[4, 2, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {4}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 4, 1, 2], {[0, 2, 0, 0, 0], [0, 0, 0, 2, 0]}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 5, 4, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 3, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], %1, {1}], [[2, 1, 3, 4], {[0, 3, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [ [2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [ [3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {4}], [[3, 1, 2, 4, 5], { [0, 0, 3, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {4}], [[3, 1, 2, 5, 4], {[0, 0, 0, 0, 0, 0]}, {2}], [[4, 1, 3, 5, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 1, 2, 5, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [[4, 5, 2, 3, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {1}], [ [4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {1}], [[3, 4, 1, 2, 5], { [0, 0, 3, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[5, 2, 3, 1, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}], [[5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {4}], [ [5, 2, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 5, 3, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 0, 1, 0], [0, 3, 0, 0]}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {}], [ [3, 1, 2, 4], {[0, 0, 3, 0, 0], [0, 1, 2, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 2, 0, 0]}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 3, 2, 4], %1, {4}]} %1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 213, 561, 1317, 2809, 5536] For the equivalence class of patterns, { {[1, 4, 3, 2], [2, 3, 4, 1], [3, 1, 2, 4]}, {[2, 4, 3, 1], [3, 2, 1, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [4, 1, 2, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 2, 1, 4], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 3, 4, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 4, 3, 2], [3, 2, 4, 1], [4, 1, 2, 3]}} the member , {[1, 3, 4, 2], [3, 2, 1, 4], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 3, 1, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 2, 1], %1, {1}], [[2, 3, 1, 4], {[0, 2, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {1}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}], [ [2, 5, 4, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0]}, {2}], [ [1, 5, 3, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 4, 3, 2], { [0, 2, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0]}, {2}], [[1, 5, 4, 2, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 1, 5, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {2}], [ [4, 2, 5, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 4, 2, 1], %1, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {3}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {5}], [[3, 2, 4, 1], %1, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 1], [0, 2, 1, 0], [0, 0, 2, 1]}, {}], [[1, 4, 3, 2], {[0, 2, 1, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 1, 1, 1], [0, 0, 2, 1]}, {}], [[2, 1, 5, 4, 3], { [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {}], [[3, 1, 2], {[0, 1, 0, 1], [0, 0, 1, 0]}, {3}], [[2, 1, 3], {[0, 2, 0, 1]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 2, 1], [0, 0, 1, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [[3, 1, 5, 4, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[4, 2, 1, 3], %1, {4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 2, 0, 1, 0], [0, 0, 0, 2, 1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {4}]} %1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 210, 589, 1592, 4218, 11069] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 1, 2, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 1, 3, 4], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 2, 3], [4, 3, 1, 2]}, {[1, 2, 3, 4], [2, 3, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 4, 3, 1], [4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[3, 2, 1], {[1, 0, 0, 0]}, {2}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {2}], [[2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [ [2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 2, 3, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 237, 668, 1667, 3750, 7743] For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 3, 4, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 2, 1, 4], [3, 4, 1, 2]}, {[1, 4, 3, 2], [2, 1, 4, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 4, 1, 2], [4, 1, 2, 3]}} the member , {[2, 1, 4, 3], [2, 3, 4, 1], [3, 4, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {}, {1}], [[1, 4, 3, 2], {}, {2}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0]}, {2}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 232, 707, 2066, 5858, 16257] For the equivalence class of patterns, { {[1, 3, 2, 4], [1, 4, 2, 3], [4, 3, 1, 2]}, {[1, 3, 2, 4], [1, 3, 4, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [4, 1, 3, 2], [4, 2, 3, 1]}, {[2, 1, 3, 4], [4, 2, 1, 3], [4, 2, 3, 1]}, {[2, 1, 3, 4], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [4, 3, 1, 2]}} the member , {[1, 3, 2, 4], [1, 4, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[4, 5, 1, 2, 3], {}, {4}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1, 3, 4], {}, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {}, {2}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {}, {3}], [[3, 4, 1, 2], {}, {}], [[2, 3, 1, 4], {}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {2}], [ [4, 1, 3, 5, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[3, 1, 2, 4], {}, {}], [[4, 2, 3, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[3, 1, 2, 4, 5], {}, {4}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 259, 853, 2684, 8120, 23782] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 3, 2, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 3, 4, 2], [4, 2, 3, 1], [4, 3, 1, 2]}, {[2, 3, 1, 4], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [4, 1, 3, 2]}, {[1, 2, 4, 3], [1, 3, 2, 4], [3, 2, 4, 1]}, {[1, 3, 2, 4], [2, 1, 3, 4], [2, 4, 3, 1]}, {[3, 1, 2, 4], [3, 4, 2, 1], [4, 2, 3, 1]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 0, 1]}, {}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1]}, {}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1]}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[3, 4, 1, 2], {[0, 0, 0, 1, 1]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [ [3, 1, 5, 2, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[4, 1, 5, 2, 3], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}], [ [4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 258, 845, 2649, 8019, 23630] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 1, 4, 2], [3, 2, 1, 4]}, {[1, 3, 4, 2], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 1, 4, 2], [4, 2, 1, 3]}, {[1, 4, 3, 2], [2, 4, 1, 3], [3, 1, 2, 4]}, {[2, 4, 1, 3], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [3, 1, 4, 2]}, {[2, 4, 3, 1], [3, 1, 4, 2], [4, 1, 2, 3]}, {[2, 3, 4, 1], [2, 4, 1, 3], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [2, 4, 1, 3], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 1]}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {2}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 1]}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {3}], [[3, 1, 2, 4], {[0, 0, 1, 1, 1], [0, 1, 0, 0, 0]}, {2}], [[2, 1, 5, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 1]}, {}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 253, 845, 2791, 9188, 30246] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 4, 3], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [4, 2, 1, 3]}, {[2, 1, 3, 4], [2, 1, 4, 3], [2, 4, 3, 1]}, {[1, 4, 2, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 4, 1, 2], [4, 3, 1, 2]}, {[2, 3, 1, 4], [3, 4, 1, 2], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 1, 4, 3], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 2, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {}, {}], [[3, 4, 1, 2], {}, {2}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[1, 2], {}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2], {}, {}], [[3, 4, 2, 1], {}, {2}], [[4, 1, 3, 2], {}, {1}], [[2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {}, {2}], [[2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {}, {}], [[4, 3, 2, 1], {}, {1}], [[4, 3, 1, 2], {}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[2, 4, 3, 1], {}, {}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[5, 3, 4, 2, 1], {}, {1}], [[3, 5, 4, 2, 1], {}, {2}], [[5, 2, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[1, 3, 2, 4], %1, {1}], [[3, 5, 4, 1, 2], {}, {2}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 1, 2, 4], %1, {1}], [[5, 3, 4, 1, 2], {}, {1}], [[3, 2, 1, 4], %1, {1}], [[2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 3, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 1, 3, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 4, 2, 1], [4, 3, 1, 2]}, {[2, 1, 3, 4], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 1, 3, 4], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 3, 1], {[0, 0, 0, 2]}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 3, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {}], [[1, 3, 2], {[0, 0, 0, 2]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 2, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 4, 3, 1], { [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], { [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2], {[0, 0, 0, 2]}, {}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 195, 458, 942, 1752, 3016] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [2, 1, 4, 3]}, {[1, 3, 2, 4], [2, 1, 4, 3], [2, 3, 1, 4]}, {[1, 3, 2, 4], [1, 4, 2, 3], [2, 1, 4, 3]}, {[3, 2, 4, 1], [3, 4, 1, 2], [4, 2, 3, 1]}, {[2, 4, 3, 1], [3, 4, 1, 2], [4, 2, 3, 1]}, {[3, 4, 1, 2], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [3, 1, 2, 4]}} the member , {[3, 4, 1, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[1], {}, {}], [[2, 1], {[1, 1, 0]}, {2}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 1, 0]}, {3}], [[2, 3, 1], {[1, 0, 1, 0], [0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 77, 287, 1079, 4082, 15522, 59280, 227240, 873886, 3370030, 13027730, 50469890, 195892565, 761615285, 2965576715, 11563073315, 45141073925] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 4, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[2, 3, 1], {[0, 1, 0, 0]}, {2}], [[1, 3, 2], {}, {1}], [[3, 1, 2], {}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 245, 797, 2530, 7878, 24153] For the equivalence class of patterns, { {[1, 3, 2, 4], [1, 4, 3, 2], [2, 4, 3, 1]}, {[3, 1, 2, 4], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 2, 3], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [4, 1, 3, 2]}, {[1, 3, 2, 4], [3, 2, 1, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [2, 3, 4, 1], [4, 2, 3, 1]}, {[2, 3, 1, 4], [2, 3, 4, 1], [4, 2, 3, 1]}} the member , {[1, 4, 2, 3], [4, 1, 2, 3], [4, 2, 3, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 1], {}, {1}], [[2, 1, 3, 4], {}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {}, {2}], [[3, 2, 1], {[0, 1, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {3}], [[3, 1, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251] For the equivalence class of patterns, { {[3, 1, 2, 4], [3, 1, 4, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 1, 4, 2], [4, 1, 3, 2]}, {[2, 1, 4, 3], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 