Warning, the protected name Chi has been redefined and unprotected There all together, 146, different equivalence classes For the equivalence class of patterns, { {[2, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 3, 2], [3, 4, 1, 2], [4, 3, 1, 2]}, {[3, 1, 2], [1, 2, 4, 3], [2, 1, 4, 3]}, {[2, 3, 1], [2, 1, 3, 4], [2, 1, 4, 3]}} the member , {[2, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[2, 1], {[0, 1, 1], [2, 2, 0]}, {1}], [[1, 1], {[2, 1, 0], [2, 0, 1]}, {1, 2}], [[1, 2], {[1, 2, 1], [0, 3, 1], [2, 1, 0]}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [2, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 1], [2, 1, 1, 0], [0, 3, 2, 0], [1, 2, 2, 0]}, {2}], [[2, 3, 1], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {2}], [[1, 2, 2], {[1, 2, 1, 0], [0, 3, 1, 0], [1, 2, 0, 1], [0, 3, 0, 1], [2, 1, 0, 0]}, {2, 3}], [[1, 2, 3], {[1, 2, 1, 0], [0, 3, 1, 0], [1, 1, 2, 1], [0, 2, 2, 1], [0, 1, 3, 1], [2, 1, 1, 0]}, {}], [[1, 2, 3, 4], { [2, 1, 1, 1, 0], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0]}, {1}], [[1, 3, 4, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {1, 3}], [[1, 2, 3, 2], { [1, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {4}], [[1, 2, 3, 3], {[1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 2, 1, 0, 0], [0, 3, 1, 0, 0], [1, 1, 2, 0, 1], [0, 2, 2, 0, 1], [0, 1, 3, 0, 1], [2, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 4, 3], {[2, 1, 1, 1, 0], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 1, 1, 1]}, {3}], [[2, 3, 4, 1], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 4, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], { [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 1, 4], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 64, 144, 320, 704, 1536] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 211, 991, 4543, 20479, 91135, 401407, 1753087] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3455, 32060, 289865, 2586854] For the equivalence class of patterns, { {[3, 2, 1], [2, 3, 4, 1], [2, 4, 1, 3]}, {[1, 2, 3], [1, 4, 3, 2], [3, 1, 4, 2]}, {[1, 2, 3], [3, 1, 4, 2], [3, 2, 1, 4]}, {[3, 2, 1], [2, 4, 1, 3], [4, 1, 2, 3]}} the member , {[3, 2, 1], [2, 3, 4, 1], [2, 4, 1, 3]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 0]}, {2}], [[1, 2], {[1, 2, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0]}, {1, 3}], [[1, 2, 2], {[1, 2, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 2, 2, 0], [1, 1, 1, 0]}, {1}], [[2, 3, 1], {[1, 1, 1, 0], [0, 1, 2, 0]}, {3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {1}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 65, 151, 351, 816, 1897] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 257, 1391, 7670, 43146, 242476, 1357654, 7599444] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5369, 66189, 871679, 11853116] For the equivalence class of patterns, { {[2, 1, 3], [1, 3, 4, 2], [2, 3, 4, 1]}, {[3, 1, 2], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 3, 2], [3, 1, 2, 4], [4, 1, 2, 3]}, {[2, 3, 1], [3, 2, 1, 4], [4, 2, 1, 3]}} the member , {[2, 1, 3], [1, 3, 4, 2], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1]}, {1}], [[1, 2], {[1, 1, 1], [0, 2, 1]}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[1, 3, 2], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 1, 1]}, {2}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [ [1, 2, 2], {[1, 1, 1, 0], [1, 1, 0, 1], [0, 2, 0, 1], [0, 2, 1, 0]}, {2, 3} ], [[1, 2, 3], {[0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [ [1, 2, 3, 3], {[0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], { [0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {1, 3}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 1]}, {3}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 1]}, {}], [[1, 2, 4, 5, 3], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 2, 0, 1], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [[2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {5}], [[1, 3, 4, 5, 2], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 64, 144, 320, 704, 1536] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 214, 1006, 4606, 20734, 92158, 405502, 1769470] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3621, 33412, 301003, 2675994] For the equivalence class of patterns, { {[2, 1, 3], [1, 2, 3, 4], [2, 4, 3, 1]}, {[2, 3, 1], [3, 1, 2, 4], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [4, 2, 1, 3]}, {[3, 1, 2], [1, 3, 4, 2], [4, 3, 2, 1]}} the member , {[2, 1, 3], [1, 2, 3, 4], [2, 4, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3]}, {}], [[2, 1], {[0, 1, 1], [1, 4, 0]}, {1}], [[1, 1], {[1, 2, 1], [1, 1, 2], [1, 3, 0], [1, 0, 3]}, {1, 2}], [[1, 2], {[1, 1, 2], [0, 2, 2], [1, 2, 0]}, {}], [[1, 2, 2], {[1, 1, 2, 0], [0, 2, 2, 0], [1, 1, 1, 1], [0, 2, 1, 1], [1, 1, 0, 2], [0, 2, 0, 2], [1, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 2, 3, 0]}, {2}], [[1, 2, 3], {[1, 2, 1, 0], [1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 2, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[1, 3, 4, 2], {[1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {3}], [ [1, 2, 3, 3], {[1, 2, 1, 0, 0], [1, 1, 2, 0, 0], [0, 2, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {2, 3}] , [[1, 2, 4, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [1, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], { [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0]}, {1, 3, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], {[0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 1, 1, 0], [1, 0, 0, 2, 1, 0]}, {4, 5}], [[1, 3, 4, 1, 2], {[1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {1, 3, 4}], [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 26, 55, 113, 227, 449, 877] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 236, 1211, 5737, 25873, 112101, 471254, 1933582] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 4831, 58235, 622124, 6261614] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 4, 1], [4, 2, 3, 1]}, {[3, 1, 2], [1, 3, 2, 4], [1, 4, 3, 2]}, {[1, 3, 2], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 1], [1, 3, 2, 4], [3, 2, 1, 4]}} the member , {[2, 1, 3], [2, 3, 4, 1], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 1]}, {}], [[2, 1], {[0, 1, 1], [1, 2, 0]}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {1, 3}], [[1, 2, 3], {[0, 2, 1, 1], [1, 1, 1, 0]}, {1}], [[1, 2, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [[1, 3, 2], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 2, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {2}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2, 3], {[0, 2, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {1, 4}], [[1, 3, 2, 2], {[1, 1, 0, 2, 0], [0, 2, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 3, 1], %1, {2, 3}], [[1, 4, 2, 3], {[0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 1]}, {1}], [[1, 3, 2, 1], %2, {1}], [[1, 4, 3, 2], {[1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 3, 1, 1], %2, {3, 4}], [[3, 4, 1, 2], {[0, 2, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {3}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[3, 4, 2, 1], %1, {1, 2}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], %2, {3, 4}], [[4, 3, 2, 1], %1, {1, 2}], [[3, 2, 1, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 2, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {3}], [[1, 5, 4, 3, 2], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]}, {2, 3}], [ [1, 5, 4, 2, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1}], [[2, 5, 4, 3, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]}, {2, 3, 4}], [[1, 4, 3, 2, 1], {[1, 0, 2, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {1, 2, 3}], [[1, 4, 3, 2, 5], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], {[1, 1, 0, 2, 1, 0], [0, 2, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4, 5}], [[1, 4, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1}]] %1 := {[1, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %2 := {[0, 0, 1, 1, 1], [1, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 208, 886, 3616, 14554, 58324, 233422, 933832] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3516, 29285, 236115, 1891766] For the equivalence class of patterns, { {[1, 2, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [1, 4, 2, 3]}, {[3, 2, 1], [1, 2, 3, 4], [2, 3, 1, 4]}, {[1, 2, 3], [3, 2, 4, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 4], [5, 0]}, {}], [[1, 1], {[0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [5, 0, 0]}, {1, 2}] , [[1, 2], {[0, 1, 1], [0, 4, 0], [2, 3, 0]}, {}], [[2, 1], {[0, 2, 3], [0, 1, 4], [3, 1, 0], [0, 3, 0]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [3, 1, 1, 0], [0, 1, 1, 1]}, {1} ], [ [1, 2, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 3, 0, 0]}, {2, 3} ], [[1, 2, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[2, 1, 2], {[0, 3, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [3, 1, 0, 0]}, {3}], [[2, 1, 1], {[0, 0, 2, 3], [0, 0, 1, 4], [3, 0, 1, 0], [0, 3, 1, 0], [0, 2, 2, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2], [2, 2, 1, 0], [2, 1, 1, 1], [0, 0, 3, 0], [2, 1, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 3, 1, 0], [3, 1, 1, 0], [0, 1, 1, 1], [0, 2, 3, 0], [0, 1, 4, 0]}, {}] , [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 0]}, {}], [[3, 1, 2], {[3, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[1, 3, 2, 2], {[3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], %7, {}], [ [1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {}], [[2, 4, 3, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 3, 2], {[3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {1}], [[2, 1, 3, 3], {[3, 1, 1, 0, 0], [0, 3, 1, 0, 0], [0, 2, 3, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[3, 1, 4, 2], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1, 3}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], { [0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0]}, {1, 2}], [[2, 1, 4, 3], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [[3, 2, 4, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [3, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {1, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], { [0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 2, 1, 3], {[0, 3, 1, 0, 0], [0, 2, 2, 0, 0], [0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[4, 2, 1, 3], %7, {2}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 2, 1, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 1, 1, 2, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[3, 2, 1, 4], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1]}, {}], [[4, 3, 1, 2], %7, {}], [[1, 4, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 1, 2], {[1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {1, 4}], [[2, 4, 3, 2, 1], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], {[0, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 3, 1, 0]}, {2, 4, 5}], [ [1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 0, 2, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %2, {4, 5}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 5, 4, 1, 3], %5, {1, 4}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 3], %6, {1, 3}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %5, {1}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2}], [ [3, 2, 1, 4, 4], {[0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 2, 2, 1, 0, 0], [0, 1, 3, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[3, 2, 1, 4, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 2, 2, 0, 1, 0], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0]}, {1, 2}], [[4, 3, 1, 5, 2], %5, {4}], [[3, 2, 1, 4, 2], %2, {1, 2, 4}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], { [0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 2, 1, 2, 0], [0, 0, 1, 2, 2, 0], [0, 0, 1, 1, 3, 0]}, {3}], [[4, 2, 1, 5, 3], %5, {2, 4}], [[3, 2, 4, 1, 2], %2, {1, 2, 3}], [[4, 3, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 2, 2, 1, 0, 0], [0, 1, 3, 1, 0, 0], [0, 2, 1, 2, 0, 0], [0, 1, 2, 2, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 3, 0, 0]}, {5}], [[4, 2, 5, 1, 3], %5, {1, 2, 3}], [[4, 3, 5, 1, 2], %5, {3}], [[3, 2, 4, 1, 3], %6, {1, 2}], [[3, 2, 5, 1, 4], %5, {1, 2}], [ [3, 2, 4, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 2, 1, 2, 0], [0, 0, 1, 2, 2, 0], [0, 0, 1, 1, 3, 0]}, {4, 5}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 2, 3, 1, 3], %6, {2, 3}], [[5, 3, 4, 1, 2], %5, {2, 3}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %2, {2}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %6 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 18, 9, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 150, 154, 20, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 1745, 1531, 51, 0] For the equivalence class of patterns, { {[2, 1, 3], [4, 1, 2, 3], [4, 2, 3, 1]}, {[1, 3, 2], [2, 3, 4, 1], [4, 2, 3, 1]}, {[2, 3, 1], [1, 3, 2, 4], [1, 4, 3, 2]}, {[3, 1, 2], [1, 3, 2, 4], [3, 2, 1, 4]}} the member , {[1, 3, 2], [2, 3, 4, 1], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[2, 1], {}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {3}], [[2, 3, 1], {[0, 1, 2, 0]}, {}], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0]}, {1}], [[2, 1, 1], {}, {2, 3}], [[3, 2, 1], {}, {}], [[2, 1, 3], {[0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 2, 3, 4], %6, {}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], %6, {}], [[2, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {2}], [[2, 3, 1, 1], {[0, 1, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[3, 4, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 1, 2, 0]}, {}], [[2, 3, 1, 4], %6, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {1}], [[3, 1, 2, 1], {[0, 0, 2, 1, 0], [0, 2, 1, 1, 0], [1, 0, 1, 1, 0]}, {2, 4}] , [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], %6, {1, 3}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {}], [[3, 2, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {1}], [[3, 2, 1, 1], {}, {3, 4}], [[3, 2, 1, 4], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}] , [[4, 3, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2}], [[4, 3, 2, 1], {}, {2}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {2, 4}], [[4, 2, 1, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], %2, {1, 2, 3, 4}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %5, {4, 5}], [[2, 1, 3, 4, 4], %5, {4, 5}], [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], %2, {1, 2, 3, 4}], [[2, 1, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %2, {1, 2, 3, 4}], [[2, 3, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], %4, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], %5, {4, 5}], [[2, 3, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [0, 