There are , 5, different equivalence classes For the equivalence class of patterns, {{[3, 2, 1], [1, 2, 3], [1, 3, 2]}, {[3, 2, 1], [1, 2, 3], [2, 1, 3]}, {[3, 2, 1], [1, 2, 3], [2, 3, 1]}, {[3, 2, 1], [1, 2, 3], [3, 1, 2]}} the member , {[3, 2, 1], [1, 2, 3], [1, 3, 2]}, has a scheme of depth , 2 here it is: {[[], {}, {}], [[1], {[0, 2], [3, 0]}, {}], [[2, 1], {[1, 0, 0], [0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1}], [[1, 2], {[0, 1, 0], [0, 0, 1], [3, 0, 0]}, {1}]} Using the scheme, the first, , 31, terms are [1, 1, 2, 3, 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] the sequence is finite For the equivalence class of patterns, {{[3, 2, 1], [1, 3, 2], [2, 1, 3]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2]}} the member , {[3, 2, 1], [1, 3, 2], [2, 1, 3]}, has a scheme of depth , 2 here it is: {[[], {}, {}], [[2, 1], {[1, 0, 0], [0, 0, 1]}, {1}], [[1, 2], {[0, 1, 0]}, {1}], [[1], {}, {}]} Using the scheme, the first, , 31, terms are [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30] the sequence seems to be polynomial -1 + n For the equivalence class of patterns, {{[3, 2, 1], [1, 3, 2], [2, 3, 1]}, {[3, 2, 1], [1, 3, 2], [3, 1, 2]}, {[3, 2, 1], [2, 1, 3], [2, 3, 1]}, {[3, 2, 1], [2, 1, 3], [3, 1, 2]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1]}, {[1, 2, 3], [1, 3, 2], [3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2]}} the member , {[3, 2, 1], [1, 3, 2], [2, 3, 1]}, has a scheme of depth , 2 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0]}, {1}], [[2, 1], {[1, 0, 0]}, {1}]} Using the scheme, the first, , 31, terms are [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30] the sequence seems to be polynomial -1 + n For the equivalence class of patterns, {{[3, 2, 1], [2, 3, 1], [3, 1, 2]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3]}} the member , {[3, 2, 1], [2, 3, 1], [3, 1, 2]}, has a scheme of depth , 2 here it is: {[[], {}, {}], [[1, 2], {[1, 0, 0], [0, 2, 0]}, {1}], [[1], {[2, 0]}, {}], [[2, 1], {[1, 0, 0], [0, 1, 0]}, {1}]} Using the scheme, the first, , 31, terms are [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269] This enumerating sequence seems to have the 1 rational generating function, - ----------- 2 -1 + x + x For the equivalence class of patterns, {{[1, 3, 2], [2, 1, 3], [2, 3, 1]}, {[1, 3, 2], [2, 1, 3], [3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2]}} the member , {[1, 3, 2], [2, 1, 3], [2, 3, 1]}, has a scheme of depth , 2 here it is: {[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0]}, {1}], [[2, 1], {[0, 0, 1], [1, 1, 0]}, {1}]} Using the scheme, the first, , 31, terms are [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30] the sequence seems to be polynomial -1 + n Out of a total of , 5, cases 5, were successful and , 0, failed Success Rate: , 1. Here are the failures {} {} It took, 2.408, seconds of CPU time .