4, 2, 3], [2, 4, 1, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 4, 1, 3], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 1, 4, 2], [3, 4, 1, 2]}} the member , {[3, 1, 2, 4], [3, 1, 4, 2], [3, 4, 1, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {2}], [[2, 3, 1], {[0, 0, 1, 1], [0, 1, 0, 0]}, {3}], [[2, 1], {[0, 1, 1]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299, 37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946, 353224531663] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 4, 3, 1], [3, 1, 2, 4]}, {[2, 4, 3, 1], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 3, 4, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, {[2, 3, 1, 4], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 4, 2, 3], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [3, 2, 4, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [4, 2, 1, 3]}, {[1, 3, 2, 4], [2, 3, 1, 4], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[4, 5, 1, 2, 3], { [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[2, 1, 3], {[1, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0], [1, 1, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {1}], [ [2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {4}], [[2, 5, 1, 4, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0]}, {1}], [[3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {3}], [[4, 5, 1, 3, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 1, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 261, 877, 2852, 9020, 27877] For the equivalence class of patterns, { {[3, 2, 1, 4], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 4, 1], [3, 2, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 4, 1], [3, 2, 1, 4]}, {[1, 3, 2, 4], [1, 4, 3, 2], [4, 1, 2, 3]}, {[1, 3, 2, 4], [3, 2, 1, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [2, 3, 4, 1]}, {[1, 4, 3, 2], [4, 1, 2, 3], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [1, 4, 3, 2], [4, 1, 2, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1], {[0, 3, 0]}, {}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 1, 0, 1, 1], [0, 0, 1, 1, 1], [0, 0, 0, 2, 0]}, {3}], [[3, 1, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {1}], [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0], [0, 3, 0, 0], [0, 0, 3, 0]}, {2}], [[1, 3, 2], {[0, 0, 2, 0], [0, 1, 0, 0], [0, 0, 0, 1]}, {1}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [ [2, 3, 1, 4], {[0, 1, 0, 2, 0], [0, 0, 0, 3, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 2, 1], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 245, 795, 2508, 7732, 23393] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 2, 3, 4], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [4, 3, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {}], [[2, 3, 1], {[0, 1, 0, 0]}, {3}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {4}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {1}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {2}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [2, 4, 3, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 4, 3, 5, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[1, 3, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 1, 2, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 1, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 2, 3, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 5, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 229, 634, 1562, 3481, 7132] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 4, 3, 2], [2, 3, 1, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 4, 3, 1], [4, 1, 2, 3]}, {[2, 1, 3, 4], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 4, 3, 2], [3, 1, 2, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 2, 4, 1], [4, 1, 2, 3]}} the member , {[1, 4, 2, 3], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: {[[2, 1, 3], {[0, 2, 0, 0]}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[], {}, {}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 2, 3], {[0, 2, 0, 0]}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[4, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [ [5, 1, 2, 3, 4], {[0, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 1], [0, 0, 0, 2, 0, 1], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {3}], [[1, 2, 3, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 2, 0, 0, 0]}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [ [3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 2, 4, 3, 5], {[0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[1, 2, 5, 3, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 5, 4, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [1, 2, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0]}, {3}], [[2, 3, 5, 4, 1], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {3}], [[3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {2}], [[2, 1, 4, 3, 5], { [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], { [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0]}, {3}], [[3, 4, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {4}], [ [2, 3, 5, 1, 4], {[0, 1, 0, 1, 0, 1], [0, 0, 1, 1, 0, 1], [0, 0, 0, 2, 0, 1], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [ [2, 3, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[4, 1, 2, 3, 5], { [0, 2, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {2}], [ [5, 1, 3, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [5, 1, 2, 4, 3], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 2, 0, 0, 0, 0]}, {1}], [ [2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[2, 4, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 2, 0, 1]}, {}], [[3, 1, 2, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {2}], [ [5, 2, 3, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {1}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 2, 0, 0]}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 2, 0, 1]}, {}], [[2, 1, 4, 3], { [1, 0, 1, 0, 1], [0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {}], [[1, 2, 4, 3], {[0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 213, 569, 1389, 3175, 6927] For the equivalence class of patterns, { {[2, 1, 3, 4], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 4, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [3, 4, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[4, 3, 1, 2], %2, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[1, 4, 3, 2], %2, {2}], [[4, 1, 3, 2], %2, {1}], [[2, 1, 3], {}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[3, 1, 2], {[1, 0, 0, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 1, 5, 3], %1, {1}], [[3, 2, 1, 5, 4], {[1, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 1, 3], %1, {1}], [[4, 2, 1, 3], %2, {2}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 3, 5, 1, 2], %1, {1}], [[4, 5, 3, 1, 2], %1, {1}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0]}, {}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {}], [[2, 5, 3, 1, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [ [2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 5, 4, 1, 2], %1, {1}], [[2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 3, 1, 5, 2], %1, {1}], [[4, 5, 2, 1, 3], %1, {1}], [[3, 5, 2, 1, 4], %1, {1}], [[3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {4}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 229, 629, 1521, 3304, 6578] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 4, 1], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [3, 2, 1, 4]}, {[1, 3, 2, 4], [1, 3, 4, 2], [3, 2, 1, 4]}, {[1, 3, 2, 4], [1, 4, 3, 2], [3, 1, 2, 4]}, {[1, 3, 2, 4], [1, 4, 3, 2], [2, 3, 1, 4]}, {[2, 4, 3, 1], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 4, 1], [4, 1, 3, 2], [4, 2, 3, 1]}} the member , {[2, 3, 4, 1], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {3}], [[2, 1], {[1, 1, 0]}, {2}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 1, 0]}, {3}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 76, 274, 978, 3463, 12201, 42869, 150415, 527426, 1848905, 6480722, 22715293, 79617891, 279063942, 978133274, 3428414441, 12016810218] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 2, 3, 4], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 4, 2, 3], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 4, 3, 2], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 4, 3, 2], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 2, 3, 4], [3, 2, 4, 1], [4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {4}], [[2, 3, 1], {}, {}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 3, 1], %4, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[3, 5, 2, 4, 1], %4, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], %3, {4}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[4, 2, 5, 3, 1], %4, {1}], [[1, 3, 2], {[1, 0, 1, 0]}, {}], [[3, 1, 2], {[1, 0, 1, 0]}, {}], [[1, 4, 2, 3], %3, {4}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {4}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {3}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {3}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[4, 2, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 5, 2, 3], %2, {1}], [[3, 1, 5, 2, 4], %1, {1}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], %1, {1}], [[4, 5, 1, 2, 3], %2, {1}], [[2, 1, 4, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 0, 1, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {}], [[3, 4, 1, 2], {[0, 1, 0, 1, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {}], [[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 4, 2], { [0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1]}, {2}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [ [4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1]}, {4}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 5, 3], %2, {4}], [[3, 1, 2, 5, 4], %1, {4}], [[3, 1, 5, 4, 2], { [0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1]}, {3}], [[2, 1, 4, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 1, 5, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2, 4, 3], %3, {3}], [[1, 4, 2, 5, 3], %2, {4}], [[1, 3, 2, 5, 4], %1, {4}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]} %3 := {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]} %4 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 221, 605, 1517, 3574, 8065] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 3, 2], [2, 1, 3, 4]}, {[2, 3, 4, 1], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [3, 2, 1, 4]}, {[3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [3, 2, 1, 4]}, {[3, 4, 2, 1], [4, 1, 2, 3], [4, 2, 1, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4]}, {[2, 3, 4, 1], [3, 2, 4, 1], [4, 3, 1, 2]}} the member , {[1, 3, 4, 2], [1, 4, 3, 2], [2, 1, 3, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 3, 2], {[0, 1, 0, 0], [0, 0, 0, 3]}, {}], [[1, 2], {}, {}], [[1], {}, {}], [[2, 1, 3], {[0, 0, 2, 0], [0, 0, 0, 1]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 0, 3, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 0, 3]}, {1}], [[2, 1], {[0, 0, 3]}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 3]}, {2}], [[4, 1, 3, 2], { [0, 0, 0, 3, 0], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 1, 0, 0, 0], [0, 0, 0, 0, 3]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 3, 0], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 0, 3], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 0, 1]}, {1}], [[2, 3, 1], {[0, 0, 2, 0], [0, 0, 1, 1], [0, 0, 0, 3]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [[3, 