Warning, the protected name Chi has been redefined and unprotected There all together, 6, different equivalence classes For the equivalence class of patterns, {{[1, 2, 3], [3, 2, 1]}} the member , {[1, 2, 3], [3, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[3, 0], [0, 3], [2, 2]}, {}], [[1, 1], {[0, 1, 2], [3, 0, 0], [0, 3, 0], [0, 2, 1], [0, 0, 3], [2, 2, 0], [2, 1, 1], [2, 0, 2] }, {1, 2}], [[2, 1], {[1, 1, 0], [0, 3, 0], [0, 2, 2], [0, 1, 3]}, {}], [[1, 2], {[0, 1, 1], [0, 3, 0], [3, 1, 0], [2, 2, 0]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 2, 2, 0], [0, 1, 3, 0]}, {1} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0], [3, 1, 0, 0], [2, 2, 0, 0]}, {2, 3}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [[1, 3, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0], [0, 0, 3, 0], [0, 1, 1, 1], [0, 0, 2, 2], [0, 0, 1, 3]}, {2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 3} ], [[2, 1, 3], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 2, 2, 0], [0, 1, 3, 0]}, {1} ], [[3, 1, 2], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 3, 1], {[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, 1, 1, 0], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 0, 2, 0]}, {3, 4}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[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, 2], { [0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 0, 2, 0]}, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 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}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 4, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 12, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 80, 40, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2]}, {[1, 2, 3], [2, 1, 3]}, {[2, 3, 1], [3, 2, 1]}, {[3, 1, 2], [3, 2, 1]}} the member , {[1, 2, 3], [1, 3, 2]}, has a scheme of depth , 1 here it is: [[[], {}, {}], [[1], {[0, 2]}, {1}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 148, 1196, 9556, 76460, 611668, 4893356, 39146836, 313174700] For the equivalence class of patterns, {{[1, 2, 3], [2, 3, 1]}, {[1, 2, 3], [3, 1, 2]}, {[1, 3, 2], [3, 2, 1]}, {[2, 1, 3], [3, 2, 1]}} the member , {[1, 2, 3], [3, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 1, 1]}, {}], [[2, 1], {[0, 2, 0]}, {}], [[2, 3, 1], {[0, 1, 2, 0], [0, 2, 1, 0], [0, 1, 1, 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, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 2, 0], [0, 2, 1, 0]}, {2}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [0, 1, 0, 2, 0]}, {3, 4}] , [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], {[0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 2, 0], [0, 0, 0, 1, 1, 1]}, {4, 5}], [[2, 4, 3, 2, 1], { [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1]}, {4}], [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %1, {1, 2, 3, 4, 5}], [[2, 5, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], {[0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1]}, {4}], [[2, 4, 3, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 1, 1]}, {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, 4, 7, 11, 16, 22, 29, 37, 46] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 40, 69, 106, 151, 204, 265, 334] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 93, 247, 509, 906, 1465, 2213, 3177, 4384] For the equivalence class of patterns, {{[1, 3, 2], [2, 1, 3]}, {[2, 3, 1], [3, 1, 2]}} the member , {[1, 3, 2], [2, 1, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[2, 1], {[0, 1, 1]}, {1}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[1, 2, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[1, 2, 3, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 1]}, {}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], {[0, 1, 0, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1]}, {1, 2, 3, 4}], [[1, 3, 4, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 2, 0], [0, 0, 0, 1, 1, 1]}, {4, 5}], [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 73, 264, 973, 3565, 13086, 48007, 176149] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 93, 761, 4832, 34177, 230601, 1587940, 10838413, 74261105] For the equivalence class of patterns, {{[1, 3, 2], [2, 3, 1]}, {[2, 1, 3], [3, 1, 2]}} the member , {[1, 3, 2], [2, 3, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {}, {}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [1, 0, 1, 0], [0, 2, 1, 0]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {}, {1}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {1}], [[2, 1, 1], {}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 3], {[0, 1, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[1, 2, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[1, 2, 3, 3], {[1, 1, 1, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[2, 1, 4, 3], {[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, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[1, 1, 1, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720] For the equivalence class of patterns, {{[1, 3, 2], [3, 1, 2]}, {[2, 1, 3], [2, 3, 1]}} the member , {[1, 3, 2], [3, 1, 2]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0]}, {}], [[1, 2], {[0, 2, 0]}, {}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], %1, {2}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {1, 3}], [[2, 3, 1], %1, {1}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], %1, {2}], [[2, 1, 2], {[0, 2, 0, 0]}, {1, 3}], [[2, 1, 3], %1, {1}]] %1 := {[0, 1, 2, 0], [0, 2, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 8, 16, 32, 64, 128, 256, 512] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 148, 1196, 9556, 76460, 611668, 4893356, 39146836, 313174700] Out of a total of , 6, cases 6, were successful and , 0, failed Success Rate: , 1. Here are the failures {}