1, 1, 2, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 5], %2, {3, 4}], [[3, 4, 1, 2, 4], %5, {1, 2, 4}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [ [3, 4, 1, 2, 1], {[0, 1, 1, 2, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0]}, {3, 5}], [ [3, 4, 1, 2, 3], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2}], [[3, 5, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [ [4, 5, 2, 1, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2}], [[3, 4, 2, 1, 2], { [0, 1, 1, 2, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0]}, {3, 5}], [[3, 4, 2, 1, 5], %2, {3, 4}], [ [4, 5, 3, 1, 2], {[0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {3}], [ [3, 4, 2, 1, 3], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1}], [ [3, 4, 2, 1, 4], {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {1, 2, 3}], [[4, 5, 3, 2, 1], {[0, 1, 1, 1, 2, 0]}, {3}], [[3, 4, 2, 1, 1], {[0, 1, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[4, 1, 2, 3, 1], %3, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %5, {1}], [ [4, 1, 2, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [ [5, 1, 2, 3, 4], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3, 5], %2, {1}], [[5, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 4], %5, {1}], [[4, 2, 1, 3, 2], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 1], %3, {1, 2, 3, 4, 5}], [[5, 2, 1, 3, 4], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3, 5], %2, {1}], [ [4, 2, 1, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[5, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 0, 1, 1, 0]} %5 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]} %6 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 178, 615, 1966, 6067, 18426, 55567, 167062] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2481, 12362, 54398, 226410] For the equivalence class of patterns, { {[2, 3, 1], [2, 1, 4, 3], [4, 3, 1, 2]}, {[2, 1, 3], [1, 2, 4, 3], [3, 4, 1, 2]}, {[3, 1, 2], [2, 1, 4, 3], [3, 4, 2, 1]}, {[1, 3, 2], [2, 1, 3, 4], [3, 4, 1, 2]}} the member , {[3, 1, 2], [2, 1, 4, 3], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0]}, {}], [[1, 2], {[2, 1, 0]}, {}], [[1, 2, 2], {[2, 1, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0], [2, 0, 1, 0]}, {1}], [[1, 2, 3], {[1, 2, 1, 0], [0, 3, 1, 0], [2, 1, 1, 0]}, {1}], [[1, 3, 2], {[0, 1, 2, 0], [2, 1, 1, 0]}, {1}], [[2, 3, 1], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 2, 0], [0, 2, 1, 0], [2, 1, 1, 0]}, {}], [[2, 1, 3, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [2, 1, 0, 1, 0]}, {4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 1, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}] , [[2, 1, 3, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {2}], [[2, 1, 3, 4], {[2, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {3, 4}], [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}] , [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[2, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [2, 1, 1, 0, 0]}, {}], [ [2, 1, 3, 4, 5], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], {[2, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[3, 1, 4, 5, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %3, {1, 2, 3}], [ [2, 1, 3, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1, 2}], [[2, 1, 3, 4, 1], %1, {1, 2, 3}], [[3, 4, 2, 5, 1], %2, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], %1, {1, 2, 3, 5}], [[2, 3, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[2, 3, 1, 5, 4], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %3, {4}], [[4, 3, 2, 5, 1], %3, {1, 2, 3}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 5, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {4}], [[4, 2, 1, 5, 3], %2, {1, 2, 3, 4, 5}], [ [3, 2, 1, 4, 4], {[2, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[3, 2, 1, 5, 4], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], %1, {1, 2, 3, 5}], [[4, 2, 1, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3, 1], {[0, 0, 2, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 1, 2, 0, 0], [1, 0, 1, 1, 0, 0]}, {1, 3, 4, 5}], [[3, 2, 1, 3, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [2, 1, 1, 0, 0, 0]}, {4, 5}], [[4, 3, 1, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 4], {[0, 1, 1, 2, 1, 0], [2, 1, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4}]] %1 := {[1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 26, 51, 92, 155, 247, 376] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 184, 570, 1426, 3077, 5964, 10660, 17886] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2584, 11328, 36729, 96893] For the equivalence class of patterns, { {[2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [2, 1, 3, 4]}, {[2, 1, 3], [1, 2, 3, 4], [1, 2, 4, 3]}} the member , {[2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 0]}, {1}], [[2, 1], {[2, 1, 0]}, {}], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0]}, {3}], [[2, 1, 1], {[2, 0, 1, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {1, 2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {2}], [[3, 1, 2], {[0, 3, 1, 0], [1, 1, 1, 0]}, {2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 29, 70, 169, 408, 985, 2378] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 257, 1537, 9058, 53270, 312837, 1836424, 10778419] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5369, 76377, 1055989, 14562243] For the equivalence class of patterns, { {[3, 2, 1], [1, 2, 3, 4], [3, 1, 4, 2]}, {[1, 2, 3], [2, 4, 1, 3], [4, 3, 2, 1]}} the member , {[3, 2, 1], [1, 2, 3, 4], [3, 1, 4, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 5], [4, 0]}, {}], [[1, 1], { [0, 3, 2], [0, 2, 3], [0, 1, 4], [0, 0, 5], [4, 0, 0], [0, 5, 0], [0, 4, 1] }, {1, 2}], [[2, 1], {[0, 2, 3], [1, 1, 0], [0, 4, 0], [0, 3, 1]}, {}], [ [1, 2], {[0, 3, 2], [0, 4, 0], [0, 1, 3], [3, 2, 0], [2, 3, 0], [4, 1, 0]}, {}], [[1, 2, 2], {[0, 4, 0, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [0, 1, 0, 3], [2, 3, 0, 0], [4, 1, 0, 0], [0, 3, 1, 1], [0, 3, 0, 2], [0, 3, 2, 0], [3, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 3, 1, 0], [0, 1, 3, 0], [0, 0, 4, 0], [0, 1, 2, 1], [0, 0, 3, 1], [0, 1, 1, 2], [0, 0, 1, 3]}, {}], [[1, 3, 2], {[0, 1, 1, 3], [0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[2, 3, 1], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 4, 1, 0], [0, 3, 1, 1], [0, 2, 2, 1], [0, 1, 3, 1], [0, 3, 2, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {}], [[1, 2, 3], {[0, 1, 3, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 3, 2, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 4, 0]}, {1}], [[2, 1, 1], {[1, 0, 1, 0], [0, 1, 1, 3], [0, 0, 2, 3], [0, 3, 1, 0], [0, 0, 4, 0], [0, 0, 3, 1], [0, 2, 2, 1], [0, 2, 1, 2], [0, 1, 2, 2], [0, 2, 3, 0]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 4, 0, 0], [0, 3, 1, 0], [0, 1, 3, 0], [0, 3, 0, 1], [0, 1, 2, 1], [0, 1, 1, 2], [0, 1, 0, 3]}, {}], [[3, 1, 2], {[0, 1, 1, 3], [0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[3, 1, 3, 2], {[0, 1, 2, 0, 1], [0, 1, 1, 1, 2], [0, 1, 1, 0, 3], [0, 1, 3, 0, 0], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 2, 1], [1, 1, 1, 0, 0], [0, 1, 1, 3, 0]}, {3}], [[2, 1, 2, 2], {[0, 3, 0, 0, 1], [0, 1, 2, 0, 1], [0, 1, 0, 2, 1], [0, 1, 1, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 0, 3], [0, 4, 0, 0, 0], [0, 3, 1, 0, 0], [0, 1, 3, 0, 0], [0, 3, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [1, 1, 0, 0, 0], [0, 1, 1, 1, 1]}, {3, 4}], [[2, 1, 2, 1], { [0, 1, 2, 0, 1], [0, 0, 3, 0, 1], [0, 0, 1, 2, 1], [0, 1, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 0, 3], [0, 3, 1, 0, 0], [0, 1, 3, 0, 0], [0, 0, 4, 0, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 1, 1, 2, 0], [0, 0, 1, 3, 0], [1, 0, 1, 0, 0], [0, 1, 1, 1, 1]}, {1, 4}], [[2, 1, 2, 3], {[0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1}], [[3, 2, 3, 1], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], { [0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[1, 2, 3, 3], {[0, 4, 1, 0, 0], [0, 1, 3, 0, 0], [0, 3, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 3, 4, 1], {[1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {}], [ [1, 3, 4, 2], {[0, 1, 3, 1, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {}], [[1, 2, 4, 3], %7, {}], [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 4, 1, 0], [0, 0, 3, 2, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], { [0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %9, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], %7, {}], [[1, 3, 2, 4], %8, {}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], %9, {1}], [ [2, 3, 1, 1], {[0, 0, 4, 1, 0], [0, 1, 1, 1, 2], [0, 0, 1, 1, 3], [0, 0, 3, 2, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 0, 1, 1, 0], [0, 0, 3, 1, 1], [0, 1, 1, 2, 1], [0, 0, 2, 2, 1], [0, 0, 1, 3, 1], [0, 1, 1, 3, 0], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0]}, {3, 4}], [[2, 4, 1, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 3, 0]}, {1}], [[2, 3, 1, 3], {[0, 1, 3, 1, 0], [0, 1, 1, 1, 2], [0, 1, 1, 0, 3], [0, 1, 4, 0, 0], [0, 2, 1, 0, 0], [0, 1, 3, 0, 1], [0, 1, 1, 2, 1], [1, 1, 1, 0, 0], [0, 1, 1, 3, 0]}, {1, 4}], [[2, 3, 1, 4], %8, {}], [[3, 4, 1, 2], {[0, 1, 3, 1, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 3, 0]}, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[3, 1, 2, 2], %9, {3, 4}], [[3, 1, 2, 4], %8, {}], [[4, 1, 2, 3], %7, {}], [[1, 3, 1, 2], {[0, 0, 1, 1, 3], [0, 0, 1, 2, 1], [0, 0, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 0, 1, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 1]}, {1}], [[1, 2, 1, 1], {[0, 1, 0, 2, 1], [0, 0, 1, 2, 1], [0, 1, 0, 1, 2], [0, 0, 1, 1, 2], [0, 0, 0, 1, 3], [0, 3, 0, 1, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [0, 0, 1, 3, 0], [0, 0, 0, 4, 0], [0, 0, 0, 3, 1], [1, 0, 0, 1, 0], [0, 1, 1, 1, 1]}, {3, 4}], [[2, 3, 2, 1], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 1, 2], { [0, 1, 2, 0, 1], [0, 0, 3, 0, 1], [0, 0, 1, 2, 1], [0, 1, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 0, 3], [0, 3, 1, 0, 0], [0, 1, 3, 0, 0], [0, 0, 4, 0, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 1, 1, 2, 0], [0, 0, 1, 3, 0], [1, 0, 1, 0, 0], [0, 1, 1, 1, 1]}, {1, 4}], [[1, 2, 1, 3], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {3}], [[1, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %4, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %4, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], %3, {4, 5}], [[1, 4, 2, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], %6, {4, 5}], [[1, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %5, {2, 3}], [[1, 3, 2, 4, 3], %3, {2}], [[2, 4, 3, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 3, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {2, 3, 5}], [[1, 3, 4, 2, 4], %6, {2, 3, 5}], [[1, 3, 4, 2, 5], %4, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 2], { [0, 1, 0, 3, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {4, 5}], [[1, 3, 5, 2, 4], %5, {2, 4}], [[1, 3, 4, 2, 3], %3, {2}], [[2, 4, 5, 3, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 5, 3, 2], %4, {1, 2, 3, 4, 5}], [[1, 4, 5, 2, 3], %5, {2, 3}], [[1, 4, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 5], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], %3, {4, 5}], [[1, 4, 2, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %4, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %4, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %4, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 3, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2, 3}], [[2, 3, 1, 5, 4], %5, {3}], [[2, 3, 1, 4, 5], %4, {1, 2, 3, 4, 5}], [ [2, 3, 1, 4, 1], {[1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 3, 0], [0, 0, 1, 2, 1, 0]}, {5}], [[2, 3, 1, 4, 4], %6, {4, 5}], [[3, 4, 5, 2, 1], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %4, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], {[0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1}], [[2, 3, 5, 1, 4], %5, {4}], [[2, 4, 5, 1, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1}], [[2, 3, 4, 1, 4], %6, {3}], [[2, 3, 4, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 3, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2, 4}], [[2, 3, 4, 1, 1], { [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 3, 0]}, {4, 5}], [[2, 3, 4, 1, 2], {[0, 1, 0, 3, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {1}], [[4, 1, 2, 5, 3], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], %6, {4, 5}], [[4, 2, 3, 5, 1], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %3, {1}], [[4, 1, 3, 5, 2], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], %5, {1}], [[3, 1, 2, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [0, 1, 0, 3, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 0, 1, 2, 1], [0, 1, 0, 2, 1, 1], [0, 2, 0, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 1], %2, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %4, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %5, {1}], [ [3, 4, 1, 2, 5], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1}], [[3, 4, 1, 2, 4], %6, {2}], [[3, 4, 1, 2, 3], %3, {1}], [[4, 5, 1, 2, 3], %5, {1, 2}], [[4, 1, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 5], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], %3, {4, 5}], [[1, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], { [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 2, 0], [0, 0, 1, 1, 3, 0]}, {1}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 2, 1, 0, 0], [0, 1, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0], [0, 0, 1, 3, 0, 0]}, {3, 4, 5}], [[2, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], { [0, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 4, 1, 0], [0, 0, 0, 3, 2, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 1, 3, 0]}, {4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 0, 3, 0]}, {1, 2, 4}], [[1, 2, 4, 1, 3], { [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %6 := {[0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 3, 0, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %8 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]} %9 := {[0, 1, 0, 1, 3], [0, 1, 0, 2, 1], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 17, 10, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 128, 110, 23, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 1004, 636, 58, 0] For the equivalence class of patterns, { {[3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, {[1, 2, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 2, 3], [3, 4, 2, 1], [4, 3, 2, 1]}} the member , {[3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 5], [4, 0]}, {}], [[1, 1], { [0, 3, 2], [0, 2, 3], [0, 1, 4], [0, 0, 5], [4, 0, 0], [0, 5, 0], [0, 4, 1] }, {1, 2}], [[1, 2], {[0, 4, 0], [3, 2, 0], [2, 3, 0], [4, 1, 0], [0, 1, 