1, 2], {[0, 0, 0, 3]}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 3], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [0, 0, 0, 1, 1]}, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 3], [0, 0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 267, 950, 3384, 12065, 43034] For the equivalence class of patterns, { {[2, 4, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[3, 1, 4, 2], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 4, 3], [2, 4, 1, 3]}, {[1, 2, 3, 4], [2, 1, 4, 3], [3, 1, 4, 2]}} the member , {[2, 4, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {[2, 0, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [1, 1, 1, 0]}, {2} ], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 1, 2], {[2, 0, 0, 0], [1, 1, 0, 0]}, {2}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [ [1, 3, 2, 4], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [1, 0, 2, 0, 0], [0, 1, 2, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2], {[3, 0, 0], [2, 1, 0]}, {}], [[1, 4, 2, 3], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {3}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0], [2, 0, 1, 0], [0, 2, 1, 0], [1, 1, 1, 0]}, {1}], [[1, 3, 2], {[2, 0, 0, 0], [1, 1, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 247, 821, 2704, 8868, 29030] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, {[2, 1, 4, 3], [3, 1, 2, 4], [3, 2, 1, 4]}, {[3, 4, 1, 2], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 3, 4, 1], [2, 4, 3, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 2, 4, 1], [3, 4, 1, 2]}, {[1, 3, 4, 2], [1, 4, 3, 2], [2, 1, 4, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 4, 3]}} the member , {[3, 4, 1, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}], [[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {2}], [[1, 3, 2, 4], {}, {1}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[1, 4, 2, 3], {[0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 301, 1197, 4875, 20235, 85294] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 4, 2, 3], [2, 4, 1, 3], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 3, 4, 2], [3, 1, 4, 2], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 1, 4, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 4, 2], [4, 1, 3, 2]}, {[2, 3, 1, 4], [2, 4, 1, 3], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [2, 4, 1, 3], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 1, 2], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 3], {}, {2}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {1}], [[4, 1, 2, 3], {}, {3}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[3, 1, 2, 4], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251] For the equivalence class of patterns, { {[1, 3, 2, 4], [1, 3, 4, 2], [3, 1, 4, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [4, 2, 3, 1]}, {[3, 1, 4, 2], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [2, 4, 1, 3]}, {[3, 1, 4, 2], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [3, 1, 4, 2]}, {[1, 3, 2, 4], [1, 4, 2, 3], [2, 4, 1, 3]}, {[2, 4, 1, 3], [4, 2, 1, 3], [4, 2, 3, 1]}} the member , {[3, 1, 4, 2], [4, 1, 3, 2], [4, 2, 3, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 1, 2], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 4, 2, 3], [2, 1, 4, 3], [2, 3, 4, 1]}, {[1, 3, 4, 2], [2, 1, 4, 3], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 4, 3, 2], [3, 2, 4, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [4, 1, 2, 3]}, {[2, 4, 3, 1], [3, 2, 1, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 4, 3, 2], [3, 4, 1, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 1, 4, 3], [4, 1, 2, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[4, 3, 1, 2], %2, {1}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], %2, {3}], [[1, 2], {}, {}], [[2, 1, 3, 4], %3, {3}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 1], %1, {2}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[3, 4, 1, 2], %2, {1}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[1, 4, 3, 2], {[0, 1, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[1, 3, 2, 4], %3, {1}], [[2, 3, 1, 4], %2, {1}], [[3, 1, 2, 4], %3, {2}], [[4, 2, 1, 3], %2, {1}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 2, 1, 4], %2, {1}], [[3, 1, 4, 2], %2, {3}], [[3, 2, 1], {[0, 0, 2, 0]}, {}], [[2, 4, 1, 3], %2, {1}], [[2, 4, 3, 1], %1, {3}], [[1, 3, 2], {[0, 1, 2, 0]}, {}], [[3, 4, 2, 1], %1, {1}]} %1 := {[0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]} %2 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} %3 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 237, 761, 2415, 7626, 24034] For the equivalence class of patterns, { {[2, 1, 3, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, {[1, 4, 2, 3], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 4, 3, 2], [3, 1, 2, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 3, 1], [4, 1, 2, 3]}, {[2, 1, 3, 4], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [3, 4, 2, 1]}, {[1, 3, 4, 2], [3, 2, 1, 4], [3, 4, 2, 1]}} the member , {[2, 1, 3, 4], [2, 3, 4, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[2, 3, 1], {[1, 0, 1, 1]}, {}], [[2, 4, 3, 1], {[1, 0, 1, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[], {}, {}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {2}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[3, 4, 1, 2], {[0, 1, 0, 1, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[1, 3, 2], {[1, 0, 1, 0]}, {}], [[3, 1, 2], {[1, 0, 1, 0]}, {}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {4}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [ [4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {3}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0]}, {4}], [ [4, 5, 1, 2, 3], {[0, 0, 1, 0, 1, 1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 239, 740, 2199, 6348, 17947] For the equivalence class of patterns, { {[1, 2, 4, 3], [2, 1, 4, 3], [2, 3, 4, 1]}, {[1, 2, 4, 3], [2, 1, 4, 3], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 1, 4, 3], [4, 1, 2, 3]}, {[3, 2, 1, 4], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 4, 3, 2], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 4, 3, 2], [3, 4, 1, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 4, 1]}} the member , {[1, 2, 4, 3], [2, 1, 4, 3], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {1}], [[1, 3, 2], {}, {2}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], %2, {1}], [[1, 3, 5, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 5, 3, 1, 2], {}, {3}], [[4, 5, 2, 3, 1], {}, {1, 2}], [[3, 4, 1, 2], {}, {}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}], [[3, 4, 2, 1], {}, {}], [[2, 3, 1, 4], %2, {1}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0]}, {1}], [[4, 5, 3, 2, 1], {}, {3}], [[1, 4, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {4}], [ [1, 4, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {2, 3}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0]}, {}], [[4, 5, 1, 3, 2], {}, {4}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1, 2}], [[2, 1, 3, 4], %2, {1}], [[1, 3, 4, 2, 5], %1, {1}], [[3, 1, 5, 2, 4], {[0, 0, 0, 0, 0, 0]}, {2}], [[3, 1, 4, 2, 5], %1, {2}], [[4, 5, 2, 1, 3], {[0, 0, 1, 0, 0, 0]}, {1, 2}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [[3, 4, 1, 2, 5], %1, {3}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0]}, {2}], [[3, 5, 2, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[3, 4, 2, 1, 5], %1, {3}], [[4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0]}, {4}], [ [4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1, 3}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 1, 0]}, {1, 3}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155] For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 4, 1, 3], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 1, 4, 3], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 4, 1, 2], [4, 2, 1, 3]}, {[2, 4, 3, 1], [3, 1, 4, 2], [3, 4, 1, 2]}, {[2, 4, 1, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 4, 3], [2, 4, 1, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 2, 4, 1], [3, 4, 1, 2]}} the member , {[1, 4, 2, 3], [2, 1, 4, 3], [3, 1, 4, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[5, 1, 4, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 1, 2, 3], {}, {3}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0], [0, 0, 1, 0]}, {3}], [[5, 1, 3, 2, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {5}], [[2, 3, 1], {[0, 0, 2, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {}], [[5, 1, 4, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [ [4, 1, 3, 2, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[5, 2, 4, 3, 1], {[0, 0, 0, 1, 0, 0], [0, 0, 2, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 288, 1093, 4203, 16359, 64377] For the equivalence class of patterns, { {[3, 1, 2, 4], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 3, 4, 2], [1, 4, 3, 2], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 3, 4, 1], [3, 2, 4, 1]}, {[1, 4, 2, 3], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 4, 2, 3], [4, 1, 2, 3], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 3, 1]}} the member , {[1, 3, 4, 2], [1, 4, 3, 2], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 4, 2, 1], {}, {3}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[2, 1, 3], {}, {1}], [[1, 3, 2], {[0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 309, 1237, 5026, 20626, 85242] For the equivalence class of patterns, { {[1, 4, 2, 3], [3, 2, 1, 4], [3, 4, 1, 2]}, {[1, 4, 3, 2], [3, 1, 2, 4], [3, 4, 1, 2]}, {[1, 3, 4, 2], [3, 2, 1, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 3, 4, 1], [4, 1, 3, 2]}, {[2, 1, 4, 3], [2, 4, 3, 1], [4, 1, 2, 3]}, {[2, 1, 4, 3], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 1, 4], [3, 4, 1, 2]}} the member , {[1, 4, 2, 3], [3, 2, 1, 4], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1, 3, 4], {}, {3}], [ [3, 5, 2, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[5, 1, 2, 4, 3], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[1, 2, 3, 4], {}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {}], [[1, 2, 4, 3], {[0, 0, 0, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 3, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 5, 3, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 4, 3, 5], {[0, 0, 0, 1, 0, 0]}, {1}], [[1, 2, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [ [1, 3, 5, 4, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 3, 5, 4, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 1, 4, 3, 5], {[0, 0, 0, 1, 0, 0]}, {1}], [[3, 1, 5, 4, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[2, 5, 1, 3, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 5, 1, 4, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 1, 2, 3, 5], {}, {2}], [[5, 2, 3, 4, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [5, 1, 3, 4, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[5, 1, 2, 3, 4], {}, {3}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[3, 1, 2, 4], {}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 222, 652, 1838, 5053, 13682] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 1, 4, 2], [4, 1, 2, 3]}, {[2, 1, 4, 3], [2, 4, 1, 3], [4, 1, 2, 3]}, {[3, 1, 4, 2], [3, 2, 1, 4], [3, 4, 1, 2]}, {[1, 4, 3, 2], [3, 1, 4, 2], [3, 4, 1, 2]}, {[2, 4, 1, 3], [3, 2, 1, 4], [3, 4, 1, 2]}, {[1, 4, 3, 2], [2, 4, 1, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [3, 1, 4, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [2, 4, 1, 3]}} the member , {[2, 4, 