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], [1, 3, 2], [2, 1, 3]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1]}} the member , {[1, 2, 3], [1, 3, 2], [2, 1, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[2, 1], {[0, 1, 1], [0, 3, 0]}, {1}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {2}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 5, 8, 13, 21, 34, 55, 89] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 53, 160, 517, 1621, 5150, 16267, 51513] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 84, 662, 3815, 25402, 157773, 1012669, 6398776, 40734026] For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2], [2, 3, 1]}, {[1, 2, 3], [2, 1, 3], [3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [3, 2, 1]}} the member , {[1, 2, 3], [1, 3, 2], [2, 3, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 1]}, {1, 2}], [[2, 1], {[0, 1, 2], [0, 3, 0], [0, 2, 1]}, {}], [[3, 2, 1], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 2, 1, 1], [0, 1, 1, 2], [0, 3, 1, 0], [0, 2, 2, 0]}, {1}] , [[3, 1, 2], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 0]}, {1}], [ [2, 1, 1], {[0, 0, 3, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 1, 1, 0]}, {2, 3} ], [[2, 1, 2], {[0, 1, 0, 1], [1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[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, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 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]}, {3, 4}], [[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}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 10, 12, 14, 16, 18, 20, 22] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 23, 26, 29, 32, 35, 38, 41, 44] For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2], [3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [3, 2, 1]}} the member , {[1, 2, 3], [1, 3, 2], [3, 1, 2]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {1}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 2]}, {}], [[2, 1, 1], {[0, 0, 2, 0], [0, 0, 1, 2], [0, 1, 1, 0]}, {2, 3}], [[2, 1, 2], {[0, 1, 0, 1], [0, 2, 0, 0], [0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 1, 2], [0, 1, 2, 0], [0, 2, 1, 0]}, {2}], [[2, 1, 3], {[0, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 15, 28, 45, 66, 91, 120, 153, 190] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060] For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2], [3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [3, 2, 1]}, {[1, 2, 3], [2, 3, 1], [3, 2, 1]}, {[1, 2, 3], [3, 1, 2], [3, 2, 1]}} the member , {[1, 2, 3], [1, 3, 2], [3, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[0, 2], [3, 0]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 1], [3, 1, 0]}, {1}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2], [3, 0, 0]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 2], [0, 3, 0], [0, 2, 1]}, {}], [[2, 1, 1], {[1, 0, 1, 0], [0, 0, 3, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 1, 1, 0]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 0, 1], [1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 0]}, {1}], [[3, 1, 2], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 2, 0], [0, 2, 1, 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], { [0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {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, 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, 3, 1, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 1, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 23, 1, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, {{[1, 2, 3], [2, 3, 1], [3, 1, 2]}, {[1, 3, 2], [2, 1, 3], [3, 2, 1]}} the member , {[1, 2, 3], [2, 3, 1], [3, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 1, 1]}, {}], [[2, 1], {[0, 2, 0]}, {}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 0, 1], [1, 1, 0, 0], [0, 1, 1, 0]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 2, 0]}, {}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 2], {[0, 1, 0, 1], [1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[1, 3, 2, 2], {[0, 1, 1, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 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], {[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], [1, 1, 1, 1, 0]}, {2, 3}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], { [0, 1, 1, 1, 0], [1, 0, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 1]}, {}], [[2, 1, 4, 3], {[0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [1, 1, 1, 1, 0]}, {2, 3}], [[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, 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}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 1, 1, 1, 0], [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[3, 2, 1, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}] , [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[3, 2, 1, 4], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [1, 1, 1, 1, 0]}, {2, 3}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 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, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], {[0, 1, 0, 0, 1, 1], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0]}, {4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], {[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}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], {[0, 1, 1, 0, 0, 1], [0, 1, 2, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 1, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[4, 3, 1, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 2, 1], {[0, 1, 0, 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, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [1, 0, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1]}, {4, 5}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 6, 8, 10, 12, 14, 16, 18, 20] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 9, 12, 15, 18, 21, 24, 27, 30] For the equivalence class of patterns, {{[1, 3, 2], [2, 1, 3], [2, 3, 1]}, {[1, 3, 2], [2, 1, 3], [3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2]}, {[2, 1, 3], [2, 3, 1], [3, 1, 2]}} the member , {[1, 3, 2], [2, 1, 3], [2, 3, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1]}, {1, 2}], [[2, 1], {[0, 1, 1], [1, 2, 0]}, {1}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[1, 2, 1], {[1, 0, 1, 0], [0, 0, 2, 0], [0, 0, 1, 1], [0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 2, 1, 0]}, {}], [[1, 2, 4, 3], {[0, 1, 1, 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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [1, 1, 1, 1, 0]}, {1, 2, 3}], [[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}], [[1, 3, 4, 2], {[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, 3, 4, 5, 6, 7, 8, 9, 10] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 8, 10, 12, 14, 16, 18, 20, 22] Using the scheme, the first, , 10, terms for , 3, copies of each letter are [1, 20, 23, 26, 29, 32, 35, 38, 41, 44] Out of a total of , 6, cases 6, were successful and , 0, failed Success Rate: , 1. Here are the failures {}