"for patterns of lengths: ", [[3, 1], [4, 0]] There all together, 71, different equivalence classes For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [2, 0], [3, 1]], %2}, {[[1, 0], [2, 0], [3, 1]], %1}, {[[1, 1], [2, 0], [3, 0]], %2}, {[[1, 1], [2, 0], [3, 0]], %1}, {[[3, 0], [2, 0], [1, 1]], %2}, {[[3, 0], [2, 0], [1, 1]], %1}, {[[3, 1], [2, 0], [1, 0]], %2}, {[[3, 1], [2, 0], [1, 0]], %1}} %1 := [[3, 0], [1, 0], [4, 0], [2, 0]] %2 := [[2, 0], [4, 0], [1, 0], [3, 0]] the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[2, 1], {[0, 0, 1], [0, 1, 0]}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 0]}, {1}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[2, 1, 3], {[0, 0, 0, 0]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%1, [[4, 0], [2, 0], [1, 0], [3, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[2, 1], {[0, 0, 1], [0, 1, 0]}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 0]}, {1}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[2, 1, 3], {[0, 0, 0, 0]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[4, 0], [3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[4, 0], [2, 0], [3, 0], [1, 0]] %2 := [[1, 0], [3, 0], [2, 0], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[3, 0], [4, 0], [1, 0], [2, 0]] %2 := [[2, 0], [1, 0], [4, 0], [3, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %1}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[2, 0], [4, 0], [1, 0], [3, 0]] %2 := [[3, 0], [1, 0], [4, 0], [2, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %1}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[3, 0], [1, 0], [4, 0], [2, 0]] %2 := [[2, 0], [4, 0], [1, 0], [3, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[2, 0], [1, 0], [4, 0], [3, 0]] %2 := [[3, 0], [4, 0], [1, 0], [2, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[1, 0], [3, 0], [2, 0], [4, 0]] %2 := [[4, 0], [2, 0], [3, 0], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0], [4, 0]] %2 := [[4, 0], [3, 0], [2, 0], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[2, 1], {[0, 0, 1], [0, 1, 0]}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 0]}, {1}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[2, 1, 3], {[0, 0, 0, 0]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1, 3, 2], {[1, 0, 0, 0]}, {2}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {3}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[3, 1, 2], {[0, 1, 0, 0]}, {2}, {3}], [[1, 2], {[0, 1, 0]}, {1}, {}], [[2, 1], {}, {}, {2}], [[3, 2, 1], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 1, 2], {[0, 1, 0, 0], [1, 0, 0, 0]}, {2}, {3}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {}, {2}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, has a scheme of depth , 5 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {2}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}, {}], [[1, 3, 2], {[1, 0, 0, 0]}, {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {}, {}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {5}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2, 4, 5], {[1, 0, 0, 0, 0, 0]}, {4}, {}], [[1, 3, 2, 5, 4], {[1, 0, 0, 0, 0, 0]}, {2, 3}, {}], [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[1, 4, 2, 5, 3], {[1, 0, 0, 0, 0, 0]}, {2, 3}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {3}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 23, 103 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319] Out of a total of , 71, cases 59, were successful and , 12, failed Success Rate: , 0.831 Here are the failures {{{%4, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 0]]}, {%1, [[4, 0], [3, 0], [1, 0], [2, 0]]}}, { {%4, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%3, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 0]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 0]]}}, {{%4, %5}, {%3, %5}, {%2, %6}, {%1, %6}}, { {%4, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%4, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%3, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 0], [1, 0]]}}, { {%4, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%1, [[3, 0], [2, 0], [1, 0], [4, 0]]}}, {{%4, %8}, {%4, %7}, {%3, %8}, {%3, %7}, {%2, %8}, {%2, %7}, {%1, %8}, {%1, %7}}, { {%4, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%3, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [4, 0], [1, 0]]}}, { {%4, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 0]]}}, {{%4, %6}, {%3, %6}, {%2, %5}, {%1, %5}}, { {%4, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%3, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%2, [[1, 0], [2, 0], [3, 0], [4, 0]]}, {%1, [[1, 0], [2, 0], [3, 0], [4, 0]]}}} %1 := [[3, 1], [1, 0], [2, 0]] %2 := [[2, 0], [3, 0], [1, 1]] %3 := [[2, 0], [1, 0], [3, 1]] %4 := [[1, 1], [3, 0], [2, 0]] %5 := [[2, 0], [1, 0], [4, 0], [3, 0]] %6 := [[3, 0], [4, 0], [1, 0], [2, 0]] %7 := [[3, 0], [1, 0], [4, 0], [2, 0]] %8 := [[2, 0], [4, 0], [1, 0], [3, 0]] {{{%4, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 0]]}, {%1, [[4, 0], [3, 0], [1, 0], [2, 0]]}}, { {%4, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%3, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 0]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 0]]}}, {{%4, %5}, {%3, %5}, {%2, %6}, {%1, %6}}, { {%4, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%4, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%3, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 