1, 3], [3, 2, 1, 4], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 1, 2], {}, {}], [[2, 1, 3, 4], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 4, 2, 1], %1, {3}], [[3, 2, 4, 1], %1, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3, 4, 5], {}, {3}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], %1, {2}], [[2, 5, 3, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3, 5], {}, {1}], [[1, 5, 3, 4, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[1, 5, 2, 4, 3], {[0, 0, 0, 0, 0, 1]}, {1}], [[3, 2, 4, 5, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[2, 1, 4, 3], {}, {2}], [[1, 3, 2, 4], {}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1]}, {1}], [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1, 2}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {}, {2}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 3, 5, 4], {}, {1, 2}], [[3, 1, 2, 4], {}, {2}], [[1, 4, 2, 3], {}, {}], [[1, 5, 2, 3, 4], {}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 267, 948, 3363, 11928, 42306] For the equivalence class of patterns, { {[3, 4, 1, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [2, 1, 4, 3]}, {[1, 2, 3, 4], [2, 1, 3, 4], [2, 1, 4, 3]}, {[3, 4, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[3, 4, 1, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2], {[3, 0, 0]}, {}], [[1], {}, {}], [[2, 3, 1], {[2, 0, 0, 0], [0, 1, 0, 0]}, {1}], [[1, 2, 3], {[3, 0, 0, 0], [2, 1, 0, 0], [1, 2, 0, 0], [0, 3, 0, 0]}, {1}], [[1, 3, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {1}], [[2, 1], {[2, 0, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 77, 286, 1066, 3977, 14841, 55386, 206702, 771421, 2878981, 10744502, 40099026, 149651601, 558507377, 2084377906, 7779004246, 29031639077] This enumerating sequence seems to have the 2 1 - 4 x + 2 x rational generating function, - -------------------- 2 3 -1 + 5 x - 5 x + x For the equivalence class of patterns, { {[2, 4, 3, 1], [3, 1, 2, 4], [4, 1, 2, 3]}, {[1, 4, 2, 3], [3, 2, 1, 4], [3, 2, 4, 1]}, {[1, 4, 3, 2], [2, 4, 3, 1], [3, 1, 2, 4]}, {[1, 4, 3, 2], [2, 3, 1, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 3, 4, 1], [4, 2, 1, 3]}, {[2, 3, 1, 4], [2, 3, 4, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 2, 4, 1], [4, 1, 2, 3]}, {[1, 3, 4, 2], [3, 2, 1, 4], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [3, 2, 1, 4], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[2, 1], {[1, 0, 1]}, {}], [[1, 2], {}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [[1], {}, {}], [[3, 2, 1], {[1, 0, 1, 0], [0, 0, 0, 1]}, {1}], [[3, 1, 2], {[1, 0, 0, 1], [0, 1, 0, 1]}, {}], [[1, 2, 3], {}, {2}], [[2, 3, 1], {[1, 0, 1, 0], [1, 0, 0, 1]}, {}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [ [4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {3}], [[1, 3, 2], {[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {1}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [ [4, 5, 1, 2, 3], {[1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 239, 738, 2178, 6220, 17351] For the equivalence class of patterns, { {[2, 1, 3, 4], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 1, 3, 4], [2, 3, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [3, 4, 2, 1]}, {[1, 3, 2, 4], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [4, 3, 1, 2]}} the member , {[2, 1, 3, 4], [2, 3, 4, 1], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 2, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[2, 3, 1], {[1, 1, 0, 1]}, {}], [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [ [4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 3, 2, 5, 1], {[1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0]}, {2}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2, 5], %2, {1}], [[4, 2, 1, 5, 3], %1, {1}], [[4, 2, 5, 1, 3], %1, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 5, 4, 3, 2], {[1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {3}], [[4, 5, 3, 1, 2], { [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1]}, {4}], [[4, 3, 2, 1], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[3, 2, 4, 1], {[1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0], [1, 0, 0, 0, 0]}, {3}], [[3, 2, 1], {[1, 1, 1, 0]}, {}], [[1, 5, 3, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 4, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0]}, {1}], [[1, 4, 3, 2], {[1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 4, 3, 1], {[1, 1, 0, 1, 0], [1, 1, 0, 0, 1], [0, 0, 1, 1, 0]}, {2}], [[3, 4, 1, 2], {[0, 1, 1, 0, 1], [1, 0, 0, 0, 0]}, {3}], [[4, 3, 5, 1, 2], %2, {4}], [[3, 2, 1, 4], {[1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [[4, 3, 1, 5, 2], %2, {3}], [[3, 2, 1, 5, 4], {[1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 1, 3], %1, {1}], [[3, 4, 2, 1, 5], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 1, 0, 1, 0], [1, 1, 1, 0, 0], [1, 1, 0, 0, 1], [0, 0, 1, 0, 1]}, {}], [[2, 5, 4, 3, 1], {[1, 1, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0], [1, 1, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[4, 5, 3, 2, 1], {[1, 1, 0, 0, 0, 1], [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [1, 1, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {3}], [[4, 3, 5, 2, 1], {[1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %2 := {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 248, 784, 2355, 6785, 18897] For the equivalence class of patterns, { {[3, 1, 4, 2], [3, 2, 1, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 4, 1, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 4, 1, 3], [4, 3, 1, 2]}, {[2, 4, 1, 3], [3, 2, 1, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 3, 4, 1], [3, 1, 4, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [2, 4, 1, 3]}, {[1, 4, 3, 2], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 1, 4, 2], [4, 1, 2, 3]}} the member , {[1, 4, 3, 2], [2, 4, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {3}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 2, 0, 0]}, {}], [[2, 1, 4, 3], %1, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], %1, {2}], [[4, 1, 3, 2], %1, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], %1, {3}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {1}], [[2, 1, 3], {[0, 1, 1, 0]}, {}], [[3, 1, 2, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 253, 840, 2728, 8719, 27541] For the equivalence class of patterns, { {[3, 1, 4, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, {[2, 4, 1, 3], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 3, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 2, 4, 1], [4, 3, 1, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [2, 4, 1, 3]}, {[1, 4, 2, 3], [2, 1, 3, 4], [2, 4, 1, 3]}, {[1, 2, 4, 3], [3, 1, 2, 4], [3, 1, 4, 2]}} the member , {[3, 1, 4, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {}, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 274, 978, 3463, 12201, 42869] For the equivalence class of patterns, { {[3, 1, 2, 4], [3, 2, 4, 1], [4, 3, 1, 2]}, {[2, 3, 1, 4], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 1, 3, 4], [4, 2, 1, 3]}, {[1, 2, 4, 3], [2, 3, 1, 4], [2, 4, 3, 1]}, {[1, 4, 2, 3], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 3, 4], [3, 2, 4, 1]}} the member , {[1, 3, 4, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[4, 1, 2, 3], %1, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[2, 1, 3], {}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 2, 5, 4, 1], {[1, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {}], [[2, 1, 3, 4], %1, {1}], [[1, 3, 2, 4], %1, {1}], [ [2, 1, 4, 3, 5], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {}, {3}], [[2, 1, 5, 4, 3], {}, {4}], [[1, 4, 2, 3], %1, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 261, 876, 2839, 8923, 27329] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 4, 3], [2, 1, 3, 4]}, {[3, 4, 2, 1], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [1, 2, 4, 3], [2, 1, 3, 4]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[3, 2, 1], {}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[0, 0, 2, 0], [0, 0, 1, 1], [0, 0, 0, 2]}, {1}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[1, 2], {[0, 0, 2]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[1, 2, 3, 4], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 2, 3, 4], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 3, 4], [2, 4, 1, 3], [3, 4, 2, 1]}, {[1, 2, 3, 4], [2, 4, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 4, 1, 3], [4, 3, 2, 1]}, {[1, 2, 4, 3], [2, 4, 1, 3], [4, 3, 2, 1]}, {[1, 2, 4, 3], [3, 1, 4, 2], [4, 3, 2, 1]}, {[2, 1, 3, 4], [3, 1, 4, 2], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [3, 1, 4, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 3, 1], {[0, 1, 1, 1]}, {}], [[3, 4, 1, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}], [[3, 4, 1, 2], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {2}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0], [0, 0, 0, 0, 1]}, {}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0]}, {4}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1]}, {4}], [[3, 1, 2], {[0, 0, 1, 1]}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 5, 1], %2, {2}], [[1, 4, 3, 5, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 1]}, {3}], [[3, 4, 2, 1], {[0, 0, 1, 1, 1], [0, 1, 0, 0, 0]}, {3}], [[4, 2, 3, 5, 1], %2, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 1]}, {3}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}], [[1, 3, 2, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {1}], [ [2, 1, 3, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 2, 4, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 5, 1], %2, {3}], [[2, 3, 1, 5, 4], %1, {1}], [[2, 3, 5, 1, 4], %1, {1}], [[3, 1, 2, 5, 4], %1, {1}], [[4, 5, 1, 2, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [ [4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {4}], [[4, 5, 2, 3, 1], { [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[3, 4, 1, 2, 5], %2, {1}], [[3, 5, 1, 2, 4], %1, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1]}, {4}], [ [2, 4, 5, 1, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0]}, {1}], [ [3, 4, 5, 1, 2], {[0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}]} %1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} %2 := {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 208, 526, 1174, 2370, 4416] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 4, 2, 3], [4, 1, 3, 2]}, {[3, 1, 2, 4], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 3, 4, 2], [2, 4, 3, 1], [3, 4, 2, 1]}, {[2, 3, 1, 4], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 2, 4, 3], [1, 3, 4, 2], [2, 4, 3, 1]}, {[2, 1, 3, 4], [2, 3, 1, 4], [3, 2, 4, 1]}, {[1, 4, 2, 3], [4, 1, 3, 2], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [1, 4, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}], [ [5, 2, 3, 1, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}], [[5, 3, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}], [[2, 1, 3], {[0, 2, 0, 0]}, {1}], [[5, 3, 4, 1, 2], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2, 3}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 2, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [2, 3, 1, 4], {[0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[4, 2, 3, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 274, 979, 3479, 12351, 43951] For the equivalence class of patterns, { {[1, 4, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 4, 3, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[3, 2, 1, 4], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [2, 