2]}, {}], [[2, 1], {[1, 1, 0], [0, 4, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 0, 4, 0], [0, 4, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 3], {[0, 4, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [ [2, 3, 1], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 4, 1, 0], [0, 3, 2, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {1}], [[1, 2, 2], {[0, 4, 0, 0], [2, 3, 0, 0], [4, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2], [3, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[2, 1, 1], {[1, 0, 1, 0], [0, 1, 1, 3], [0, 0, 4, 0], [0, 4, 1, 0], [0, 3, 1, 1], [0, 2, 2, 1], [0, 1, 3, 1], [0, 2, 1, 2], [0, 1, 2, 2], [0, 3, 2, 0], [0, 2, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 4, 1, 0], [0, 3, 2, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {1}] , [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 4, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[3, 1, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], { [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {1, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], {[0, 1, 0, 2, 1], [0, 1, 0, 1, 2], [0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], %3, {}], [[1, 4, 2, 3], %3, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 1, 2, 3], {[0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {2, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 1, 0, 2, 1], [0, 1, 0, 1, 2], [0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[3, 1, 2, 4], %3, {}], [[4, 1, 2, 3], %3, {}], [[1, 4, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [ [1, 3, 2, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {2, 5}], [[1, 3, 2, 4, 4], {[0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[1, 3, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[1, 4, 2, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], { [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [ [3, 1, 2, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1, 5}], [[4, 1, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 5], %1, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 17, 9, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 159, 183, 45, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 1945, 1966, 252, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 4, 3], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]}} the member , {[1, 2, 3], [2, 1, 4, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 4], [2, 3], [5, 0]}, {}], [[1, 1], {[2, 1, 2], [2, 0, 3], [0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [2, 3, 0], [5, 0, 0], [2, 2, 1]}, {1, 2}], [[1, 2], {[0, 1, 1], [0, 4, 0], [2, 3, 0]}, {}], [[2, 1], {[3, 1, 0], [0, 4, 0], [2, 3, 0], [0, 1, 2]}, {}], [ [1, 2, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 3, 0, 0]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[3, 0, 1, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1], [2, 0, 3, 0]}, {1} ], [[1, 3, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[2, 3, 1], {[0, 1, 3, 0], [3, 1, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 3, 2, 0]}, {}] , [[2, 1, 1], {[3, 0, 1, 0], [0, 3, 1, 0], [0, 0, 4, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2], [2, 0, 3, 0]}, {2, 3}], [ [2, 1, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 3, 0, 0], [3, 1, 0, 0]}, {3} ], [[3, 2, 1], {[0, 3, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [1, 1, 1, 0]}, {}] , [[2, 1, 3], {[3, 1, 1, 0], [0, 4, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[1, 3, 2, 2], %8, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 4, 3, 2], %7, {}], [[2, 4, 3, 1], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 3, 2], %8, {1}], [[3, 1, 4, 2], %9, {1, 3}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [3, 1, 1, 0, 0], [0, 4, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [0, 0, 4, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {1, 2, 4}], [ [3, 2, 4, 1], {[0, 3, 1, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 3, 1, 3], {[3, 1, 1, 0, 0], [0, 4, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], %8, {1}], [[2, 4, 1, 3], %9, {1}], [[3, 4, 1, 2], %9, {1, 2}], [[3, 4, 2, 1], {[0, 3, 1, 1, 0], [0, 1, 3, 1, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {1}], [[2, 3, 1, 1], {[0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [0, 0, 4, 1, 0], [0, 0, 3, 2, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0]}, {3, 4} ], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %8, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[4, 2, 3, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[4, 1, 3, 2], %7, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 1, 2, 0, 0], [0, 3, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[4, 2, 1, 3], {[0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {2}], [[3, 2, 1, 1], { [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [0, 0, 3, 1, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 2], { [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[4, 3, 1, 2], %7, {}], [[3, 2, 1, 4], { [0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %2, {4, 5}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 5, 4, 1, 3], %5, {1, 4}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %5, {1}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %6, {1, 3, 5}], [ [3, 2, 1, 4, 1], {[0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {5}], [[3, 2, 1, 4, 4], {[0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[4, 3, 1, 5, 2], %5, {4}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 4}], [[3, 2, 1, 4, 3], %3, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 5, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %5, {3}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {3}], [ [4, 2, 5, 1, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2, 3}], [ [3, 2, 4, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[3, 2, 4, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 4, 1, 3], %6, {1, 2}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], %5, {2, 3}], [[4, 2, 3, 1, 2], %2, {2}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], %6, {2, 3, 5}], [[5, 2, 4, 1, 3], %5, {2, 4}], [ [4, 2, 3, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %3 := {[0, 1, 1, 0, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %6 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %8 := {[3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]} %9 := {[0, 3, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 17, 9, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 161, 176, 49, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 1884, 1856, 441, 0] For the equivalence class of patterns, { {[1, 2, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [3, 1, 2, 4]}, {[1, 2, 3], [2, 4, 3, 1], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [1, 3, 4, 2]}} the member , {[1, 2, 3], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 4], [5, 0]}, {}], [[1, 1], {[0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [5, 0, 0]}, {1, 2}] , [[1, 2], {[0, 1, 1], [0, 4, 0], [2, 3, 0]}, {}], [[2, 1], { [0, 3, 2], [1, 2, 2], [0, 2, 3], [0, 1, 4], [3, 1, 0], [0, 4, 0], [1, 3, 0] }, {}], [ [1, 2, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 3, 0, 0]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[3, 0, 1, 0], [1, 0, 3, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1} ], [[2, 3, 1], {[1, 3, 1, 0], [3, 1, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 3, 2, 0], [1, 2, 2, 0], [1, 1, 3, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {1}] , [[1, 3, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[2, 1, 1], {[0, 0, 2, 3], [0, 0, 1, 4], [1, 2, 1, 0], [3, 0, 1, 0], [0, 3, 1, 0], [0, 2, 2, 0], [1, 0, 3, 0], [0, 1, 3, 0], [0, 0, 4, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2], [2, 1, 1, 1], [1, 0, 2, 2], [0, 0, 3, 2], [2, 1, 2, 0]}, {2, 3}], [[2, 1, 2], {[0, 4, 0, 0], [1, 3, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [3, 1, 0, 0]}, {3} ], [[3, 1, 2], {[1, 2, 1, 0], [0, 3, 1, 0], [3, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[3, 2, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[1, 3, 1, 0], [3, 1, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 3, 2, 0], [1, 2, 2, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {}], [[1, 3, 2, 2], { [3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 4, 3, 2], %6, {}], [[2, 4, 3, 1], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 3, 3], {[1, 3, 1, 0, 0], [3, 1, 1, 0, 0], [0, 4, 1, 0, 0], [0, 3, 2, 0, 0], [1, 2, 2, 0, 0], [0, 2, 3, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4} ], [[2, 1, 3, 1], {[0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [1, 0, 3, 1, 0], [0, 0, 4, 1, 0], [1, 0, 2, 2, 0], [0, 0, 3, 2, 0], [0, 1, 1, 1, 0], [1, 0, 1, 3, 0], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0]}, {1, 2}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], { [1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [[3, 1, 4, 2], {[1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {3}], [[2, 1, 3, 2], {[3, 1, 0, 1, 0], [1, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {1}], [[3, 2, 4, 1], {[0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1]}, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [3, 1, 0, 1, 0], [1, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[4, 2, 3, 1], {[0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[4, 1, 3, 2], %6, {}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 1, 2, 0, 0], [0, 3, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[3, 2, 1, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 1]}, {3, 4} ], [[3, 2, 1, 2], {[0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[4, 3, 1, 2], %6, {}], [ [3, 2, 1, 4], {[0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1]}, {}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %2, {4, 5}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 5, 4, 1, 3], %5, {1, 4}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %5, {1}], [[2, 4, 3, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 2, 2, 0, 1, 0], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0]}, {1, 3, 5}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0]}, {1, 2}], [[4, 3, 1, 5, 2], %5, {4}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], { [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0]}, {3, 5}], [[3, 2, 1, 4, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 4}], [ [3, 2, 1, 5, 4], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[3, 2, 4, 1, 1], { [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 3, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %5, {3}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 5, 1, 4], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2}], [[4, 2, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [ [3, 2, 4, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 4, 1, 4], {[0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {3, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0]}, {1, 2}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[5, 3, 4, 1, 2], %5, {2, 3}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %2, {2}], [[4, 2, 3, 1, 3], %3, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %3 := {[0, 1, 1, 0, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %6 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 18, 9, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 144, 154, 41, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 1346, 1175, 207, 0] For the equivalence class of patterns, { {[2, 1, 3], [1, 2, 3, 4], [2, 3, 4, 1]}, {[3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [4, 1, 2, 3]}, {[2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}} the member , {[2, 1, 3], [1, 2, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1]}, {1}], [[1, 2], {[1, 1, 1]}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[1, 2, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 1, 1]}, {3}], [[1, 3, 2], {[1, 1, 2, 0], [0, 1, 1, 1]}, {2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 64, 144, 320, 704, 1536] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 257, 1434, 7613, 38974, 194040, 944960, 4519936] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5369, 70424, 854903, 9842469] For the equivalence class of patterns, { {[1, 2, 3], [3, 1, 4, 2], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [2, 4, 1, 3]}} the member , {[1, 2, 3], [3, 1, 4, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 4], [5, 0]}, {}], [[1, 1], {[0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [5, 0, 0]}, {1, 2}] , [[1, 2], {[0, 1, 1], [0, 4, 0]}, {}], [[2, 1], {[0, 1, 4], [3, 1, 0], [0, 4, 0], [2, 3, 0], [0, 2, 1]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [ [1, 2, 1], {[3, 0, 1, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1], [2, 0, 3, 0]}, {1} ], [[2, 3, 1], {[0, 2, 2, 0], [3, 1, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}] , [[1, 3, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[2, 1, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 3, 0, 0], [3, 1, 0, 0]}, {3} ], [[2, 1, 1], {[0, 0, 1, 4], [3, 0, 1, 0], [0, 1, 3, 0], [0, 0, 4, 0], [0, 1, 1, 2], [2, 1, 1, 1], [0, 0, 2, 1], [0, 2, 1, 0], [2, 1, 2, 0], [2, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[3, 1, 1, 0], [0, 1, 1, 1], [0, 2, 1, 0], [0, 1, 4, 0]}, {}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 2, 1, 1], [0, 1, 2, 1], [1, 1, 1, 0], [0, 1, 4, 0]}, {}], [[3, 1, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[1, 3, 2, 2], %7, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 4, 3, 2], %6, {}], [[2, 4, 3, 1], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [3, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {1}], [[2, 1, 3, 1], {[0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 4, 0]}, {2, 4}], [[2, 1, 3, 3], {[3, 1, 1, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 3, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 2, 4, 1], {[0, 3, 1, 1, 0], [0, 2, 1, 2, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1]}, {}], [[2, 3, 1, 1], {[0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [0, 0, 4, 1, 0], [0, 0, 2, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 4, 0]}, {3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], %7, {1}], [[3, 4, 1, 2], {[0, 3, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1, 2}], [[2, 3, 1, 3], {[3, 1, 1, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1]}, {2, 4}], [[3, 4, 2, 1], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1]}, {}], [[2, 4, 1, 3], {[0, 1, 3, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %7, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[4, 2, 3, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[4, 1, 3, 2], %6, {}], [[4, 2, 1, 3], { [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {2}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 