0], [1, 0]]}}, { {%4, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%1, [[3, 0], [2, 0], [1, 0], [4, 0]]}}, {{%4, %8}, {%4, %7}, {%3, %8}, {%3, %7}, {%2, %8}, {%2, %7}, {%1, %8}, {%1, %7}}, { {%4, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%3, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [4, 0], [1, 0]]}}, { {%4, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 0]]}}, {{%4, %6}, {%3, %6}, {%2, %5}, {%1, %5}}, { {%4, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%3, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%2, [[1, 0], [2, 0], [3, 0], [4, 0]]}, {%1, [[1, 0], [2, 0], [3, 0], [4, 0]]}}} %1 := [[3, 1], [1, 0], [2, 0]] %2 := [[2, 0], [3, 0], [1, 1]] %3 := [[2, 0], [1, 0], [3, 1]] %4 := [[1, 1], [3, 0], [2, 0]] %5 := [[2, 0], [1, 0], [4, 0], [3, 0]] %6 := [[3, 0], [4, 0], [1, 0], [2, 0]] %7 := [[3, 0], [1, 0], [4, 0], [2, 0]] %8 := [[2, 0], [4, 0], [1, 0], [3, 0]] "for patterns of lengths: ", [[3, 1], [4, 1]] There all together, 240, different equivalence classes For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%2, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 15, 52 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346, 445958869294805289, 4638590332229999353, 49631246523618756274, 545717047936059989389, 6160539404599934652455, 71339801938860275191172] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 24, 120 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000, 304888344611713860501504000000, 8841761993739701954543616000000] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, has a scheme of depth , 5 here it is: {[[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 1, 3], {}, {1}, {3}], [[1, 3, 2], {}, {}, {3}], [[1, 4, 3, 2], {}, {3}, {4}], [[3, 5, 4, 1, 2], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[2, 5, 3, 1, 4], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[2, 4, 3, 1], {}, {}, {}], [[2, 3, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}], [[3, 2, 1], {}, {2}, {}], [[3, 5, 4, 2, 1], {}, {4}, {}], [[2, 1], {}, {}, {}], [[2, 4, 3, 1, 5], {}, {1, 2, 3}, {5}], [[1, 3, 2, 4], {}, {2}, {4}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 15, 52 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346, 445958869294805289, 4638590332229999353, 49631246523618756274, 545717047936059989389, 6160539404599934652455, 71339801938860275191172] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 24, 120 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000, 304888344611713860501504000000, 8841761993739701954543616000000] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, {{%2, [[1, 0], [4, 0], [2, 0], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 1], [2, 0]]}, {%2, [[2, 1], [3, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 1], [2, 0], [4, 0]]}, {%1, [[2, 0], [4, 1], [3, 0], [1, 0]]}, {%1, [[3, 1], [2, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [2, 0], [1, 1], [3, 0]]}, {%1, [[4, 0], [1, 0], [3, 0], [2, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[1, 0], [4, 1], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 1]]}, {%2, [[3, 1], [2, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [2, 0], [1, 1], [4, 0]]}, {%1, [[2, 0], [3, 0], [4, 1], [1, 0]]}, {%1, [[2, 1], [3, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [2, 0], [3, 1]]}, {%1, [[4, 0], [1, 1], [2, 0], [3, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%2, [[3, 1], [1, 0], [2, 0], [4, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[4, 0], [2, 0], [1, 0], [3, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 15, 52 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346, 445958869294805289, 4638590332229999353, 49631246523618756274, 545717047936059989389, 6160539404599934652455, 71339801938860275191172] For the equivalence class of patterns, {{%1, [[1, 0], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 1], [4, 0]]}, {%2, [[2, 0], [4, 0], [3, 1], [1, 0]]}, {%2, [[3, 0], [2, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 1], [2, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 1], [4, 0], [2, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [1, 1], [4, 0], [3, 0]]}, {%2, [[2, 1], [1, 0], [4, 0], [3, 0]]}, {%2, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%2, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%1, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%1, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%1, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%1, [[3, 0], [4, 0], [1, 0], [2, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 24, 120 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000, 304888344611713860501504000000, 8841761993739701954543616000000] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%2, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%2, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 0], [2, 1]]}, {%1, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%1, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [3, 0], [4, 1], [1, 0]]}, {%2, [[2, 1], [3, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 1], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 1]]}, {%1, [[1, 0], [4, 1], [3, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 1]]}, {%1, [[3, 0], [2, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [2, 0], [1, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%2, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%2, [[3, 