3, 4, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [4, 1, 2, 3]}, {[1, 2, 3, 4], [2, 1, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 4, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[1, 2], {}, {}], [[1, 3, 2], {[2, 0, 0, 0], [0, 1, 0, 0]}, {3}], [[1], {}, {}], [[3, 1, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {3}], [[1, 2, 3], {}, {2}], [[2, 1, 3], {[2, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {4}], [[2, 3, 1], {[2, 0, 0, 0]}, {}], [[2, 1], {[2, 0, 0]}, {}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {4}], [[2, 3, 1, 4], {[2, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 294, 1108, 4165, 15638, 58762] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [4, 3, 1, 2]}, {[1, 3, 4, 2], [1, 4, 2, 3], [3, 4, 2, 1]}, {[1, 2, 4, 3], [4, 1, 3, 2], [4, 2, 1, 3]}, {[2, 1, 3, 4], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 2, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 2, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [4, 1, 3, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0]}, {3}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0]}, {4}], [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 260, 869, 2817, 8920, 27745] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 3, 1, 4], [4, 3, 2, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 2, 3, 4], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 2, 3, 4], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 2, 3, 4], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[2, 1], {[1, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}], [ [3, 4, 2, 5, 1], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0]}, {3}], [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 1, 0]}, {2}], [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {}], [[2, 1, 3], {[1, 1, 0, 0]}, {1}], [[2, 3, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {1}], [ [1, 3, 4, 2], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[3, 4, 1, 5, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {4}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {3}], [[2, 4, 1, 5, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [ [2, 3, 1, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0]}, {4}], [[3, 4, 5, 1, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {1}], [[2, 4, 5, 1, 3], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {1}], [ [3, 4, 5, 2, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [1, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 232, 654, 1639, 3705, 7678] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 3, 2, 4], [3, 2, 1, 4], [4, 1, 3, 2]}, {[1, 3, 2, 4], [1, 4, 3, 2], [3, 2, 4, 1]}, {[2, 3, 1, 4], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 4, 2, 3], [2, 3, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [4, 2, 1, 3]}, {[1, 3, 4, 2], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 4, 1], [3, 1, 2, 4], [4, 2, 3, 1]}} the member , {[1, 3, 2, 4], [2, 4, 3, 1], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [[3, 1, 2], {}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[4, 5, 1, 2, 3], {[0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 1, 0, 0]}, {3}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 0, 1]}, {2}], [[3, 1, 5, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}], [[4, 1, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {2}], [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {2}], [[3, 4, 1, 2, 5], { [0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {2}], [[2, 3, 1, 4], {[1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 0, 1, 1, 0]}, {2}], [ [4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {}], [ [4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[3, 1, 2, 4], {[0, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {3}], [[2, 1, 3], {[1, 0, 1, 0]}, {}], [[2, 1, 3, 4], {[1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 249, 797, 2451, 7318, 21380] For the equivalence class of patterns, { {[1, 4, 3, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [2, 3, 4, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [4, 2, 3, 1], [4, 3, 2, 1]}} the member , {[1, 4, 3, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[4, 5, 3, 1, 2], %2, {4}], [[], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 1, 3, 4], {}, {3}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0]}, {1}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], %3, {2}], [[4, 3, 1, 2], %3, {3}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3], {}, {2}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], %3, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 1, 2], %2, {4}], [[4, 2, 1, 3], %3, {2}], [[4, 1, 2, 3], %3, {2}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {}, {1}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 1, 3], %2, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {}], [[4, 5, 1, 2, 3], %2, {3}], [[3, 5, 1, 4, 2], %1, {3}], [[4, 5, 1, 3, 2], %2, {3}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[3, 5, 4, 1, 2], %1, {4}], [[2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 1, 2, 4], %1, {3}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 1, 4], %1, {3}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 284, 1041, 3789, 13730, 49679] For the equivalence class of patterns, { {[3, 1, 2, 4], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 4, 2, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 3, 4, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [2, 4, 3, 1]}, {[1, 2, 3, 4], [1, 2, 4, 3], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [3, 2, 4, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [4, 2, 1, 3]}} the member , {[1, 4, 2, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 2, 1], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[1, 2], {[0, 3, 0]}, {}], [[1], {}, {}], [[3, 1, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {3}], [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}], [[2, 1, 3], {[2, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {1} ], [[2, 1], {[2, 0, 0]}, {}], [[2, 3, 1], {[2, 0, 0, 0], [0, 0, 3, 0]}, {}], [[3, 4, 1, 2], {[0, 0, 0, 3, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0]}, {4}], [[3, 4, 2, 1], {[0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [ [2, 4, 1, 3], {[0, 0, 0, 1, 0], [2, 0, 0, 0, 0], [1, 1, 0, 0, 0], [0, 2, 0, 0, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[2, 3, 1, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [2, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0], [0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 256, 826, 2535, 7474, 21370] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 1, 3, 4], [4, 1, 3, 2]}, {[1, 4, 2, 3], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 1, 3, 4], [2, 4, 3, 1]}, {[2, 3, 1, 4], [3, 2, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 4, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[1, 1, 0, 0]}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [ [3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {4}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 1, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {4}], [ [3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0]}, {3}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {4}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 4, 1, 2], {[1, 1, 0, 0, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0]}, {}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[1, 3, 2], {[1, 0, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 244, 782, 2415, 7232, 21122] For the equivalence class of patterns, { {[3, 2, 4, 1], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 3, 4, 1], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 4, 2, 3], [1, 4, 3, 2], [2, 3, 1, 4]}, {[2, 4, 3, 1], [4, 1, 2, 3], [4, 2, 1, 3]}, {[1, 3, 4, 2], [1, 4, 3, 2], [3, 1, 2, 4]}, {[1, 4, 2, 3], [2, 3, 1, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 2, 4], [3, 2, 1, 4]}} the member , {[2, 3, 4, 1], [2, 4, 3, 1], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[4, 1, 2, 3], {[0, 0, 1, 2, 0], [1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {2}], [[2, 1, 3], {[1, 1, 0, 0]}, {2}], [[], {}, {}], [[1, 2], {}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {[1, 2, 0]}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 1, 2], {[1, 1, 0, 0], [1, 0, 1, 0], [0, 1, 2, 0]}, {}], [[4, 2, 3, 1], {[1, 2, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[1, 0, 1, 0], [1, 2, 0, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0]}, {2}], [[3, 4, 2, 1], {[1, 2, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 1], {[0, 0, 1, 0], [1, 2, 0, 0]}, {1}], [[2, 4, 1, 3], {[0, 0, 1, 2, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 2, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2], {[1, 0, 0, 0], [0, 1, 2, 0]}, {1}], [[3, 4, 1, 2], { [0, 1, 2, 0, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 257, 881, 2995, 10132, 34182] For the equivalence class of patterns, { {[3, 1, 2, 4], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 3, 4, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 4, 2, 3], [2, 4, 3, 1], [4, 3, 2, 1]}, {[2, 3, 1, 4], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [3, 2, 4, 1]}, {[1, 2, 3, 4], [1, 4, 2, 3], [4, 2, 1, 3]}, {[1, 2, 3, 4], [2, 3, 1, 4], [2, 4, 3, 1]}} the member , {[1, 3, 4, 2], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {3}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {3}], [[2, 1, 3, 4], %1, {3}], [[3, 2, 1], {[1, 0, 0, 0]}, {2}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[2, 1, 4, 3], {}, {1}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], %1, {1}], [[2, 4, 1, 3], %1, {3}], [[1, 4, 2, 3], %1, {3}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {3}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 247, 769, 2247, 6238, 16649] For the equivalence class of patterns, { {[1, 3, 4, 2], [3, 1, 2, 4], [3, 4, 2, 1]}, {[1, 4, 2, 3], [2, 3, 1, 4], [4, 3, 1, 2]}, {[1, 4, 2, 3], [2, 3, 1, 4], [3, 4, 2, 1]}, {[1, 3, 4, 2], [3, 1, 2, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 3, 1], [4, 2, 1, 3]}, {[2, 1, 3, 4], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 2, 4, 3], [3, 2, 4, 1], [4, 1, 3, 2]}, {[2, 1, 3, 4], [3, 2, 4, 1], [4, 1, 3, 2]}} the member , {[1, 3, 4, 2], [3, 1, 2, 4], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 3], {[0, 1, 0, 1]}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1]}, {1}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {3}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1], [0, 0, 0, 1, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 2], {[0, 0, 0, 1]}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 1]}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 1]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 230, 692, 2004, 5683, 15948] For the equivalence class of patterns, { {[1, 2, 4, 3], [3, 4, 2, 1], [4, 2, 3, 1]}, {[2, 1, 3, 4], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 2], {[1, 0, 0, 0]}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[2, 1, 4, 3], {[1, 1, 0, 0, 0]}, {1}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 233, 677, 1819, 4606, 11171] For the equivalence class of patterns, { {[3, 2, 1, 4], [3, 4, 2, 1], [4, 1, 2, 3]}, {[2, 3, 4, 1], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 4, 3, 2], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 1, 3, 4], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [2, 1, 3, 4], [2, 3, 4, 1]}, {[1, 2, 4, 3], [3, 