2, 1, 3], {[0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {1, 2, 4}], [[3, 2, 1, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1]}, {2}], [[3, 2, 1, 1], {[0, 0, 1, 2, 1], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0], [0, 0, 2, 1, 1], [0, 0, 1, 4, 0]}, {3, 4} ], [[3, 2, 1, 2], {[0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[4, 3, 1, 2], %6, {}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %2, {4, 5}], [[2, 1, 4, 3, 4], %3, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {2}], [[2, 1, 4, 3, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %5, {1, 2}], [ [2, 1, 4, 3, 1], {[0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {1, 2, 5}], [[2, 1, 4, 3, 2], %2, {1}], [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 4], %3, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 1], { [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {1, 3, 5}], [[2, 4, 1, 3, 2], %2, {1}], [[2, 4, 1, 3, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 1, 4, 3], %5, {1, 3}], [[3, 5, 1, 4, 2], %1, {1, 2, 3, 4, 5}], [ [2, 4, 1, 3, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[2, 5, 1, 3, 4], %1, {1, 2, 3, 4, 5}], [[3, 5, 2, 4, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {3}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 5, 4, 1, 3], %5, {1, 4}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [ [2, 4, 3, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %5, {1}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %4, {1, 3, 5}], [ [3, 2, 4, 1, 1], {[0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 2, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 3, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [ [3, 2, 4, 1, 4], {[0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {2, 3}], [[4, 3, 5, 1, 2], %5, {3}], [[3, 2, 4, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 5, 1, 4], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {2}], [[4, 2, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [[4, 5, 3, 1, 2], %5, {1, 2}], [[3, 5, 2, 1, 4], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {3}], [[4, 5, 2, 1, 3], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {2, 3}], [[4, 5, 3, 2, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], %4, {1, 3}], [ [3, 4, 2, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [[3, 4, 2, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 2, 1, 2, 0], [0, 0, 1, 2, 2, 0]}, {4, 5}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], %5, {2, 3}], [[4, 2, 3, 1, 2], %2, {2}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %5, {2, 4}], [[4, 2, 3, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[4, 2, 3, 1, 3], %4, {2, 3, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %3 := {[0, 1, 1, 1, 0, 0]} %4 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %5 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %6 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %7 := {[3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 17, 10, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 171, 204, 66, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2305, 2880, 703, 0] For the equivalence class of patterns, { {[1, 2, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [1, 3, 2, 4]}} the member , {[1, 2, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 4], [5, 0]}, {}], [[1, 1], {[0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [0, 0, 4], [5, 0, 0]}, {1, 2}] , [[1, 2], {[0, 1, 1], [0, 4, 0]}, {}], [[2, 1], {[0, 3, 2], [0, 2, 3], [0, 1, 4], [3, 1, 0], [2, 2, 0], [0, 4, 0]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [ [1, 2, 1], {[3, 0, 1, 0], [2, 0, 2, 0], [0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1} ], [[2, 3, 1], {[3, 1, 1, 0], [2, 2, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [2, 1, 2, 0], [0, 3, 2, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {1}], [[1, 3, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[2, 1, 2], {[0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [3, 1, 0, 0], [2, 2, 0, 0]}, {3} ], [[2, 1, 1], {[0, 0, 2, 3], [0, 0, 1, 4], [3, 0, 1, 0], [0, 3, 1, 0], [2, 0, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 0, 4, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2], [2, 2, 1, 0], [2, 1, 1, 1], [0, 0, 3, 2]}, {2, 3}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [1, 1, 1, 0], [0, 1, 4, 0]}, {}], [[2, 1, 3], {[3, 1, 1, 0], [2, 2, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 3, 2, 0], [0, 2, 3, 0], [0, 1, 4, 0]}, {}], [[3, 1, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2, 2], {[3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 4, 3, 2], %7, {}], [[2, 4, 3, 1], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 3, 2], {[3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {1}], [[3, 1, 4, 2], {[0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1, 3}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [[2, 1, 3, 3], {[3, 1, 1, 0, 0], [2, 2, 1, 0, 0], [0, 4, 1, 0, 0], [0, 3, 2, 0, 0], [0, 2, 3, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 3, 1], { [0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [2, 0, 2, 1, 0], [0, 0, 4, 1, 0], [2, 0, 1, 2, 0], [0, 0, 3, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0]}, {1, 2}], [[3, 2, 4, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1]}, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[4, 1, 3, 2], %7, {}], [[3, 2, 1, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 1, 1, 2, 0], [0, 0, 2, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 1], [0, 0, 1, 4, 0]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 3, 1, 0, 0], [0, 2, 2, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[3, 2, 1, 2], {[0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[4, 3, 1, 2], %7, {}], [[4, 2, 1, 3], {[0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 2, 1, 4], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1]}, {}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %2, {4, 5}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 5, 4, 1, 3], %5, {1, 4}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %5, {1}], [[2, 4, 3, 1, 3], %6, {1, 3, 5}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2}], [ [3, 2, 1, 4, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {3, 5}], [[3, 2, 1, 4, 3], %6, {1, 2}], [[4, 3, 1, 5, 2], %5, {4}], [ [3, 2, 1, 4, 4], {[0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 2, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 4}], [ [4, 2, 1, 5, 3], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [[4, 3, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %5, {3}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 2, 5, 1, 3], { [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {3}], [[3, 2, 4, 1, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 2, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {3, 5}], [[3, 2, 4, 1, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [ [3, 2, 5, 1, 4], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2}], [ [3, 2, 4, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[3, 2, 4, 1, 3], %6, {1, 2}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[4, 1, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 1], %3, {1, 2, 3, 4, 5}], [[5, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[4, 2, 1, 3, 2], %2, {2}], [[4, 2, 1, 3, 5], %1, {1, 2, 3, 4, 5}], [[5, 2, 1, 3, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], %5, {2, 3}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %6 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 2, 2, 0, 1, 0], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 19, 14, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 156, 203, 78, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 1598, 1754, 464, 0] For the equivalence class of patterns, { {[3, 2, 1], [2, 1, 3, 4], [2, 3, 4, 1]}, {[3, 2, 1], [1, 2, 4, 3], [4, 1, 2, 3]}, {[1, 2, 3], [1, 4, 3, 2], [4, 3, 1, 2]}, {[1, 2, 3], [3, 2, 1, 4], [3, 4, 2, 1]}} the member , {[3, 2, 1], [2, 1, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 4]}, {}], [[1, 1], {[1, 2, 2], [1, 1, 3], [1, 0, 4], [1, 4, 0], [1, 3, 1]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 3]}, {}], [[1, 2], {[1, 2, 2], [1, 1, 3], [1, 3, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [0, 0, 1, 3]}, {1} ], [[1, 2, 2], {[1, 1, 0, 3], [1, 3, 0, 0], [1, 2, 1, 1], [1, 1, 2, 1], [1, 2, 0, 2], [1, 1, 1, 2], [1, 2, 2, 0], [1, 1, 3, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0]}, {1}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 3, 0]}, {1}], [[2, 3, 1], {[0, 1, 1, 3], [0, 1, 3, 0], [1, 1, 1, 0], [0, 1, 2, 2]}, {}], [[3, 1, 2], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0]}, {2}], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [0, 1, 0, 3]}, {3} ], [[2, 1, 1], {[1, 0, 1, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [0, 0, 1, 3]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3, 3], {[0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {2}], [[2, 1, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {2, 4}], [[2, 1, 4, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 3, 2], {[0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {3}], [ [2, 3, 1, 3], {[0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {2, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 2], [0, 0, 1, 1, 3], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 0, 1, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 1]}, {3, 4} ], [[2, 3, 1, 2], {[0, 1, 0, 2, 2], [0, 1, 0, 1, 3], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 1]}, {}], [[2, 4, 1, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 3, 1, 4], { [0, 1, 3, 1, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], { [0, 1, 0, 3, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {4}], [[3, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [ [2, 4, 1, 2, 3], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {4}], [[2, 3, 1, 2, 3], {[0, 2, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0], [1, 1, 0, 1, 0, 0], [0, 1, 0, 3, 0, 0]}, {5}], [[2, 3, 1, 2, 2], { [0, 1, 0, 0, 2, 2], [0, 2, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 0, 3, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 0, 1, 3], [0, 1, 2, 0, 1, 0], [0, 1, 0, 2, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %3, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %3, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], %2, {4, 5}], [[3, 1, 5, 4, 2], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 3], %2, {2}], [[3, 4, 1, 5, 2], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 5, 4], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2}], [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], {[0, 1, 1, 1, 1, 0], [0, 1, 3, 1, 0, 0], [0, 1, 2, 2, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[2, 3, 1, 4, 5], %3, {1, 2, 3, 4, 5}], [ [2, 3, 1, 4, 2], {[0, 1, 0, 3, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {2, 5}], [[2, 4, 1, 5, 3], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {2, 4}], [[2, 5, 1, 4, 3], %3, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 5], %3, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 1, 4, 2], %3, {1, 2, 3, 4, 5}], [[3, 5, 2, 4, 1], %3, {1, 2, 3, 4, 5}], [[2, 5, 1, 3, 4], %3, {1, 2, 3, 4, 5}], [[2, 4, 1, 3, 3], %2, {4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {4}], [ [2, 1, 3, 2, 2], {[0, 1, 0, 0, 1, 1], [0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 2, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 3, 0]}, {1, 2, 4, 5}], [[2, 1, 3, 2, 3], {[0, 2, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0], [1, 1, 0, 1, 0, 0], [0, 1, 0, 3, 0, 0]}, {5}], [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 23, 36, 51, 68, 87, 108] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 189, 529, 1167, 2255, 3977, 6549, 10219] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2777, 12199, 40673, 112526] For the equivalence class of patterns, { {[2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [2, 3, 1, 4]}, {[3, 1, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[2, 1, 3], [1, 2, 3, 4], [1, 4, 2, 3]}} the member , {[2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 0]}, {1}], [[2, 1], {}, {}], [[2, 1, 1], {}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {2}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[1, 1, 1, 0]}, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 2, 1, 0], [0, 2, 1, 1, 0], [1, 0, 1, 1, 0]}, {2, 4}] , [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[3, 1, 2, 4], %6, {2, 3}], [[4, 1, 2, 3], %6, {}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {2, 4}], [[3, 2, 1, 4], %6, {2, 3}], [[3, 2, 1, 1], {[1, 0, 1, 1, 0]}, {3, 4}], [[4, 2, 1, 3], %6, {}], [[4, 3, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {}], [[4, 1, 2, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %5, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %4, {2, 3, 4}], [[5, 1, 2, 4, 3], %5, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], %3, {4, 5}], [[4, 1, 2, 3, 4], %1, {2, 3, 5}], [[4, 1, 2, 3, 5], %4, {2, 3, 4}], [[5, 3, 2, 4, 1], %5, {1, 2, 3, 4, 5}], [[5, 2, 1, 3, 4], %4, {2, 3, 4}], [[5, 2, 1, 4, 3], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 5], %4, {2, 3, 4}], [[4, 2, 1, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], %3, {4, 5}], [[5, 3, 1, 4, 2], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 4], %1, {2, 3, 5}], [[5, 4, 1, 3, 2], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %4, {2, 3, 4}], [ [5, 4, 1, 2, 3], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 1, 2, 3], %3, {2}], [[5, 3, 1, 2, 4], %4, {2, 3, 4}], [[4, 3, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0]}, {4, 5}], [[4, 3, 1, 2, 4], %1, {3, 4}], [[3, 1, 2, 3, 3], {[0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 4], %3, {1, 2, 3, 4}], [[4, 1, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 2, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0]}, {5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %1, {4}], [[3, 2, 1, 3, 3], {[0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[3, 2, 1, 3, 4], %3, {1, 2, 3, 4}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 2], {[0, 2, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0]}, {5}], [[4, 2, 1, 4, 3], %1, {4}]] %1 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0]} %2 := {[0, 1, 1, 1, 0, 0]} %3 := {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %4 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %5 := {[0, 1, 1, 1, 1, 0]} %6 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 65, 151, 351, 816, 1897] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 201, 995, 5119, 25907, 130934, 663329, 3359344] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3254, 36251, 412198, 4451842] For the equivalence