0], [1, 1], [4, 0], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%1, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%1, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%1, [[3, 0], [1, 0], [4, 0], [2, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [4, 0], [3, 1], [1, 0]]}, {%2, [[3, 0], [2, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 1], [2, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 1], [4, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 1], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, {{%2, [[2, 0], [4, 1], [3, 0], [1, 0]]}, {%2, [[3, 1], [2, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 1], [3, 0]]}, {%1, [[1, 0], [3, 0], [4, 1], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 1]]}, {%1, [[2, 1], [3, 0], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 1], [2, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%2, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%1, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%2, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%2, [[3, 0], [4, 0], [1, 0], [2, 1]]}, {%2, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%2, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%1, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%1, [[2, 1], [1, 0], [4, 0], [3, 0]]}, {%1, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%1, [[2, 0], [1, 1], [4, 0], [3, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[3, 0], [4, 1], [2, 0], [1, 0]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 1]]}, {%2, [[4, 0], [3, 0], [1, 1], [2, 0]]}, {%1, [[1, 0], [2, 0], [4, 1], [3, 0]]}, {%1, [[1, 0], [2, 0], [4, 0], [3, 1]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 0]]}, {%1, [[2, 1], [1, 0], [3, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%1, [[1, 0], [2, 0], [4, 1], [3, 0]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 0]]}, {%1, [[2, 1], [1, 0], [3, 0], [4, 0]]}, {%2, [[3, 0], [4, 1], [2, 0], [1, 0]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 0]]}, {%2, [[4, 0], [3, 0], [1, 1], [2, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 1]]}, {%1, [[1, 0], [2, 0], [4, 0], [3, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] Out of a total of , 240, cases 229, were successful and , 11, failed Success Rate: , 0.954 Here are the failures {{{%4, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%4, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%3, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%3, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%1, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 0]]}}, { {%4, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%4, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 1], [1, 0], [2, 0], [4, 0]]}, {%3, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%4, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%4, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%4, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%3, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%2, [[3, 0], [4, 0], [1, 0], [2, 1]]}, {%2, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%1, [[2, 0], [1, 1], [4, 0], [3, 0]]}, {%1, [[2, 1], [1, 0], [4, 0], [3, 0]]}}, { {%4, [[4, 1], [1, 0], [2, 0], [3, 0]]}, {%3, [[3, 0], [2, 0], [1, 0], [4, 1]]}, {%2, [[2, 0], [3, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [4, 0], [3, 0], [2, 0]]}}, { {%4, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%4, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}}, { {%3, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%3, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%2, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%2, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%4, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%4, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[4, 1], [3, 0], [1, 0], [2, 0]]}}, { {%3, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%4, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%4, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%1, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [2, 0], [3, 0], [1, 0]]}}, { {%4, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%3, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%2, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 0]]}}} %1 := [[2, 0], [1, 0], [3, 1]] %2 := [[3, 1], [1, 0], [2, 0]] %3 := [[1, 1], [3, 0], [2, 0]] %4 := [[2, 0], [3, 0], [1, 1]] {{{%4, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%4, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%3, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%3, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%1, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 0]]}}, { {%4, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%4, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 1], [1, 0], [2, 0], [4, 0]]}, {%3, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%4, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%4, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%4, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%3, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%2, [[3, 0], [4, 0], [1, 0], [2, 1]]}, {%2, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%1, [[2, 0], [1, 1], [4, 0], [3, 0]]}, {%1, [[2, 1], [1, 0], [4, 0], [3, 0]]}}, { {%4, [[4, 1], [1, 0], [2, 0], [3, 0]]}, {%3, [[3, 0], [2, 0], [1, 0], [4, 