2, 1, 4], [4, 1, 2, 3]}} the member , {[2, 3, 4, 1], [3, 2, 1, 4], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}], [[1], {}, {}], [[2, 3, 1], {[1, 0, 0, 1]}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 3, 2], {[1, 0, 0, 1], [2, 0, 1, 0], [1, 1, 1, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}], [[4, 3, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {2}], [[3, 2, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], { [0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [2, 4, 1, 3], {[0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {3}], [[2, 1, 3], {[1, 0, 0, 1]}, {}], [ [3, 1, 4, 2], {[1, 1, 1, 0, 0], [2, 0, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[3, 2, 1], {[0, 1, 0, 0], [0, 0, 0, 1]}, {}], [[4, 3, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}, {2}], [ [2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [4, 2, 5, 3, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [ [4, 1, 5, 2, 3], {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {2}], [[4, 1, 5, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}], [ [3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {2}], [[3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}], [[4, 5, 2, 3, 1], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 3, 2], { [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 1], [2, 0, 1, 0], [1, 1, 1, 0]}, {}], [[3, 4, 1, 2], {[1, 1, 1, 0, 0], [2, 0, 1, 0, 0], [1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}], [ [1, 4, 2, 3], {[0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 219, 635, 1776, 4853, 13068] For the equivalence class of patterns, { {[2, 1, 4, 3], [2, 3, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 2, 1, 4], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [2, 3, 4, 1], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[4, 3, 1, 2], %2, {1}], [[4, 1, 3, 2], %2, {3}], [[1, 2], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 5, 4, 3, 1], { [0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 1], {[0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {2}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 1, 4, 2], %2, {4}], [[4, 2, 1, 3], %2, {1}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1, 4], %2, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 4, 3, 2, 5], %1, {1}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 5, 4, 1, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[3, 2, 1], {[0, 0, 2, 0]}, {}], [[3, 4, 1, 2], %2, {4}], [[2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {}], [[3, 5, 4, 2, 1], {[0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {4}], [[3, 4, 2, 1], {[0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[1, 4, 3, 2], {[1, 0, 1, 1, 0], [1, 0, 2, 0, 0], [0, 0, 0, 2, 0]}, {}], [[1, 3, 2], {[1, 0, 2, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 4, 1, 3], %2, {2}], [[1, 5, 3, 2, 4], %1, {1}], [[1, 5, 4, 2, 3], %1, {1}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [ [1, 5, 4, 3, 2], {[1, 0, 1, 1, 0, 0], [1, 0, 2, 0, 0, 0], [1, 0, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {3}], [[2, 5, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]} %2 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 70, 212, 597, 1610, 4248, 11107] For the equivalence class of patterns, { {[3, 1, 2, 4], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [4, 2, 1, 3]}, {[1, 3, 2, 4], [1, 4, 2, 3], [4, 1, 3, 2]}, {[1, 4, 2, 3], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [2, 4, 3, 1]}, {[2, 3, 1, 4], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 4, 2], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [3, 2, 4, 1]}} the member , {[1, 3, 2, 4], [1, 4, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}], [[1, 2, 3], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}], [[2, 1, 3], {[0, 2, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {3}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 2, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 285, 1054, 3889, 14330, 52800] For the equivalence class of patterns, { {[3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1]}, {[3, 1, 2, 4], [3, 1, 4, 2], [4, 1, 2, 3]}, {[2, 4, 1, 3], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 3, 4, 2], [2, 3, 4, 1], [3, 1, 4, 2]}, {[2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3]}, {[1, 4, 2, 3], [2, 4, 1, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 1, 4, 2], [4, 1, 3, 2]}, {[1, 4, 3, 2], [2, 4, 1, 3], [2, 4, 3, 1]}} the member , {[1, 4, 2, 3], [2, 4, 1, 3], [4, 1, 2, 3]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[3, 1, 2], {[0, 0, 1, 0]}, {1}], [[1, 2, 3], {}, {2}], [[2, 1, 3], {}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895] For the equivalence class of patterns, { {[4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, {[2, 4, 3, 1], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2]}, {[1, 2, 4, 3], [1, 3, 2, 4], [1, 4, 2, 3]}, {[3, 2, 4, 1], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 3, 4], [2, 3, 1, 4]}, {[1, 3, 2, 4], [2, 1, 3, 4], [3, 1, 2, 4]}, {[4, 1, 3, 2], [4, 2, 3, 1], [4, 3, 1, 2]}} the member , {[4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 2, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {2}], [[2, 1, 4, 3], {[1, 1, 0, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1, 2}], [[2, 1, 3, 4], {[1, 1, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {4}], [[2, 1, 3], {[1, 1, 0, 0]}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {1, 2}] } Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 309, 1237, 5026, 20626, 85242] For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 3, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [3, 2, 4, 1]}, {[1, 4, 2, 3], [1, 4, 3, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 4, 1], [2, 4, 3, 1]}, {[2, 1, 4, 3], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 1, 4, 3], [4, 1, 2, 3], [4, 2, 1, 3]}, {[3, 1, 2, 4], [3, 2, 1, 4], [3, 4, 1, 2]}, {[2, 3, 1, 4], [3, 2, 1, 4], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [2, 3, 4, 1], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: {[[5, 4, 2, 3, 1], {}, {1}], [[4, 5, 2, 3, 1], {}, {1}], [[5, 1, 3, 2, 4], %1, {1}], [[3, 4, 1, 2, 5], %2, {1}], [[], {}, {}], [[3, 1, 2], {}, {}], [[1, 2], {}, {}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[4, 2, 3, 1], {}, {1}], [[1], {}, {}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], {}, {2}], [[1, 3, 2], {}, {}], [[1, 5, 4, 2, 3], {[1, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {}, {2}], [[3, 4, 1, 2], {}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}], [[2, 3, 1, 4], %3, {1}], [[2, 1, 3, 4], %3, {3}], [[5, 1, 4, 3, 2], {}, {1}], [[2, 5, 4, 3, 1], {}, {2}], [[2, 4, 3, 1], {}, {2}], [[1, 4, 3, 2], {}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}], [[4, 1, 3, 2], {}, {}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[5, 1, 4, 2, 3], {[1, 0, 0, 0, 0, 0]}, {2}], [[5, 4, 1, 2, 3], {[1, 0, 0, 0, 0, 0]}, {3}], [[3, 2, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0]}, {3}], [[1, 5, 4, 3, 2], {}, {2}], [[4, 3, 2, 1], {}, {1}], [[4, 3, 1, 2], {}, {}], [[3, 2, 1, 4], %3, {1}], [[5, 4, 1, 3, 2], {}, {1}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[5, 2, 4, 3, 1], {}, {1}], [[3, 5, 1, 2, 4], %1, {2}], [[4, 3, 1, 2, 5], %2, {1}], [[5, 3, 1, 2, 4], %1, {1}], [[1, 4, 3, 2, 5], %2, {1}], [[4, 1, 3, 2, 5], %2, {1}], [[1, 5, 3, 2, 4], %1, {1}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %2 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} %3 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 75, 267, 948, 3363, 11928, 42306] For the equivalence class of patterns, { {[1, 3, 4, 2], [2, 4, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 4, 1, 3], [4, 1, 3, 2]}, {[2, 3, 1, 4], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [3, 2, 4, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 1, 2, 4], [3, 4, 2, 1]}, {[1, 4, 2, 3], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 1, 4, 2], [4, 2, 1, 3]}} the member , {[1, 3, 4, 2], [2, 4, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {[0, 1, 0, 1, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 253, 840, 2728, 8719, 27541] For the equivalence class of patterns, { {[1, 2, 4, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [4, 3, 1, 2]}, {[1, 2, 3, 4], [1, 4, 2, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 2, 4, 1], [4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: {[[3, 5, 2, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {4}], [[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2], {[1, 1, 0, 0]}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}], [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 4, 3], {[1, 1, 0, 0, 0]}, {1}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[4, 1, 3, 2], %1, {1}], [[3, 1, 4, 2], {[1, 1, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {}], [ [2, 4, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}], [[2, 5, 3, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {}], [[3, 4, 1, 2], {[1, 1, 0, 0, 0]}, {1}], [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {}], [ [4, 2, 3, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[4, 3, 1, 2], %1, {1}], [[5, 2, 3, 1, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], %1, {2}], [[4, 2, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 3, 4, 1, 2], { [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0], [1, 1, 0, 0, 0]}, {3}], [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 2, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {3}], [ [4, 5, 3, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 5, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 2, 1, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {4}], [[3, 2, 1, 5, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[4, 5, 2, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [4, 3, 1, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}]} %1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 72, 220, 590, 1409, 3055, 6118] For the equivalence class of patterns, { {[1, 3, 2, 4], [2, 3, 1, 4], [4, 3, 1, 2]}, {[1, 2, 4, 3], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [3, 4, 2, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [4, 3, 1, 2]}, {[2, 1, 3, 4], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 2, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [3, 2, 4, 1], [4, 2, 3, 1]}} the member , {[1, 2, 4, 3], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth , 4 here it is: {[[2, 3, 1, 4], {[0, 0, 0, 1, 0], [1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}], [[], {}, {}], [[1, 2], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 3, 2], {[1, 0, 1, 0], [0, 1, 1, 0]}, {2}], [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {}], [[2, 1, 3], {[1, 1, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 238, 724, 2075, 5667, 14892] For the equivalence class of patterns, { {[3, 1, 4, 2], [3, 2, 4, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [3, 1, 2, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 3, 1, 4], [2, 4, 1, 3]}} the member , {[1, 3, 4, 2], [3, 1, 2, 4], [3, 1, 4, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[1], {}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {2}], [[2, 1], {[0, 1, 1]}, {1}], [[2, 3, 1], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 0, 1, 1]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 77, 286, 1066, 3977, 14841, 55386, 206702, 771421, 2878981, 10744502, 40099026, 149651601, 558507377, 2084377906, 7779004246, 29031639077] This