class of patterns, { {[2, 1, 3], [1, 2, 3, 4], [3, 4, 1, 2]}, {[2, 3, 1], [2, 1, 4, 3], [4, 3, 2, 1]}, {[3, 1, 2], [2, 1, 4, 3], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [3, 4, 1, 2]}} the member , {[2, 1, 3], [1, 2, 3, 4], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1]}, {1}], [[1, 2], {}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1]}, {3}], [[1, 3, 2], {[0, 1, 1, 1]}, {2}], [[1, 2, 2], {}, {2, 3}], [[1, 2, 3], {[0, 1, 1, 1]}, {}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {3}], [[1, 3, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [ [1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {1}], [[1, 2, 3, 3], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[2, 3, 4, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {4}], [[2, 3, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 3, 4, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[3, 4, 5, 2, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 5, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], {[0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 5, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 26, 51, 92, 155, 247, 376] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 203, 714, 2025, 4906, 10564, 20775, 38032] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3200, 17851, 73019, 239253] For the equivalence class of patterns, { {[1, 3, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, {[2, 1, 3], [2, 3, 4, 1], [2, 4, 3, 1]}, {[3, 1, 2], [1, 3, 4, 2], [1, 4, 3, 2]}, {[2, 3, 1], [3, 1, 2, 4], [3, 2, 1, 4]}} the member , {[1, 3, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[2, 1], {[0, 3, 0]}, {}], [[1, 2, 3], {[0, 1, 2, 0], [0, 2, 1, 0]}, {2}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {1, 3}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 2, 0]}, {1}], [[2, 1, 2], {[0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 2, 0], [0, 2, 1, 0]}, {3}], [[3, 2, 1], {[0, 3, 1, 0], [0, 1, 2, 0]}, {2}], [[2, 1, 1], {[0, 3, 1, 0], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 2, 0], [0, 2, 1, 0]}, {1}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 29, 70, 169, 408, 985, 2378] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 257, 1557, 9334, 55947, 335155, 2007564, 12024837] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5369, 78690, 1129957, 16270068] For the equivalence class of patterns, { {[2, 3, 1], [2, 1, 3, 4], [3, 2, 1, 4]}, {[2, 1, 3], [2, 3, 4, 1], [3, 4, 2, 1]}, {[3, 1, 2], [1, 2, 4, 3], [1, 4, 3, 2]}, {[1, 3, 2], [4, 1, 2, 3], [4, 3, 1, 2]}} the member , {[2, 3, 1], [2, 1, 3, 4], [3, 2, 1, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 0]}, {1}], [[2, 1], {[1, 1, 1]}, {}], [[3, 1, 2], {[0, 2, 1, 1], [1, 1, 1, 0]}, {2}], [[3, 2, 1], {[1, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[1, 1, 1, 0], [1, 0, 1, 1]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {3}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 220, 969, 4018, 16279, 65400, 261973, 1048366] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3780, 32163, 261112, 2095528] For the equivalence class of patterns, { {[3, 1, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 3, 2], [2, 1, 3, 4], [2, 3, 1, 4]}, {[2, 1, 3], [1, 2, 4, 3], [1, 4, 2, 3]}, {[2, 3, 1], [4, 1, 3, 2], [4, 3, 1, 2]}} the member , {[2, 1, 3], [1, 2, 4, 3], [1, 4, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1]}, {1}], [[1, 2], {}, {}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1]}, {3}], [[1, 2, 2], {}, {2, 3}], [[1, 2, 3], {[0, 1, 2, 0]}, {}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 4, 1], %6, {2, 3}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {2, 4}] , [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 3, 4, 2], %6, {}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {2, 4}] , [[2, 4, 3, 1], %6, {2, 3}], [[1, 3, 2, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[1, 4, 3, 2], %6, {}], [[1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {}], [[1, 4, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 2, 1], %3, {1, 2, 3, 4}], [[1, 3, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], {[0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 1, 1, 0]}, {1, 2, 4, 5}], [[1, 4, 3, 1, 2], %1, {4}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0]}, {5}], [[1, 2, 4, 5, 3], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], %3, {2}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %4, {2, 3, 4}], [[1, 3, 4, 5, 2], %4, {2, 3, 4}], [[1, 2, 3, 4, 4], {[0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[1, 2, 3, 4, 1], %1, {3, 4}], [[1, 2, 3, 4, 5], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {3, 4}], [[1, 3, 4, 2, 1], %1, {2, 3, 5}], [[1, 3, 4, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 2], %3, {4, 5}], [[1, 3, 4, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 5, 3, 1], %4, {2, 3, 4}], [[1, 4, 5, 3, 2], %4, {2, 3, 4}], [[1, 3, 4, 2, 5], %5, {1, 2, 3, 4, 5}], [[1, 3, 5, 2, 4], %5, {1, 2, 3, 4, 5}], [[1, 4, 5, 2, 3], %5, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %5, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %4, {2, 3, 4}], [[1, 4, 3, 2, 5], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %4, {2, 3, 4}], [[1, 4, 3, 2, 2], %3, {4, 5}], [[1, 4, 3, 2, 1], %1, {2, 3, 5}], [[1, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], %3, {1, 2, 3, 4}], [[1, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0]}, {5}], [[1, 3, 4, 1, 2], %1, {4}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 1, 1, 0]}, {1, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]} %4 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]} %5 := {[0, 1, 1, 1, 1, 0]} %6 := {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 65, 151, 351, 816, 1897] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 201, 995, 5119, 25907, 130934, 663329, 3359344] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3254, 36251, 412198, 4451842] For the equivalence class of patterns, { {[3, 1, 2], [1, 4, 3, 2], [2, 1, 4, 3]}, {[2, 1, 3], [2, 3, 4, 1], [3, 4, 1, 2]}, {[1, 3, 2], [3, 4, 1, 2], [4, 1, 2, 3]}, {[2, 3, 1], [2, 1, 4, 3], [3, 2, 1, 4]}} the member , {[2, 1, 3], [2, 3, 4, 1], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1]}, {1}], [[1, 2], {[1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 1], [1, 1, 1, 0]}, {1}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1]}, {3}], [[1, 2, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [[1, 3, 2], {[1, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {4}], [[2, 3, 1, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 5, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], {[0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 5, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 213, 921, 3787, 15291, 61353, 245653, 982911] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3557, 29696, 239750, 1921574] For the equivalence class of patterns, { {[3, 1, 2], [2, 1, 3, 4], [2, 1, 4, 3]}, {[1, 3, 2], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 3, 1], [1, 2, 4, 3], [2, 1, 4, 3]}, {[2, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}} the member , {[3, 1, 2], [2, 1, 3, 4], [2, 1, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 2]}, {}], [[1, 2], {}, {}], [ [1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 2, 1, 0]}, {1, 3} ], [[1, 2, 2], {}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 2], [0, 1, 2, 0]}, {1}], [[1, 2, 3], {}, {1}], [[2, 3, 1], {[0, 1, 1, 2], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 2, 1, 0]}, {2, 3} ], [ [2, 1, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3} ], [[2, 1, 3], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {1, 2}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 1, 2], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1]}, {1, 4}], [[2, 3, 1, 1], {[0, 0, 1, 1, 2], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 2], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {1, 3}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 1, 2], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 2], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[3, 2, 1, 3], {[0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 0, 1]}, {2, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 4, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], { [0, 1, 1, 1, 1, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[2, 3, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1, 4, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {1, 2, 3, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], { [0, 1, 1, 1, 1, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[3, 2, 1, 4, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {1, 2, 3, 5}], [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1, 5, 4], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 64, 144, 320, 704, 1536] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 210, 927, 3834, 15147, 57834, 215055, 782946] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3524, 27092, 184208, 1152896] For the equivalence class of patterns, { {[3, 1, 2], [2, 4, 3, 1], [4, 3, 2, 1]}, {[2, 3, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [3, 1, 2, 4]}, {[2, 1, 3], [1, 2, 3, 4], [1, 3, 4, 2]}} the member , {[2, 3, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 0]}, {1}], [[2, 1], {[1, 2, 0]}, {}], [[2, 1, 1], {[1, 2, 1, 0], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 2, 2, 0], [1, 1, 1, 0]}, {2}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {2}], [[3, 2, 1], {[1, 1, 1, 0], [0, 1, 2, 0]}, {3}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 65, 151, 351, 816, 1897] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 234, 1223, 6585, 35661, 192394, 1037143, 5593569] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 4194, 48123, 594047, 7210769] For the equivalence class of patterns, { {[2, 3, 1], [1, 4, 3, 2], [4, 3, 2, 1]}, {[2, 1, 3], [1, 2, 3, 4], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [2, 3, 4, 1]}} the member , {[2, 3, 1], [1, 4, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {}, {}], [[1, 2], {[1, 1, 0]}, {}], [[1, 2, 2], {[1, 1, 0, 0]}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0]}, {3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 1], {}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {1}], [[3, 2, 1], {[1, 1, 1, 0]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 1, 2], {[1, 1, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %7, {3, 4}], [[1, 2, 3, 4], %6, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {4}], [[1, 2, 4, 3], %6, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 2, 1, 0], [0, 2, 1, 1, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 3, 2, 3], %7, {2}], [[1, 3, 2, 4], %6, {1, 3}], [[1, 3, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], %6, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %7, {3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], %6, {1, 2}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {4}], [[2, 1, 4, 3], %6, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], %5, {2}], [[3, 1, 2, 4], %6, {2, 3}], [[3, 1, 2, 2], {[1, 1, 0, 1, 0]}, {3, 4}], [[4, 1, 3, 2], %5, {2}], [[3, 1, 2, 3], %7, {1}], [[3, 1, 2, 1], {[1, 0, 1, 1, 0]}, {2, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], %5, {3}], [[3, 2, 1, 2], {[1, 1, 0, 1, 0]}, {2, 4}], [[3, 2, 1, 3], %7, {1}], [[3, 2, 1, 4], %6, {2, 3}], [[3, 2, 1, 1], {[1, 0, 1, 1, 0]}, {3, 4}], [[4, 2, 1, 3], %5, {3}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %4, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], %1, {4, 5}], [[1, 2, 5, 4, 3], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %2, {1, 2, 4}], [[1, 2, 4, 3, 4], %3, {1, 2, 3, 5}], [[1, 2, 5, 3, 4], %2, {1, 2, 4}], [[1, 4, 2, 3, 3], %1, {4, 5}], [[1, 4, 2, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 4], %3, {1, 2, 3, 5}], [[1, 5, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 5], %2, {1, 3, 4}], [[2, 5, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %2, {3, 4}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %2, {1, 2, 4}], [[3, 1, 5, 4, 2], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %3, {1, 2, 3, 5}], [[2, 1, 5, 3, 4], %2, {1, 2, 4}], [[2, 1, 4, 3, 3], %1, {4, 5}]] %1 := {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %2 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %3 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0]} %6 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]} %7 := {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 64, 144, 320, 704, 1536] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 204, 972, 4512, 20544, 92160, 408576, 1794048] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3232, 31124, 287608, 2613500] For the equivalence class of patterns, { {[3, 2, 1], [1, 4, 2, 3], [2, 4, 1, 3]}, {[1, 2, 3], [3, 1, 4, 2], [3, 2, 4, 1]}, {[1, 2, 3], [3, 1, 4, 2], [4, 1, 3, 2]}, {[3, 2, 1], [2, 3, 1, 4], [2, 4, 1, 3]}} the member , {[3, 2, 1], [1, 4, 2, 3], [2, 4, 1, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 2, 0], [0, 3, 0]}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1, 2, 2], {[1, 2, 0, 0], [0, 3, 0, 0]}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 3, 1, 0], [0, 0, 3, 0]}, {1, 3}], [ [1, 2, 3], {[1, 2, 1, 0], [0, 3, 1, 0], [1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0]}, {}] , [[2, 3, 1], {[1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 3, 0, 0]}, {1, 3}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 0]}, {}], [[1, 2, 3, 3], {[1, 2, 1, 0, 0], [0, 3, 1, 0, 0], [1, 1, 2, 0, 0], [0, 2, 2, 0, 0], [0, 1, 3, 0, 0]}, {3, 4}], [[1, 2, 3, 2], %3, {2}], [[1, 2, 4, 3], %4, {1, 2}], [[1, 2, 3, 4], {[1, 2, 1, 1, 0], [0, 3, 1, 1, 0], [1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 2, 0], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {3}], [[1, 2, 3, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[2, 3, 4, 1], {[1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2}], [[1, 3, 4, 2], %4, {2}], [[1, 3, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %3, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 3, 0]}, {}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], %4, {1}], [[2, 1, 3, 2], %3, {1}], [[2, 1, 3, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[2, 1, 4, 3], %4, {1, 2}], [[2, 1, 3, 4], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 3, 0]}, {3}], [[2, 1, 3, 3], {[0, 3, 1, 0, 0], [0, 2, 2, 0, 0], [0, 1, 3, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 3, 1, 0, 0], [1, 1, 1, 0, 0]}, {2}], [[2, 3, 1, 2], %3, {1}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 1, 2, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {3, 4}] , [[2, 3, 1, 4], {[0, 3, 1, 1, 0], [0, 2, 1, 2, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 3, 0]}, {2}], [[3, 4, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {2, 3}] , [[3, 1, 2, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {}], [[3, 1, 2, 4], {[0, 1, 3, 1, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {}], [[1, 4, 2, 5, 3], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], { [0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2, 4, 4], { [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[1, 3, 2, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {2, 3}], [[1, 3, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [[1, 3, 2, 5, 4], %1, {1, 2, 3}], [[3, 1, 2, 5, 4], %1, {1, 2, 3}], [[4, 2, 3, 5, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2, 3}], [[4, 1, 3, 5, 2], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], { [0, 1, 3, 1, 0, 0], [0, 1, 2, 2, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[4, 1, 2, 5, 3], %1, {1, 2, 3}], [[3, 1, 2, 4, 5], {[1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [ [3, 1, 2, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1, 3}], [ [4, 1, 2, 4, 3], {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [1, 1, 0, 1, 0, 0], [0, 1, 2, 1, 0, 0]}, {1, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 3, 0, 0, 0]}, {4, 5}], [ [3, 1, 2, 3, 4], {[0, 1, 1, 0, 3, 0], [0, 1, 3, 0, 1, 0], [0, 1, 2, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4}]] %1 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]} %4 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 208, 886, 3616, 14554, 58324, 233422, 933832] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3516, 29285, 236115, 1891766] For the equivalence class of patterns, { {[1, 2, 3], [1, 4, 3, 2], [2, 1, 4, 3]}, {[1, 2, 3], [2, 1, 4, 3], [3, 2, 1, 4]}, {[3, 2, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, {[3, 2, 1], [2, 3, 4, 1], [3, 4, 1, 2]}} the member , {[1, 2, 3], [1, 4, 3, 2], [2, 1, 4, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}], [[2, 1], {[0, 4, 0], [0, 3, 1], [0, 1, 2]}, {1}], [[1, 2], {[0, 1, 1], [0, 3, 0]}, {2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 29, 70, 169, 408, 985, 2378] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 257, 1557, 9424, 57064, 345454, 2091417, 12661567] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5369, 78690, 1162205, 17120833] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 4, 3], [3, 2, 4, 1]}, {[1, 2, 3], [2, 1, 4, 3], [4, 1, 3, 2]}, {[3, 2, 1], [2, 3, 1, 4], [3, 4, 1, 2]}, {[3, 2, 1], [1, 4, 2, 3], [3, 4, 1, 2]}} the member , {[1, 2, 3], [2, 1, 4, 3], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 3, 0], [0, 1, 2]}, {}], [[1, 2], {[0, 1, 1]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3}], [[2, 3, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {2, 3}], [[2, 1, 2], {[0, 3, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[2, 1, 3], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2]}, {}] , [[3, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {2, 3}] , [[1, 3, 2, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {}], [[2, 4, 3, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 4, 1, 3], %4, {1}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 3, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 4}], [[3, 4, 2, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {1}], [[2, 3, 1, 2], %5, {1}], [[3, 4, 1, 2], %4, {1, 2}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {4}], [[3, 1, 2, 2], %5, {3, 4}], [[4, 2, 3, 1], {[0, 3, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[4, 3, 2, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 1, 1, 1, 2], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 3, 0]}, {2}], [[4, 3, 1, 2], %4, {1, 2}], [ [3, 2, 1, 1], {[0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 2], %5, {2}], [[3, 2, 1, 3], {[0, 1, 2, 0, 0], [0, 3, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {2, 4}], [[4, 2, 1, 3], %4, {2}], [[3, 2, 1, 4], {[0, 3, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 1, 2], {[0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], {[0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 3, 1, 0]}, {4, 5}], [[2, 4, 3, 2, 1], { [0, 2, 0, 2, 1, 0], [0, 1, 0, 3, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4}], [ [1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0], [0, 0, 1, 0, 2, 0]}, {1, 3, 4, 5}], [[2, 5, 4, 1, 3], %1, {1, 2, 3}], [[2, 4, 3, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %3, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]}, {4}], [[2, 4, 3, 1, 2], %2, {1, 2, 3}], [[2, 4, 3, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 3}], [[3, 5, 4, 1, 2], %1, {1, 2, 3}], [ [4, 3, 2, 5, 1], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]}, {1}], [[3, 2, 1, 4, 5], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], %2, {1, 2, 4}], [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], {[0, 0, 3, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {1, 5}], [[4, 2, 1, 5, 3], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 5, 2], %1, {1, 2, 4}], [[3, 2, 1, 5, 4], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %3, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %2, {1, 2, 3}], [ [5, 3, 4, 2, 1], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]}, {4}], [ [4, 2, 3, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {2, 3}], [ [4, 2, 3, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[5, 3, 4, 1, 2], %1, {1, 2, 3}]] %1 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %5 := {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 26, 54, 110, 222, 446, 894] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 209, 885, 3599, 14467, 57951, 231899, 927703] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3530, 29408, 237017, 1898951] For the equivalence class of patterns, { {[2, 1, 3], [1, 2, 3, 4], [4, 2, 3, 1]}, {[1, 3, 2], [1, 2, 3, 4], [4, 2, 3, 1]}, {[3, 1, 2], [1, 3, 2, 4], [4, 3, 2, 1]}, {[2, 3, 1], [1, 3, 2, 4], [4, 3, 2, 1]}} the member , {[2, 1, 3], [1, 2, 3, 4], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1], [1, 2, 0]}, {}], [[1, 2], {}, {}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {1, 3}], [[1, 2, 2], {}, {2, 3}], [[1, 2, 3], {[0, 1, 1, 1]}, {}], [[1, 3, 2], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 2, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 3, 4, 1], %13, {2, 3}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 1], %14, {1}], [[1, 2, 3, 2], {[1, 1, 0, 2, 0], [0, 2, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[1, 2, 4, 3], {[0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[1, 3, 4, 2], {[1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[1, 3, 2, 2], {[1, 1, 0, 2, 0], [0, 2, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 3, 1], %13, {2, 3}], [[1, 3, 2, 1], %14, {1}], [[1, 3, 2, 3], {[1, 1, 2, 0, 0], [0, 2, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {4}], [[1, 4, 3, 2], {[1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[1, 4, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 3, 1, 1], %14, {3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[3, 4, 2, 1], %13, {1, 2}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], %12, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {2}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 2, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {4}], [[3, 1, 2, 2], {[0, 2, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[4, 1, 3, 2], %12, {}], [[4, 1, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], %14, {3, 4}], [[4, 3, 2, 1], %13, {1, 2}], [[3, 2, 1, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], %12, {}], [[1, 2, 4, 3, 4], %7, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %4, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %10, {2, 3, 4}], [[1, 3, 5, 4, 2], %11, {3, 4}], [[1, 2, 4, 3, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0]}, {4, 5}], [[1, 2, 4, 3, 1], %9, {1, 3, 4}], [[1, 2, 5, 4, 3], %11, {3, 4}], [[1, 2, 4, 3, 2], %8, {2}], [[1, 3, 4, 2, 4], %7, {1, 2, 3, 4, 5}], [[2, 4, 5, 3, 1], %10, {2, 3, 4}], [[1, 3, 4, 2, 5], %4, {1, 2, 3, 4, 5}], [[1, 4, 5, 2, 3], %2, {2, 3}], [[1, 3, 4, 2, 1], %9, {1, 2, 3}], [[1, 3, 5, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 4, 5, 3, 2], %11, {2, 3}], [[1, 3, 4, 2, 2], %8, {4, 5}], [[1, 3, 4, 2, 3], %5, {2}], [[1, 4, 2, 3, 4], %7, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 5], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {5}], [[1, 4, 2, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %2, {4}], [[2, 5, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], %5, {4, 5}], [[1, 5, 4, 3, 2], %11, {2, 3}], [[2, 5, 4, 3, 1], %10, {2, 3, 4}], [[1, 4, 3, 2, 1], %9, {1, 2, 3}], [[1, 4, 3, 2, 5], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %8, {4, 5}], [[1, 4, 3, 2, 4], %7, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %2, {2, 3}], [[1, 4, 3, 2, 3], %5, {3}], [[3, 4, 1, 2, 2], %1, {4, 5}], [[3, 4, 1, 2, 3], %5, {1}], [[3, 4, 1, 2, 4], %7, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], %3, {1, 2, 3}], [[4, 5, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %4, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %2, {1, 2}], [[4, 5, 1, 3, 2], %6, {1, 2}], [[4, 1, 2, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 5], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {5}], [[4, 1, 2, 3, 4], %7, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], %5, {4, 5}], [[5, 1, 2, 4, 3], %2, {4}], [[5, 1, 4, 2, 3], %2, {1, 3}], [[4, 1, 3, 2, 2], %1, {4, 5}], [[4, 1, 3, 2, 4], %7, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %5, {3}], [[4, 1, 3, 2, 1], %3, {1, 2, 3}], [[4, 1, 3, 2, 5], %4, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %6, {1, 3}], [[4, 3, 1, 2, 4], %7, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %6, {1, 2}], [[4, 3, 1, 2, 5], %4, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %5, {2}], [[5, 4, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], %3, {1, 2, 3}], [[5, 4, 1, 2, 3], %2, {1, 2}], [[4, 3, 1, 2, 2], %1, {4, 5}]] %1 := {[0, 2, 0, 2, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]} %2 := {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %3 := {[1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %6 := {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]} %7 := {[0, 1, 1, 1, 0, 0]} %8 := {[1, 1, 0, 2, 1, 0], [0, 2, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]} %9 := {[1, 0, 2, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]} %10 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]} %11 := {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0]} %12 := {[0, 2, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %13 := {[1, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]} %14 := {[0, 0, 1, 1, 1], [1, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 25, 47, 82, 135, 212, 320] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 199, 731, 2198, 5728, 13341, 28333, 55724] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3218, 22867, 120372, 498926] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1, 4], [2, 3, 4, 1]}, {[2, 1, 3], [1, 4, 2, 3], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1], [1, 4, 3, 2], [4, 1, 3, 2]}} the member , {[1, 3, 2], [2, 3, 1, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {}, {}], [[1, 2], {[0, 2, 0], [1, 1, 1]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1]}, {1, 2}], [[1, 2, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [ [1, 2, 1], {[1, 1, 1, 0], [0, 0, 2, 0], [1, 0, 1, 1], [0, 2, 1, 0]}, {1, 3} ], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 1], {}, {2, 3}], [[3, 2, 1], {}, {1}], [[2, 1, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[1, 1, 2, 0], [1, 1, 1, 1], [0, 2, 1, 0]}, {1}], [[2, 1, 3], {[1, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {2, 4}], [[1, 2, 3, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0]}, {1, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[1, 1, 1, 0, 1], [0, 1, 2, 0, 0], [1, 1, 1, 1, 0], [0, 2, 1, 0, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [ [2, 1, 3, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[2, 1, 3, 4, 4], {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 28, 64, 144, 320, 704, 1536] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 192, 846, 3618, 15174, 62802, 257526, 1049058] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2994, 25370, 207222, 1676234] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 4, 1], [4, 1, 2, 3]}, {[2, 3, 1], [1, 4, 3, 2], [3, 2, 1, 4]}, {[3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, {[2, 1, 3], [2, 3, 4, 1], [4, 1, 2, 3]}} the member , {[2, 3, 1], [1, 4, 3, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 1]}, {}], [[1, 2], {[1, 1, 0]}, {}], [[1, 2, 2], {[1, 1, 0, 0]}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0]}, {3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[1, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[1, 1, 1, 0], [1, 0, 1, 1]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {1}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 1, 2], {[0, 2, 1, 1], [1, 1, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %6, {3, 4}], [[1, 2, 3, 4], %7, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {4}], [[1, 2, 4, 3], %7, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], %6, {2}], [[1, 3, 2, 4], %7, {1, 3}], [[1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 3, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], %7, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %6, {3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], %7, {1, 2}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {4}], [[2, 1, 4, 3], %7, {}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {1, 4}] , [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], %7, {2, 3}], [[3, 1, 2, 3], %6, {1}], [[3, 1, 2, 2], {[0, 2, 0, 1, 1], [0, 2, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}] , [[4, 1, 3, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 1]}, {1}], [[4, 1, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 1]}, {}], [[1, 2, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %3, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], %5, {4, 5}], [[1, 2, 5, 4, 3], %3, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %1, {1, 2, 4}], [[1, 2, 4, 3, 4], %2, {1, 2, 3, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 4}], [[1, 4, 2, 3, 3], %5, {4, 5}], [[1, 4, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 4], %2, {1, 2, 3, 5}], [[1, 5, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 5], %1, {1, 3, 4}], [[2, 5, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %1, {3, 4}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %1, {1, 2, 4}], [[3, 1, 5, 4, 2], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %2, {1, 2, 3, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 4}], [[2, 1, 4, 3, 3], %5, {4, 5}], [[4, 1, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %2, {1, 2, 3}], [ [5, 1, 2, 4, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1}], [[4, 1, 2, 3, 5], %1, {2, 3, 4}], [[4, 1, 2, 3, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 2, 0, 1, 1], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [ [4, 1, 2, 3, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {1, 5}], [[5, 1, 2, 3, 4], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {2, 3}]] %1 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %2 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 0, 1, 1, 1, 0]} %5 := {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %6 := {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 190, 771, 3082, 12307, 49182, 196651, 786490] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2749, 20044, 154806, 1226670] For the equivalence class of patterns, { {[3, 2, 1], [1, 4, 2, 3], [4, 1, 2, 3]}, {[1, 2, 3], [1, 4, 3, 2], [4, 1, 3, 2]}, {[1, 2, 3], [3, 2, 1, 4], [3, 2, 4, 1]}, {[3, 2, 1], [2, 3, 1, 4], [2, 3, 4, 1]}} the member , {[3, 2, 1], [1, 4, 2, 3], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 3, 0]}, {}], [[1, 2], {[3, 1, 0], [2, 2, 0], [0, 3, 0]}, {}], [[1, 2, 2], {[0, 3, 0, 0], [3, 1, 0, 0], [2, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 3, 1, 0], [0, 0, 3, 0]}, {1, 3}], [ [1, 2, 3], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [3, 1, 1, 0], [2, 2, 1, 0], [2, 1, 2, 0]}, {2}], [[2, 3, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 0]}, {1}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 3, 0, 0]}, {1, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 3, 1, 0], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 0]}, {1}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[1, 3, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 3, 0]}, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {4}], [ [3, 1, 2, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[3, 1, 2, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 3, 0]}, {}], [[1, 4, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], { [0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2, 3}], [[1, 3, 2, 4, 4], { [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[1, 3, 2, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {2, 3}], [[1, 3, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [ [1, 3, 2, 5, 4], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3}], [[4, 1, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2, 4, 4], { [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[4, 2, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [ [3, 1, 2, 4, 5], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [[3, 1, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2, 3}], [[4, 1, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1, 3}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 234, 1065, 4480, 18255, 73494, 294613, 1179276] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 4194, 36999, 303604, 2443000] For the equivalence class of patterns, { {[2, 3, 1], [1, 2, 4, 3], [3, 2, 1, 4]}, {[3, 1, 2], [1, 4, 3, 2], [2, 1, 3, 4]}, {[1, 3, 2], [3, 4, 2, 1], [4, 1, 2, 3]}, {[2, 1, 3], [2, 3, 4, 1], [4, 3, 1, 2]}} the member , {[2, 3, 1], [1, 2, 4, 3], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 1]}, {}], [[1, 2], {[1, 1, 0]}, {}], [[1, 2, 2], {[1, 1, 0, 0]}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0]}, {3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 1, 1], [1, 1, 1, 0]}, {}], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[1, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[1, 1, 1, 0], [1, 0, 1, 1]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {1}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 1, 2], {[0, 2, 1, 1], [1, 1, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %8, {3, 4}], [[1, 2, 3, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], %7, {}], [[1, 3, 2, 1], {[0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {2, 4}] , [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 2, 1, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1]}, {2}], [[1, 3, 2, 3], %8, {2}], [[1, 3, 2, 2], {[0, 2, 0, 1, 1], [0, 2, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}] , [[1, 4, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {}], [[1, 3, 2, 4], %7, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], %7, {1, 2}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {}], [[2, 1, 4, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 1]}, {}], [[4, 1, 3, 2], {[0, 2, 1, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1]}, {1}], [[3, 1, 2, 3], %8, {1}], [[3, 1, 2, 1], {[0, 0, 1, 1, 1], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0]}, {1, 4}] , [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 1], [0, 2, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}] , [[4, 1, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {}], [[3, 1, 2, 4], %7, {}], [[1, 2, 4, 5, 3], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %6, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], %2, {1, 2, 3, 4}], [[1, 2, 3, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %4, {4, 5}], [[1, 4, 2, 5, 3], %5, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], %4, {4, 5}], [[1, 3, 2, 4, 5], %2, {2, 3, 4}], [[1, 3, 2, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], %6, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %5, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %5, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %5, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[1, 4, 2, 3, 4], %4, {2}], [[1, 4, 2, 3, 1], %6, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %5, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %5, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %3, {2}], [ [1, 4, 2, 3, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {2, 5}], [[1, 4, 2, 3, 5], %2, {1, 2, 3, 4}], [[1, 5, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %6, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %4, {1, 2, 3}], [ [2, 1, 4, 3, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0]}, {3}], [[2, 1, 5, 3, 4], %3, {1, 2}], [[3, 1, 5, 4, 2], %5, {1, 2, 3, 4, 5}], [ [2, 1, 5, 4, 3], {[0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {3}], [ [2, 1, 4, 3, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 2, 0, 1, 1], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 5], %2, {1, 2}], [[4, 1, 2, 5, 3], %5, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %2, {1, 4}], [[4, 2, 3, 5, 1], %5, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %6, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %5, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], %5, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], %4, {4, 5}], [[4, 1, 2, 3, 1], %6, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %5, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %5, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %4, {1}], [ [4, 1, 2, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {4, 5}], [ [4, 1, 2, 3, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1, 5}], [[5, 1, 2, 3, 4], %3, {1}], [[4, 1, 2, 3, 5], %2, {1, 2, 3, 4}], [[2, 1, 3, 2, 2], {[0, 2, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0]}, {4, 5}], [[3, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1}], [[3, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], { [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [1, 1, 0, 1, 0, 0], [0, 1, 2, 1, 0, 0]}, {1, 3, 5}], [[2, 1, 4, 2, 3], {[0, 1, 2, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %3 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %4 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]} %5 := {[0, 1, 1, 1, 1, 0]} %6 := {[0, 0, 1, 1, 1, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]} %8 := {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 25, 46, 77, 120, 177, 250] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 183, 515, 1140, 2174, 3749, 6013, 9130] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2642, 10147, 28179, 64271] For the equivalence class of patterns, { {[3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[1, 2, 3], [3, 2, 1, 4], [4, 3, 2, 1]}} the member , {[1, 2, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3], [5, 0]}, {}], [[1, 1], {[5, 0, 0], [0, 3, 0], [0, 2, 1], [0, 1, 2], [0, 0, 3]}, {1, 2}], [[2, 1], {[3, 1, 0], [0, 4, 0], [0, 3, 1], [0, 2, 2], [0, 1, 3], [2, 3, 0]}, {}], [[1, 2], {[0, 1, 1], [0, 3, 0]}, {}], [[1, 2, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 3, 0], [3, 1, 1, 0], [0, 4, 1, 0], [0, 1, 1, 1], [0, 3, 2, 0]}, {1} ], [[1, 2, 2], {[0, 3, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [[1, 3, 2], {[3, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[0, 3, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [3, 1, 0, 0]}, {3}], [[2, 1, 1], {[3, 0, 1, 0], [0, 0, 4, 0], [0, 0, 3, 1], [0, 0, 2, 2], [0, 0, 1, 3], [0, 1, 2, 0], [0, 1, 1, 1], [0, 2, 1, 0], [2, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0], [3, 1, 1, 0], [0, 1, 1, 1]}, {}] , [[3, 2, 1], {[0, 1, 1, 3], [0, 3, 1, 0], [1, 1, 1, 0], [0, 2, 2, 1], [0, 1, 3, 1], [0, 2, 1, 2], [0, 1, 2, 2], [0, 2, 3, 0], [0, 1, 4, 0]}, {}], [[3, 1, 2], {[0, 3, 1, 0], [3, 1, 1, 0], [2, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {2, 4}], [[1, 3, 2, 2], {[3, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[2, 4, 3, 1], {[0, 3, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[2, 1, 4, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1}], [[3, 1, 4, 2], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {1, 3}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [3, 1, 0, 1, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {1}], [[2, 1, 3, 1], {[0, 0, 1, 1, 1], [3, 0, 1, 1, 0], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 1, 1, 1, 0]}, {1, 4} ], [[2, 1, 3, 3], {[3, 1, 1, 0, 0], [0, 3, 1, 0, 0], [0, 2, 2, 0, 0], [0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[3, 2, 4, 1], {[0, 3, 1, 1, 0], [0, 1, 3, 1, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [3, 1, 0, 1, 0], [2, 2, 0, 1, 0], [0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 1], { [0, 0, 1, 1, 1], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[4, 2, 3, 1], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [ [4, 1, 3, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], { [0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {2}], [[3, 2, 1, 1], {[0, 0, 2, 1, 2], [0, 0, 1, 2, 2], [0, 0, 1, 1, 3], [0, 0, 3, 1, 0], [0, 1, 1, 1, 0], [1, 0, 1, 1, 0], [0, 0, 2, 2, 1], [0, 0, 1, 3, 1], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0]}, {3, 4}], [[3, 2, 1, 2], {[0, 3, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[4, 3, 1, 2], { [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 1]}, {}], [[3, 2, 1, 3], {[0, 3, 1, 0, 0], [0, 2, 2, 0, 0], [0, 1, 3, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [1, 1, 1, 0, 0]}, {}], [ [3, 2, 1, 4], {[0, 3, 1, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [1, 1, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 3, 0]}, {}], [[2, 4, 3, 1, 2], %3, {1}], [[3, 5, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %4, {1}], [[2, 4, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], { [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0]}, {1, 3, 5}], [[2, 5, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 3, 1, 5, 2], %4, {4}], [[3, 2, 1, 4, 4], {[0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 2, 2, 1, 0, 0], [0, 1, 3, 1, 0, 0], [0, 2, 1, 2, 0, 0], [0, 1, 2, 2, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[3, 2, 1, 4, 2], %3, {1, 2, 4}], [[3, 2, 1, 4, 5], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], { [0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 2, 1, 2, 0], [0, 0, 1, 2, 2, 0], [0, 0, 1, 1, 3, 0]}, {5}], [[3, 2, 1, 5, 4], %4, {1, 2}], [[4, 2, 1, 5, 3], %4, {1, 2}], [ [3, 2, 1, 4, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2}], [[4, 3, 5, 2, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %4, {3}], [[3, 2, 4, 1, 5], %2, {1, 2, 3, 4, 5}], [ [4, 2, 5, 1, 3], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2, 3}], [ [3, 2, 4, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 2, 0], [0, 0, 1, 1, 3, 0]}, {4, 5}], [[3, 2, 4, 1, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [ [3, 2, 4, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0]}, {1, 2}], [[3, 2, 4, 1, 4], {[0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 2, 2, 1, 0, 0], [0, 1, 3, 1, 0, 0], [0, 2, 1, 2, 0, 0], [0, 1, 2, 2, 0, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 3, 0, 0]}, {3}], [[3, 2, 5, 1, 4], { [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1}], [[4, 1, 3, 2, 2], %3, {4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], %4, {2, 3}], [[4, 2, 3, 1, 2], %3, {2}], [[5, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [ [4, 2, 3, 1, 3], {[0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 3, 1, 0, 1, 0], [0, 2, 2, 0, 1, 0], [0, 1, 3, 0, 1, 0], [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0]}, {2, 3, 5}], [[5, 2, 4, 1, 3], %4, {2, 4}], [[4, 2, 3, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[5, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %3, {4, 5}], [[5, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], { [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 2], { [0, 2, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 0, 1, 1, 0], [1, 1, 0, 1, 0, 0]}, {1, 2, 4}], [[3, 2, 1, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 1, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0], [0, 0, 1, 3, 0, 0], [0, 0, 3, 1, 0, 0], [0, 0, 2, 2, 0, 0]}, {5}], [[3, 2, 1, 3, 3], {[0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0], [1, 1, 1, 0, 0, 0], [0, 3, 1, 0, 0, 0], [0, 2, 2, 0, 0, 0], [0, 1, 3, 0, 0, 0]}, {4, 5}], [ [4, 2, 1, 4, 3], {[0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {1, 2}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %4 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 20, 12, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 172, 235, 84, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2216, 2786, 840, 0] For the equivalence class of patterns, { {[2, 3, 1], [2, 1, 4, 3], [4, 2, 1, 3]}, {[1, 3, 2], [3, 1, 2, 4], [3, 4, 1, 2]}, {[2, 1, 3], [1, 3, 4, 2], [3, 4, 1, 2]}, {[3, 1, 2], [2, 1, 4, 3], [2, 4, 3, 1]}} the member , {[2, 3, 1], [2, 1, 4, 3], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 0]}, {1}], [[2, 1], {[1, 2, 0]}, {}], [[2, 1, 1], {[1, 2, 1, 0], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {3}], [[3, 1, 2], {[0, 2, 2, 0], [1, 1, 1, 0]}, {2}], [[3, 2, 1], {[1, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[2, 1, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[2, 1, 3, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[1, 1, 1, 1, 0], [1, 0, 2, 1, 0], [0, 1, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[4, 3, 1, 2], {[0, 2, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {3}], [[3, 2, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[3, 2, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {1}], [[4, 3, 2, 1], {[1, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [ [3, 2, 1, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 1, 3, 4, 5], %3, {3, 4}], [[2, 1, 3, 4, 4], %2, {4, 5}], [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %3, {1, 2, 3, 4}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], %2, {4, 5}], [[4, 3, 2, 1, 5], %3, {1, 2, 3, 4}], [[4, 3, 2, 1, 4], %2, {1}], [ [4, 3, 2, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0]}, {5}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [1, 0, 2, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[5, 4, 3, 2, 1], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {2, 3}], [ [5, 4, 3, 1, 2], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {4}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]} %3 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 197, 796, 3140, 12417, 49367, 196938, 786910] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 2972, 21187, 158391, 1235476] For the equivalence class of patterns, { {[3, 2, 1], [1, 3, 4, 2], [2, 3, 4, 1]}, {[1, 2, 3], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 2, 3], [3, 2, 1, 4], [4, 2, 1, 3]}, {[3, 2, 1], [3, 1, 2, 4], [4, 1, 2, 3]}} the member , {[3, 2, 1], [1, 3, 4, 2], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {}, {}], [[2, 1], {[1, 1, 0]}, {}], [[1, 2, 2], {}, {2, 3}], [[1, 2, 1], {[1, 0, 1, 0]}, {3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 0]}, {}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3], {[1, 1, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], %5, {1, 2}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], %6, {2}], [[1, 2, 3, 1], {[0, 0, 2, 1, 0], [0, 2, 1, 1, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 4], %5, {}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], %5, {3}], [[1, 3, 2, 2], %6, {3, 4}], [[1, 3, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 4], %5, {}], [[2, 1, 4, 3], %5, {1, 2}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {1}], [[2, 1, 3, 2], %6, {1}], [[2, 1, 3, 3], {[1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 1], {[1, 0, 1, 1, 0]}, {4}], [[2, 1, 3, 4], %5, {}], [[2, 3, 1, 1], {[1, 0, 1, 1, 0]}, {3, 4}], [[2, 3, 1, 4], %5, {3}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], %5, {3}], [[3, 4, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {3}], [[2, 3, 1, 3], {[1, 1, 1, 0, 0]}, {2}], [[2, 3, 1, 2], %6, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %6, {3, 4}], [[3, 1, 2, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2}], [[4, 1, 2, 3], %5, {2, 3}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {}], [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], {[0, 2, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 3], {[0, 2, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0]}, {1}], [ [2, 4, 1, 2, 3], {[0, 1, 2, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {3, 4}], [[2, 3, 1, 2, 4], { [0, 1, 2, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {1, 3, 4}], [[1, 2, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], %3, {1, 2, 3}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %2, {1, 2, 3, 5}], [[1, 2, 3, 4, 4], %1, {4, 5}], [[1, 2, 3, 5, 4], %3, {1, 2, 3}], [[1, 4, 2, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %3, {1, 2, 3}], [[1, 3, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], %1, {4, 5}], [[1, 3, 2, 4, 5], %3, {1, 2, 3}], [[2, 4, 3, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %2, {1, 2, 3, 5}], [[3, 2, 4, 5, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], %1, {4, 5}], [[2, 1, 3, 5, 4], %3, {1, 2, 3}], [[2, 1, 3, 4, 3], %2, {1, 2, 3, 5}], [[2, 1, 3, 4, 5], %3, {1, 2, 3}], [[3, 1, 2, 3, 4], %2, {1}], [[3, 1, 2, 3, 3], {[0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[4, 1, 2, 4, 3], %1, {1, 2, 3}], [[3, 1, 2, 3, 2], {[0, 2, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0]}, {1, 3, 5}], [[4, 1, 3, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0]} %2 := {[1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]} %3 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]} %6 := {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 27, 58, 121, 248, 503, 1014] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 199, 827, 3335, 13355, 53415, 213627, 854439] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3037, 24158, 192277, 1535993] For the equivalence class of patterns, { {[2, 1, 3], [4, 1, 2, 3], [4, 1, 3, 2]}, {[1, 3, 2], [2, 3, 4, 1], [3, 2, 4, 1]}, {[2, 3, 1], [1, 4, 2, 3], [1, 4, 3, 2]}, {[3, 1, 2], [2, 3, 1, 4], [3, 2, 1, 4]}} the member , {[1, 3, 2], [2, 3, 4, 1], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[2, 1], {}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {1, 3}], [[2, 3, 1], {[0, 1, 2, 0]}, {}], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0]}, {1, 3}], [[2, 1, 1], {}, {2, 3}], [[3, 1, 2], {[0, 2, 1, 0]}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %8, {3, 4}], [[1, 2, 3, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[1, 2, 3, 4], %7, {}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0]}, {4}], [[2, 1, 3, 3], %8, {3, 4}], [[2, 1, 3, 4], %7, {}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 1, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2}], [[2, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0]}, {1, 4}] , [[2, 3, 1, 3], %8, {2}], [[3, 4, 2, 1], {[0, 1, 1, 2, 0]}, {2}], [[2, 3, 1, 4], %7, {}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], %8, {1}], [[3, 1, 2, 1], {[0, 0, 2, 1, 0], [0, 2, 1, 1, 0]}, {2, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 2, 1, 0]}, {1}], [[4, 1, 2, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {1}], [[3, 1, 2, 4], %7, {}], [[3, 2, 1, 1], {}, {3, 4}], [[4, 3, 2, 1], {}, {1}], [[4, 3, 1, 2], {[0, 2, 1, 1, 0]}, {1}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0]}, {2, 4}], [[3, 2, 1, 3], %8, {1}], [[4, 2, 1, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0]}, {1}], [[3, 2, 1, 4], %7, {}], [[1, 2, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], %6, {1, 2, 3, 4}], [[1, 2, 3, 4, 3], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %1, {4, 5}], [[2, 1, 3, 4, 4], %1, {4, 5}], [[3, 2, 4, 5, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], %6, {1, 2, 3, 4}], [[2, 1, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %2, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 5, 2], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %6, {1, 2, 3, 4}], [[2, 3, 1, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], %5, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], %1, {4, 5}], [[2, 3, 1, 5, 4], %2, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %6, {1, 2, 3, 4}], [[4, 2, 3, 5, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], %5, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], %1, {4, 5}], [[3, 2, 1, 4, 5], %6, {1, 2, 3, 4}], [[3, 2, 1, 4, 2], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 5, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], %1, {4, 5}]] %1 := {[1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 1, 0, 1, 0]} %5 := {[0, 1, 0, 1, 1, 0]} %6 := {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]} %7 := {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]} %8 := {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 12, 29, 70, 169, 408, 985, 2378] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 210, 1135, 5967, 31603, 167046, 883438, 4671471] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3524, 41908, 460180, 5188994] Out of a total of , 146, cases 38, were successful and , 108, failed Success Rate: , 0.260 Here are the failures {{{[2, 1, 3], [1, 3, 4, 2], [4, 1, 3, 2]}, {[1, 3, 2], [3, 1, 2, 4], [3, 2, 4, 1]}, {[3, 1, 2], [2, 3, 1, 4], [2, 4, 3, 1]}, {[2, 3, 1], [1, 4, 2, 3], [4, 2, 1, 3]}}, { {[3, 2, 1], [1, 3, 2, 4], [2, 4, 1, 3]}, {[1, 2, 3], [3, 1, 4, 2], [4, 2, 3, 1]}}, { {[3, 2, 1], [1, 3, 4, 2], [4, 1, 2, 3]}, {[1, 2, 3], [1, 4, 3, 2], [4, 2, 1, 3]}, {[3, 2, 1], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 2, 3], [2, 4, 3, 1], [3, 2, 1, 4]}}, { {[1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3]}, {[3, 2, 1], [2, 3, 1, 4], [3, 1, 2, 4]}, {[3, 2, 1], [1, 3, 4, 2], [1, 4, 2, 3]}, {[1, 2, 3], [2, 4, 3, 1], [3, 2, 4, 1]}}, { {[3, 1, 2], [1, 2, 3, 4], [2, 3, 1, 4]}, {[1, 3, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[2, 1, 3], [4, 1, 3, 2], [4, 3, 2, 1]}, {[2, 3, 1], [1, 2, 3, 4], [1, 4, 2, 3]}}, { {[2, 1, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, {[3, 1, 2], [2, 1, 3, 4], [3, 2, 1, 4]}, {[1, 3, 2], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 3, 1], [1, 2, 4, 3], [1, 4, 3, 2]}}, { {[3, 2, 1], [2, 4, 1, 3], [3, 1, 2, 4]}, {[1, 2, 3], [2, 4, 3, 1], [3, 1, 4, 2]}, {[1, 2, 3], [3, 1, 4, 2], [4, 2, 1, 3]}, {[3, 2, 1], [1, 3, 4, 2], [2, 4, 1, 3]}}, { {[3, 2, 1], [1, 2, 3, 4], [2, 1, 4, 3]}, {[1, 2, 3], [3, 4, 1, 2], [4, 3, 2, 1]}}, { {[1, 3, 2], [1, 2, 3, 4], [3, 2, 1, 4]}, {[2, 3, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[3, 1, 2], [2, 3, 4, 1], [4, 3, 2, 1]}, {[2, 1, 3], [1, 2, 3, 4], [1, 4, 3, 2]}}, { {[2, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[2, 3, 1], [1, 2, 3, 4], [1, 3, 2, 4]}, {[3, 1, 2], [1, 2, 3, 4], [1, 3, 2, 4]}, {[1, 3, 2], [4, 2, 3, 1], [4, 3, 2, 1]}}, { {[2, 3, 1], [1, 2, 3, 4], [3, 2, 1, 4]}, {[2, 1, 3], [2, 3, 4, 1], [4, 3, 2, 1]}, {[3, 1, 2], [1, 2, 3, 4], [1, 4, 3, 2]}, {[1, 3, 2], [4, 1, 2, 3], [4, 3, 2, 1]}}, { {[1, 3, 2], [1, 2, 3, 4], [4, 3, 2, 1]}, {[2, 1, 3], [1, 2, 3, 4], [4, 3, 2, 1]}, {[3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}, {[2, 3, 1], [1, 2, 3, 4], [4, 3, 2, 1]}}, { {[1, 3, 2], [3, 1, 2, 4], [4, 2, 3, 1]}, {[2, 1, 3], [1, 3, 4, 2], [4, 2, 3, 1]}, {[3, 1, 2], [1, 3, 2, 4], [2, 4, 3, 1]}, {[2, 3, 1], [1, 3, 2, 4], [4, 2, 1, 3]}}, { {[1, 2, 3], [3, 4, 1, 2], [4, 2, 3, 1]}, {[3, 2, 1], [1, 3, 2, 4], [2, 1, 4, 3]}}, { {[1, 2, 3], [2, 1, 4, 3], [4, 2, 3, 1]}, {[3, 2, 1], [1, 3, 2, 4], [3, 4, 1, 2]}}, { {[3, 2, 1], [2, 1, 4, 3], [2, 4, 1, 3]}, {[1, 2, 3], [3, 1, 4, 2], [3, 4, 1, 2]}}, { {[2, 3, 1], [3, 1, 2, 4], [4, 1, 3, 2]}, {[1, 3, 2], [2, 3, 1, 4], [4, 2, 1, 3]}, {[3, 1, 2], [1, 3, 4, 2], [3, 2, 4, 1]}, {[2, 1, 3], [1, 4, 2, 3], [2, 4, 3, 1]}}, { {[3, 1, 2], [1, 2, 3, 4], [3, 2, 4, 1]}, {[1, 3, 2], [2, 3, 1, 4], [4, 3, 2, 1]}, {[2, 1, 3], [1, 4, 2, 3], [4, 3, 2, 1]}, {[2, 3, 1], [1, 2, 3, 4], [4, 1, 3, 2]}}, { {[2, 1, 3], [1, 4, 2, 3], [4, 1, 3, 2]}, {[1, 3, 2], [2, 3, 1, 4], [3, 2, 4, 1]}, {[3, 1, 2], [2, 3, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1], [1, 4, 2, 3], [4, 1, 3, 2]}}, { {[2, 1, 3], [1, 4, 2, 3], [4, 2, 3, 1]}, {[3, 1, 2], [1, 3, 2, 4], [3, 2, 4, 1]}, {[1, 3, 2], [2, 3, 1, 4], [4, 2, 3, 1]}, {[2, 3, 1], [1, 3, 2, 4], [4, 1, 3, 2]}}, { {[1, 3, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, {[2, 3, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[2, 1, 3], [1, 4, 3, 2], [4, 3, 2, 1]}}, { {[3, 1, 2], [1, 2, 4, 3], [3, 2, 4, 1]}, {[1, 3, 2], [2, 3, 1, 4], [4, 3, 1, 2]}, {[2, 3, 1], [2, 1, 3, 4], [4, 1, 3, 2]}, {[2, 1, 3], [1, 4, 2, 3], [3, 4, 2, 1]}}, { {[1, 3, 2], [3, 2, 1, 4], [4, 3, 1, 2]}, {[2, 1, 3], [1, 4, 3, 2], [3, 4, 2, 1]}, {[3, 1, 2], [1, 2, 4, 3], [2, 3, 4, 1]}, {[2, 3, 1], [2, 1, 3, 4], [4, 1, 2, 3]}}, { {[3, 2, 1], [1, 2, 4, 3], [2, 1, 4, 3]}, {[1, 2, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 2, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[3, 2, 1], [2, 1, 3, 4], [2, 1, 4, 3]}}, { {[2, 1, 3], [1, 2, 3, 4], [4, 3, 1, 2]}, {[2, 3, 1], [1, 2, 4, 3], [4, 3, 2, 1]}, {[1, 3, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, {[3, 1, 2], [2, 1, 3, 4], [4, 3, 2, 1]}}, { {[1, 2, 3], [1, 4, 3, 2], [3, 4, 1, 2]}, {[3, 2, 1], [2, 1, 4, 3], [4, 1, 2, 3]}, {[1, 2, 3], [3, 2, 1, 4], [3, 4, 1, 2]}, {[3, 2, 1], [2, 1, 4, 3], [2, 3, 4, 1]}}, { {[2, 1, 3], [1, 2, 4, 3], [4, 2, 3, 1]}, {[1, 3, 2], [2, 1, 3, 4], [4, 2, 3, 1]}, {[3, 1, 2], [1, 3, 2, 4], [3, 4, 2, 1]}, {[2, 3, 1], [1, 3, 2, 4], [4, 3, 1, 2]}}, { {[3, 2, 1], [1, 4, 2, 3], [2, 3, 1, 4]}, {[1, 2, 3], [3, 2, 4, 1], [4, 1, 3, 2]}}, { {[1, 3, 2], [2, 3, 4, 1], [3, 4, 1, 2]}, {[3, 1, 2], [2, 1, 4, 3], [3, 2, 1, 4]}, {[2, 3, 1], [1, 4, 3, 2], [2, 1, 4, 3]}, {[2, 1, 3], [3, 4, 1, 2], [4, 1, 2, 3]}}, { {[1, 2, 3], [3, 4, 2, 1], [4, 3, 1, 2]}, {[3, 2, 1], [1, 2, 4, 3], [2, 1, 3, 4]}}, { {[1, 2, 3], [2, 1, 4, 3], [2, 4, 1, 3]}, {[3, 2, 1], [3, 1, 4, 2], [3, 4, 1, 2]}}, { {[3, 2, 1], [1, 3, 4, 2], [3, 4, 1, 2]}, {[1, 2, 3], [2, 1, 4, 3], [2, 4, 3, 1]}, {[1, 2, 3], [2, 1, 4, 3], [4, 2, 1, 3]}, {[3, 2, 1], [3, 1, 2, 4], [3, 4, 1, 2]}}, { {[3, 1, 2], [1, 3, 2, 4], [2, 1, 4, 3]}, {[1, 3, 2], [3, 4, 1, 2], [4, 2, 3, 1]}, {[2, 1, 3], [3, 4, 1, 2], [4, 2, 3, 1]}, {[2, 3, 1], [1, 3, 2, 4], [2, 1, 4, 3]}}, { {[2, 3, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[3, 1, 2], [1, 2, 3, 4], [1, 2, 4, 3]}, {[2, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]}}, { {[2, 1, 3], [1, 4, 3, 2], [4, 1, 2, 3]}, {[1, 3, 2], [2, 3, 4, 1], [3, 2, 1, 4]}, {[3, 1, 2], [2, 3, 4, 1], [3, 2, 1, 4]}, {[2, 3, 1], [1, 4, 3, 2], [4, 1, 2, 3]}}, { {[2, 1, 3], [2, 4, 3, 1], [4, 1, 2, 3]}, {[1, 3, 2], [2, 3, 4, 1], [4, 2, 1, 3]}, {[2, 3, 1], [1, 4, 3, 2], [3, 1, 2, 4]}, {[3, 1, 2], [1, 3, 4, 2], [3, 2, 1, 4]}}, { {[1, 2, 3], [1, 4, 3, 2], [2, 4, 1, 3]}, {[3, 2, 1], [3, 1, 4, 2], [4, 1, 2, 3]}, {[1, 2, 3], [2, 4, 1, 3], [3, 2, 1, 4]}, {[3, 2, 1], [2, 3, 4, 1], [3, 1, 4, 2]}}, { {[1, 3, 2], [3, 4, 2, 1], [4, 2, 1, 3]}, {[2, 1, 3], [2, 4, 3, 1], [4, 3, 1, 2]}, {[3, 1, 2], [1, 3, 4, 2], [2, 1, 3, 4]}, {[2, 3, 1], [1, 2, 4, 3], [3, 1, 2, 4]}}, { {[2, 3, 1], [2, 1, 3, 4], [3, 1, 2, 4]}, {[3, 1, 2], [1, 2, 4, 3], [1, 3, 4, 2]}, {[2, 1, 3], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 3, 2], [4, 2, 1, 3], [4, 3, 1, 2]}}, { {[1, 3, 2], [3, 2, 4, 1], [4, 1, 2, 3]}, {[2, 1, 3], [2, 3, 4, 1], [4, 1, 3, 2]}, {[3, 1, 2], [1, 4, 3, 2], [2, 3, 1, 4]}, {[2, 3, 1], [1, 4, 2, 3], [3, 2, 1, 4]}}, { {[2, 1, 3], [1, 3, 4, 2], [1, 4, 3, 2]}, {[1, 3, 2], [3, 1, 2, 4], [3, 2, 1, 4]}, {[2, 3, 1], [4, 1, 2, 3], [4, 2, 1, 3]}, {[3, 1, 2], [2, 3, 4, 1], [2, 4, 3, 1]}}, { {[3, 2, 1], [1, 4, 2, 3], [2, 1, 3, 4]}, {[1, 2, 3], [3, 2, 4, 1], [4, 3, 1, 2]}, {[3, 2, 1], [1, 2, 4, 3], [2, 3, 1, 4]}, {[1, 2, 3], [3, 4, 2, 1], [4, 1, 3, 2]}}, { {[3, 2, 1], [2, 1, 3, 4], [2, 4, 1, 3]}, {[1, 2, 3], [3, 1, 4, 2], [3, 4, 2, 1]}, {[1, 2, 3], [3, 1, 4, 2], [4, 3, 1, 2]}, {[3, 2, 1], [1, 2, 4, 3], [2, 4, 1, 3]}}, { {[2, 3, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, {[3, 1, 2], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 3, 2], [3, 4, 2, 1], [4, 3, 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