1]]}, {%2, [[2, 0], [3, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [4, 0], [3, 0], [2, 0]]}}, { {%4, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%4, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}}, { {%3, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%3, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%2, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%2, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%4, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%4, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[4, 1], [3, 0], [1, 0], [2, 0]]}}, { {%3, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%4, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%4, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%1, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [2, 0], [3, 0], [1, 0]]}}, { {%4, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%3, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%2, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 0]]}}} %1 := [[2, 0], [1, 0], [3, 1]] %2 := [[3, 1], [1, 0], [2, 0]] %3 := [[1, 1], [3, 0], [2, 0]] %4 := [[2, 0], [3, 0], [1, 1]] "for patterns of lengths: ", [[3, 1], [4, 2]] There all together, 364, different equivalence classes For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 0], [3, 1], [2, 1], [4, 0]] %2 := [[4, 0], [2, 1], [3, 1], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 1], [2, 0], [3, 0], [4, 1]] %2 := [[4, 1], [3, 0], [2, 0], [1, 1]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 0], [2, 1], [3, 1], [4, 0]] %2 := [[4, 0], [3, 1], [2, 1], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 1], [3, 0], [2, 0], [1, 1]] %2 := [[1, 1], [2, 0], [3, 0], [4, 1]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 0], [3, 1], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 1], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 1], [2, 0], [3, 0], [1, 1]] %2 := [[1, 1], [3, 0], [2, 0], [4, 1]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 0], [2, 1], [3, 1], [1, 0]] %2 := [[1, 0], [3, 1], [2, 1], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1, 3], {}, {}, {3}], [[2, 1, 3, 4], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {3, 4}], [[3, 2, 1], {}, {2}, {3, 4}], [[3, 2, 4, 1], {}, {1, 2}, {4, 5}], [[2, 1, 4, 3], {}, {1, 2}, {4, 5}], [[2, 1], {}, {}, {2, 3}], [[3, 1, 4, 2], {}, {1, 2}, {4, 5}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 2, 6, 24 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000, 304888344611713860501504000000] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%1, [[1, 1], [4, 1], [3, 0], [2, 0]]}, {%2, [[2, 1], [3, 0], [4, 0], [1, 1]]}, {%2, [[2, 0], [3, 0], [4, 1], [1, 1]]}, {%2, [[4, 1], [1, 0], [2, 0], [3, 1]]}, {%2, [[4, 1], [1, 1], [2, 0], [3, 0]]}, {%1, [[3, 1], [2, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [2, 0], [1, 1], [4, 1]]}, {%1, [[1, 1], [4, 0], [3, 0], [2, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%1, [[2, 1], [1, 0], [3, 0], [4, 1]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 1]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 1]]}, {%2, [[3, 0], [4, 1], [2, 0], [1, 1]]}, {%2, [[4, 1], [3, 0], [1, 0], [2, 1]]}, {%2, [[4, 1], [3, 0], [1, 1], [2, 0]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 1]]}, {%1, [[1, 1], [2, 0], [4, 1], [3, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{%1, [[2, 1], [1, 0], [3, 1], [4, 0]]}, {%1, [[2, 0], [1, 1], [3, 1], [4, 0]]}, {%2, [[3, 1], [4, 0], [2, 1], [1, 0]]}, {%2, [[3, 0], [4, 1], [2, 1], [1, 0]]}, {%2, [[4, 0], [3, 1], [1, 1], [2, 0]]}, {%2, [[4, 0], [3, 1], [1, 0], [2, 1]]}, {%1, [[1, 0], [2, 1], [4, 1], [3, 0]]}, {%1, [[1, 0], [2, 1], [4, 0], [3, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 1], [3, 0], [1, 0], [4, 1]]}, {%2, [[3, 0], [1, 1], [2, 0], [4, 1]]}, {%1, [[3, 1], [2, 0], [4, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 0], [2, 1]]}, {%1, [[4, 1], [2, 0], [1, 1], [3, 0]]}, {%2, [[1, 1], [3, 0], [4, 1], [2, 0]]}, {%2, [[1, 1], [4, 0], [2, 0], [3, 1]]}, {%1, [[2, 0], [4, 1], [3, 0], [1, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{%2, [[2, 1], [3, 0], [1, 1], [4, 0]]}, {%2, [[3, 1], [1, 1], [2, 0], [4, 0]]}, {%1, [[3, 1], [2, 0], [4, 1], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 1]]}, {%1, [[4, 0], [2, 0], [1, 1], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 1], [2, 1]]}, {%2, [[1, 0], [4, 1], [2, 0], [3, 1]]}, {%1, [[2, 1], [4, 1], [3, 0], [1, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [3, 0], [1, 1], [4, 1]]}, {%2, [[3, 1], [1, 0], [2, 0], [4, 1]]}, {%1, [[3, 0], [2, 0], [4, 1], [1, 1]]}, {%1, [[4, 1], [1, 1], [3, 0], [2, 0]]}, {%1, [[4, 1], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 1], [3, 0], [4, 0], [2, 1]]}, {%2, [[1, 1], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [3, 1], [1, 1], [4, 0]]}, {%2, [[3, 1], [1, 0], [2, 1], [4, 0]]}, {%1, [[3, 0], [2, 1], [4, 1], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 1], [2, 0]]}, {%1, [[4, 0], [2, 1], [1, 0], [3, 1]]}, {%2, [[1, 0], [3, 1], [4, 0], [2, 1]]}, {%2, [[1, 0], [4, 1], [2, 1], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 1], [1, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[1], {[0, 1]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, {{%2, [[2, 0], [3, 1], [1, 0], [4, 1]]}, {%2, [[3, 0], [1, 0], [2, 1], [4, 1]]}, {%1, [[3, 0], [2, 1], [4, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 1],