enumerating sequence seems to have the 2 1 - 4 x + 2 x rational generating function, - -------------------- 2 3 -1 + 5 x - 5 x + x For the equivalence class of patterns, { {[2, 4, 3, 1], [3, 2, 1, 4], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 3, 1, 4], [4, 1, 2, 3]}, {[2, 1, 3, 4], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 2, 4, 3], [1, 3, 4, 2], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 4, 3, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 4, 2, 3], [2, 3, 4, 1]}, {[3, 2, 1, 4], [4, 1, 3, 2], [4, 3, 1, 2]}} the member , {[2, 4, 3, 1], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: {[[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 1, 2], {}, {}], [[1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[2, 1, 3, 4, 5], {[1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [1, 0, 0, 0, 1, 0]}, {3}], [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[3, 1, 4, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 4, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}], [[2, 1, 3, 5, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [ [2, 1, 4, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}], [[4, 1, 2, 3], {}, {2}], [[2, 1, 3, 4], {[1, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {}], [[2, 1, 3], {[1, 0, 1, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}], [[1, 3, 2], {[1, 0, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 993, 3593, 13068, 47838] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 3, 4, 1], [2, 4, 3, 1]}, {[1, 2, 3, 4], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 2, 3, 4], [4, 1, 2, 3], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 3, 4, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 4, 1], [3, 2, 4, 1]}, {[1, 4, 2, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, {[3, 1, 2, 4], [3, 2, 1, 4], [4, 3, 2, 1]}} the member , {[1, 2, 3, 4], [4, 1, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {[0, 0, 2, 0]}, {}], [[1, 2], {}, {}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[1], {}, {}], [[2, 1], {[0, 2, 0]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[2, 1, 3], {[0, 2, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 2, 0, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {3}], [[3, 2, 1], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {2}], [[2, 3, 1], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 0, 2, 0]}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {2}], [[2, 4, 3, 1], { [0, 2, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 2, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 263, 843, 2501, 6941, 18245] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 4, 3, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 1, 2, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 2, 4, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 1, 4, 3], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 4, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 3, 1, 4], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [3, 4, 1, 2], [4, 2, 1, 3]}, has a scheme of depth , 4 here it is: {[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}], [[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 1, 2], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[4, 2, 3, 1], %1, {1}], [[3, 4, 2, 1], %1, {3}], [[1, 3, 2], {}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 2, 4, 1], %1, {1}], [[2, 3, 1, 4], %1, {1}], [[3, 1, 2, 4], {[0, 0, 0, 1, 0]}, {2}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[4, 1, 2, 3], {}, {2}], [[2, 1, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[1, 4, 2, 3], {}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0]}, {3}]} %1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 244, 790, 2505, 7839, 24320] For the equivalence class of patterns, { {[2, 3, 4, 1], [3, 1, 2, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [2, 4, 3, 1], [3, 2, 1, 4]}, {[1, 4, 3, 2], [3, 1, 4, 2], [3, 2, 4, 1]}, {[1, 4, 3, 2], [2, 4, 1, 3], [4, 2, 1, 3]}, {[1, 4, 2, 3], [2, 3, 4, 1], [2, 4, 1, 3]}, {[1, 3, 4, 2], [3, 1, 4, 2], [4, 1, 2, 3]}, {[2, 3, 1, 4], [2, 4, 1, 3], [4, 1, 2, 3]}, {[3, 1, 4, 2], [3, 2, 1, 4], [4, 1, 3, 2]}} the member , {[2, 3, 4, 1], [3, 1, 2, 4], [3, 1, 4, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1, 2], {}, {}], [[1], {}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 1, 1, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {3}], [[1, 3, 2], {[0, 0, 1, 1]}, {2}], [[3, 4, 1, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1, 2}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {3}], [[2, 1], {[0, 1, 1]}, {1}], [[2, 3, 1], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 0, 1, 1]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 76, 275, 991, 3563, 12800, 45976] For the equivalence class of patterns, { {[1, 4, 3, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [2, 3, 4, 1], [4, 1, 2, 3]}, {[2, 1, 3, 4], [2, 3, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 2, 1, 4], [4, 3, 1, 2]}} the member , {[1, 4, 3, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: {[[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[], {}, {}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[2, 1, 3, 4], {[1, 1, 0, 1, 0], [1, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {[0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {3}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[1, 2, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}], [[5, 2, 3, 4, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}], [[2, 1, 3], {[1, 1, 1, 0]}, {}], [[4, 1, 2, 3, 5], {[1, 0, 0, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {3}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}], [[3, 4, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {4}], [[2, 3, 4, 1, 5], {[1, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 5, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [ [2, 4, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [ [2, 5, 1, 3, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [ [3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {3}], [[4, 2, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {2}], [ [4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [ [4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [5, 1, 2, 4, 3], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [ [5, 1, 3, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [[5, 1, 2, 3, 4], {}, {3}], [[3, 1, 2, 4, 5], {[1, 0, 1, 0, 1, 0], [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0]}, {4}], [[4, 1, 2, 3], {}, {}], [[1, 3, 2, 4], {[1, 0, 1, 1, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[3, 1, 2, 4], {[1, 0, 1, 1, 0], [0, 1, 0, 1, 0]}, {}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0]}, {}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 74, 249, 804, 2551, 8139, 26500] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 1, 4, 2], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [2, 4, 1, 3], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 1, 4, 2], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 4, 1, 3], [4, 3, 1, 2]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[3, 1, 2], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[3, 4, 1, 2], {[0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {2}], [[1, 3, 2], {}, {}], [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 1, 4, 3], {}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 73, 239, 734, 2133, 5924, 15859] For the equivalence class of patterns, { {[4, 1, 3, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, {[2, 4, 3, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, {[3, 2, 4, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, {[4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [1, 3, 4, 2]}, {[1, 2, 3, 4], [1, 3, 2, 4], [1, 4, 2, 3]}, {[1, 2, 3, 4], [1, 3, 2, 4], [2, 3, 1, 4]}, {[1, 2, 3, 4], [1, 3, 2, 4], [3, 1, 2, 4]}} the member , {[4, 1, 3, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[2, 1, 3, 4], {}, {3}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2], {}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {2}], [[3, 1, 2], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1, 2}], [[2, 1, 4, 3], {}, {1, 2}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1, 2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900] For the equivalence class of patterns, { {[3, 4, 1, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 1, 3, 4], [2, 1, 4, 3]}} the member , {[3, 4, 1, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, has a scheme of depth , 3 here it is: {[[], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}], [[2, 1, 3], {[2, 0, 0, 0], [1, 1, 0, 0], [0, 2, 0, 0]}, {1}], [[3, 1, 2], {[2, 0, 0, 0]}, {2}], [[1, 2], {[2, 0, 0]}, {1}]} Using the scheme, the first, , 21, terms are [1, 1, 2, 6, 21, 77, 286, 1066, 3977, 14841, 55386, 206702, 771421, 2878981, 10744502, 40099026, 149651601, 558507377, 2084377906, 7779004246, 29031639077] This enumerating sequence seems to have the 2 1 - 4 x + 2 x rational generating function, - -------------------- 2 3 -1 + 5 x - 5 x + x For the equivalence class of patterns, { {[1, 3, 4, 2], [1, 4, 2, 3], [2, 1, 4, 3]}, {[2, 4, 3, 1], [3, 2, 4, 1], [3, 4, 1, 2]}, {[3, 4, 1, 2], [4, 1, 3, 2], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 3, 1, 4], [3, 1, 2, 4]}} the member , {[1, 3, 4, 2], [1, 4, 2, 3], [2, 1, 4, 3]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 3], {[0, 0, 1, 0]}, {}], [[1], {}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 2, 0]}, {2}], [[4, 2, 3, 1], {[0, 0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 77, 290, 1118, 4398, 17595, 71385] For the equivalence class of patterns, { {[2, 1, 4, 3], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [3, 4, 1, 2]}} the member , {[2, 1, 4, 3], [3, 4, 1, 2], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1, 2, 3], {}, {1}], [[4, 3, 2, 1], {}, {2}], [[1, 5, 4, 3, 2], {}, {3}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 3, 2], {}, {}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}], [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {[1, 1, 0, 0], [0, 0, 1, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0]}, {3}], [[1, 5, 3, 2, 4], { [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 4, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 2, 1, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {3}], [ [1, 4, 3, 2, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [[2, 5, 4, 3, 1], {[0, 1, 0, 0, 0, 0]}, {3}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0]}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0], [0, 1, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 222, 648, 1797, 4807, 12548] For the equivalence class of patterns, { {[1, 4, 3, 2], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [4, 1, 2, 3]}, {[1, 3, 2, 4], [3, 1, 2, 4], [4, 1, 2, 3]}, {[3, 2, 1, 4], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [2, 3, 4, 1]}, {[1, 4, 3, 2], [2, 4, 3, 1], [4, 2, 3, 1]}, {[3, 2, 1, 4], [3, 2, 4, 1], [4, 2, 3, 1]}} the member , {[1, 4, 3, 2], [4, 1, 3, 2], [4, 2, 3, 1]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 1], {}, {1}], [[2, 1, 3, 4], {}, {3}], [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}], [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 2, 4, 1], {}, {1}], [[1, 2, 3], {}, {2}], [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[3, 1, 2], {[1, 0, 0, 0], [0, 1, 0, 0]}, {2}], [[1, 3, 2], {[0, 1, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 78, 297, 1143, 4419, 17119, 66386] For the equivalence class of patterns, { {[2, 1, 3, 4], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 2, 4, 3], [3, 4, 2, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [2, 1, 3, 4], [3, 4, 2, 1]}, {[1, 4, 3, 2], [2, 1, 3, 4], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 2, 4, 3], [3, 2, 1, 4], [4, 3, 1, 2]}} the member , {[1, 2, 4, 3], [2, 3, 4, 1], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: {[[3, 4, 1, 2, 5], %1, {1}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {2}], [[], {}, {}], [[3, 1, 2], {}, {}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 3, 5, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[1, 3, 2], {}, {}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {2}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}], [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2], {}, {}], [[2, 1, 4, 3], {}, {2}], [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0]}, {4}], [[2, 4, 1, 3], {}, {3}], [[3, 1, 4, 2, 5], %1, {1}], [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {1}], [[3, 1, 4, 2], {}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [ [1, 4, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [1, 4, 5, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {4}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[4, 2, 5, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0]}, {4}], [[3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 3, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [ [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}], [[1, 3, 4, 2, 5], %1, {1}], [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {}]} %1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 21, 71, 209, 533, 1205, 2473, 4696] Out of a total of , 317, cases 235, were successful and , 82, failed Success Rate: , 0.741 Here are the failures {{{[1, 3, 2, 4], [2, 4, 3, 1], [4, 3, 2, 1]}, {[1, 3, 2, 4], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [4, 2, 3, 1]}, {[1, 2, 3, 4], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 2, 3, 4], [1, 4, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 1, 3, 2], [4, 3, 2, 1]}}, { {[1, 2, 3, 4], [1, 2, 4, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 1, 3, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [4, 3, 1, 2], [4, 3, 2, 1]}}, { {[1, 4, 2, 3], [3, 4, 1, 2], [4, 1, 2, 3]}, {[2, 1, 4, 3], [3, 2, 1, 4], [3, 2, 4, 1]}, {[1, 3, 4, 2], [2, 3, 4, 1], [3, 4, 1, 2]}, {[2, 3, 1, 4], [2, 3, 4, 1], [3, 4, 1, 2]}, {[1, 4, 3, 2], [2, 1, 4, 3], [4, 1, 3, 2]}, {[2, 1, 4, 3], [3, 2, 1, 4], [4, 2, 1, 3]}, {[1, 4, 3, 2], [2, 1, 4, 3], [2, 4, 3, 1]}, {[3, 1, 2, 4], [3, 4, 1, 2], [4, 1, 2, 3]}}, { {[2, 4, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [2, 4, 1, 3]}, {[1, 2, 3, 4], [1, 3, 2, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [4, 2, 3, 1], [4, 3, 2, 1]}}, { {[1, 3, 2, 4], [1, 4, 2, 3], [3, 1, 4, 2]}, {[1, 3, 2, 4], [2, 4, 1, 3], [3, 1, 2, 4]}, {[3, 1, 4, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [3, 1, 4, 2]}, {[2, 4, 3, 1], [3, 1, 4, 2], [4, 2, 3, 1]}, {[2, 4, 1, 3], [3, 2, 4, 1], [4, 2, 3, 1]}, {[2, 4, 1, 3], [4, 1, 3, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [2, 4, 1, 3]}}, { {[1, 3, 2, 4], [2, 1, 3, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 2, 3, 1], [4, 3, 1, 2]}}, { {[2, 1, 4, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 2, 4], [3, 4, 1, 2]}}, { {[2, 4, 3, 1], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3]}, {[1, 3, 2, 4], [2, 3, 1, 4], [3, 1, 2, 4]}, {[4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1]}}, { {[2, 4, 1, 3], [3, 1, 2, 4], [3, 4, 1, 2]}, {[1, 3, 4, 2], [2, 4, 1, 3], [3, 4, 1, 2]}, {[1, 4, 2, 3], [3, 1, 4, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 1, 4, 2], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 4, 1, 3], [4, 1, 3, 2]}, {[2, 1, 4, 3], [2, 4, 3, 1], [3, 1, 4, 2]}, {[2, 1, 4, 3], [2, 4, 1, 3], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 4, 2], [3, 4, 1, 2]}}, { {[2, 1, 3, 4], [2, 4, 1, 3], [3, 1, 2, 4]}, {[2, 4, 1, 3], [4, 1, 3, 2], [4, 3, 1, 2]}, {[2, 4, 3, 1], [3, 1, 4, 2], [3, 4, 2, 1]}, {[3, 1, 4, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3, 4], [2, 3, 1, 4], [3, 1, 4, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [2, 4, 1, 3]}, {[1, 2, 4, 3], [1, 4, 2, 3], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 2, 4, 1], [3, 4, 2, 1]}}, { {[3, 2, 4, 1], [4, 1, 3, 2], [4, 2, 3, 1]}, {[2, 4, 3, 1], [4, 2, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 3, 4, 2], [3, 1, 2, 4]}, {[1, 3, 2, 4], [1, 4, 2, 3], [2, 3, 1, 4]}}, { {[1, 2, 3, 4], [2, 4, 1, 3], [4, 2, 3, 1]}, {[1, 2, 3, 4], [3, 1, 4, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 4, 2], [4, 3, 2, 1]}, {[1, 3, 2, 4], [2, 4, 1, 3], [4, 3, 2, 1]}}, { {[2, 1, 3, 4], [2, 4, 1, 3], [3, 2, 1, 4]}, {[2, 1, 3, 4], [3, 1, 4, 2], [3, 2, 1, 4]}, {[1, 2, 4, 3], [1, 4, 3, 2], [2, 4, 1, 3]}, {[3, 1, 4, 2], [4, 1, 2, 3], [4, 3, 1, 2]}, {[2, 3, 4, 1], [3, 1, 4, 2], [3, 4, 2, 1]}, {[2, 3, 4, 1], [2, 4, 1, 3], [3, 4, 2, 1]}, {[1, 2, 4, 3], [1, 4, 3, 2], [3, 1, 4, 2]}, {[2, 4, 1, 3], [4, 1, 2, 3], [4, 3, 1, 2]}}, { {[1, 2, 4, 3], [2, 4, 1, 3], [3, 1, 4, 2]}, {[2, 1, 3, 4], [2, 4, 1, 3], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 1, 4, 2], [4, 3, 1, 2]}, {[2, 4, 1, 3], [3, 1, 4, 2], [3, 4, 2, 1]}}, { {[1, 2, 4, 3], [2, 1, 3, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 4, 2, 1], [4, 3, 1, 2]}}, { {[1, 2, 3, 4], [3, 4, 1, 2], [4, 1, 2, 3]}, {[1, 2, 3, 4], [2, 3, 4, 1], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 4, 3, 2], [2, 1, 4, 3], [4, 3, 2, 1]}}, { {[2, 4, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, {[2, 4, 1, 3], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [2, 4, 1, 3]}, {[1, 2, 4, 3], [1, 3, 2, 4], [3, 1, 4, 2]}, {[3, 1, 4, 2], [3, 4, 2, 1], [4, 2, 3, 1]}, {[3, 1, 4, 2], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [2, 4, 1, 3]}, {[1, 3, 2, 4], [2, 1, 3, 4], [3, 1, 4, 2]}}, { {[2, 1, 3, 4], [2, 3, 1, 4], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 4, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 2, 1, 3], [4, 3, 1, 2]}, {[1, 2, 4, 3], [1, 3, 4, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 3, 2, 4], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 1, 3, 4], [3, 1, 2, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 1, 3, 2], [4, 3, 1, 2]}}, { {[2, 1, 4, 3], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 1, 4, 3], [4, 1, 3, 2], [4, 2, 1, 3]}, {[2, 3, 1, 4], [3, 1, 2, 4], [3, 4, 1, 2]}, {[1, 3, 4, 2], [1, 4, 2, 3], [3, 4, 1, 2]}}, { {[2, 1, 4, 3], [3, 1, 4, 2], [4, 2, 3, 1]}, {[2, 1, 4, 3], [2, 4, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 4, 1, 3], [3, 4, 1, 2]}, {[1, 3, 2, 4], [3, 1, 4, 2], [3, 4, 1, 2]}}, { {[1, 3, 2, 4], [2, 1, 4, 3], [2, 4, 1, 3]}, {[3, 1, 4, 2], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 4, 1, 2], [4, 2, 3, 1]}}, { {[2, 1, 4, 3], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 4, 3], [1, 3, 2, 4], [3, 4, 1, 2]}, {[1, 3, 2, 4], [2, 1, 3, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [4, 2, 3, 1], [4, 3, 1, 2]}}, { {[1, 3, 4, 2], [2, 4, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 4, 1, 3], [3, 2, 4, 1]}, {[1, 3, 2, 4], [2, 4, 3, 1], [3, 1, 4, 2]}, {[1, 3, 2, 4], [2, 4, 1, 3], [4, 1, 3, 2]}, {[1, 3, 2, 4], [3, 1, 4, 2], [4, 2, 1, 3]}, {[2, 4, 1, 3], [3, 1, 2, 4], [4, 2, 3, 1]}, {[2, 3, 1, 4], [3, 1, 4, 2], [4, 2, 3, 1]}, {[1, 4, 2, 3], [3, 1, 4, 2], 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4, 2]}, {[2, 4, 1, 3], [3, 2, 4, 1], [4, 1, 3, 2]}}, { {[1, 2, 3, 4], [2, 4, 1, 3], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 1, 4, 2], [4, 3, 2, 1]}}, { {[1, 3, 4, 2], [2, 1, 3, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 2, 4, 1], [4, 3, 1, 2]}, {[2, 1, 4, 3], [3, 4, 2, 1], [4, 1, 3, 2]}, {[1, 2, 4, 3], [2, 3, 1, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 4, 2, 1], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 4, 3, 1], [4, 3, 1, 2]}, {[1, 2, 4, 3], [3, 1, 2, 4], [3, 4, 1, 2]}, {[1, 4, 2, 3], [2, 1, 3, 4], [3, 4, 1, 2]}}, { {[1, 3, 2, 4], [2, 1, 4, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 4, 1, 2], [4, 2, 3, 1]}}, { {[1, 4, 3, 2], [2, 4, 1, 3], [3, 1, 4, 2]}, {[2, 3, 4, 1], [2, 4, 1, 3], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 1, 4, 2], [4, 1, 2, 3]}, {[2, 4, 1, 3], [3, 1, 4, 2], [3, 2, 1, 4]}}, { {[1, 3, 2, 4], [3, 2, 1, 4], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 3, 2], [4, 2, 3, 1]}}, { {[1, 3, 2, 4], [2, 3, 4, 1], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 2, 1, 4], [4, 2, 3, 1]}}, { {[2, 3, 4, 1], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 3, 1, 4], [3, 2, 1, 4]}, {[1, 3, 2, 4], [3, 1, 2, 4], [3, 2, 1, 4]}, {[2, 3, 4, 1], [2, 4, 3, 1], [4, 2, 3, 1]}, {[1, 3, 2, 4], [1, 4, 2, 3], [1, 4, 3, 2]}, {[1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 3, 2]}, {[4, 1, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1]}, {[4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 3, 1]}}, { {[1, 3, 4, 2], [1, 4, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 4, 3, 1], [3, 2, 4, 1]}, {[2, 3, 1, 4], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [4, 1, 3, 2], [4, 2, 1, 3]}}, { {[2, 1, 4, 3], [2, 4, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 1, 2, 4], [3, 4, 1, 2]}, {[2, 1, 4, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[2, 1, 4, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [3, 4, 1, 2]}, {[1, 2, 3, 4], [1, 4, 2, 3], [3, 4, 1, 2]}, {[2, 1, 4, 3], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [2, 3, 1, 4], [3, 4, 1, 2]}}, { {[2, 4, 1, 3], [3, 1, 4, 2], [3, 4, 1, 2]}, {[2, 1, 4, 3], [2, 4, 1, 3], [3, 1, 4, 2]}}, { {[2, 3, 1, 4], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 3, 4, 2], [2, 4, 1, 3], [3, 4, 2, 1]}, {[1, 4, 2, 3], [3, 1, 4, 2], [4, 3, 1, 2]}, {[1, 2, 4, 3], [2, 4, 1, 3], [4, 1, 3, 2]}, {[2, 1, 3, 4], [3, 1, 4, 2], [4, 2, 1, 3]}, {[2, 1, 3, 4], [2, 4, 1, 3], [3, 2, 4, 1]}, {[1, 2, 4, 3], [2, 4, 3, 1], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 1, 2, 4], [4, 3, 1, 2]}}, { {[1, 4, 2, 3], [2, 4, 1, 3], [4, 2, 3, 1]}, {[1, 3, 2, 4], [3, 1, 4, 2], [3, 2, 4, 1]}, {[1, 3, 2, 4], [3, 1, 4, 2], [4, 1, 3, 2]}, {[1, 3, 2, 4], [2, 4, 1, 3], [2, 4, 3, 1]}, {[1, 3, 2, 4], [2, 4, 1, 3], [4, 2, 1, 3]}, {[1, 3, 4, 2], [3, 1, 4, 2], [4, 2, 3, 1]}, {[3, 1, 2, 4], [3, 1, 4, 2], [4, 2, 3, 1]}, {[2, 3, 1, 4], [2, 4, 1, 3], [4, 2, 3, 1]}}, { {[1, 2, 3, 4], [2, 4, 1, 3], [3, 1, 2, 4]}, {[2, 4, 1, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[2, 4, 3, 1], [3, 1, 4, 2], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 3, 4, 2], [2, 4, 1, 3]}, {[1, 2, 3, 4], [1, 4, 2, 3], [3, 1, 4, 2]}, {[1, 2, 3, 4], [2, 3, 1, 4], [3, 1, 4, 2]}, {[2, 4, 1, 3], [3, 2, 4, 1], [4, 3, 2, 1]}, {[3, 1, 4, 2], [4, 2, 1, 3], [4, 3, 2, 1]}}, { {[2, 1, 4, 3], [3, 2, 4, 1], [4, 2, 1, 3]}, {[2, 1, 4, 3], [2, 4, 3, 1], [4, 1, 3, 2]}, {[1, 3, 4, 2], [2, 3, 1, 4], [3, 4, 1, 2]}, {[1, 4, 2, 3], [3, 1, 2, 4], [3, 4, 1, 2]}}, { {[1, 3, 2, 4], [2, 1, 4, 3], [2, 3, 4, 1]}, {[3, 2, 1, 4], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 1, 4, 3], [4, 1, 2, 3]}, {[1, 4, 3, 2], [3, 4, 1, 2], [4, 2, 3, 1]}}, { {[1, 2, 3, 4], [2, 3, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3, 4], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3, 4], [4, 1, 2, 3], [4, 3, 2, 1]}, {[1, 2, 3, 4], [1, 4, 3, 2], [4, 3, 2, 1]}}, { {[2, 4, 1, 3], [3, 1, 4, 2], [4, 2, 3, 1]}, {[1, 3, 2, 4], [2, 4, 1, 3], [3, 1, 4, 2]}}} This took, 169053.901, seconds of CPU time