Warning, the protected name Chi has been redefined and unprotected There all together, 24, different equivalence classes For the equivalence class of patterns, {{[1, 2, 3], [1, 4, 3, 2]}, {[1, 2, 3], [3, 2, 1, 4]}, {[3, 2, 1], [2, 3, 4, 1]}, {[3, 2, 1], [4, 1, 2, 3]}} the member , {[1, 2, 3], [1, 4, 3, 2]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[2, 1], {[0, 4, 0], [0, 2, 2], [0, 3, 1], [0, 1, 3]}, {1}], [[1, 1], {[0, 1, 2], [0, 3, 0], [0, 2, 1], [0, 0, 3]}, {1, 2}], [[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, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 290, 1902, 12393, 80642, 524665, 3413594, 22209990] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 6078, 95256, 1487198, 23230433] For the equivalence class of patterns, {{[1, 2, 3], [2, 1, 4, 3]}, {[3, 2, 1], [3, 4, 1, 2]}} the member , {[1, 2, 3], [2, 1, 4, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {}, {}], [[2, 1], {[0, 1, 2]}, {1}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 1, 1]}, {2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 286, 1914, 12837, 86067, 577025, 3868644, 25937187] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5952, 97437, 1599926, 26217885] For the equivalence class of patterns, {{[1, 2, 3], [3, 2, 4, 1]}, {[1, 2, 3], [4, 1, 3, 2]}, {[3, 2, 1], [1, 4, 2, 3]}, {[3, 2, 1], [2, 3, 1, 4]}} the member , {[1, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 1, 1]}, {}], [[2, 1], {[0, 3, 0]}, {}], [[2, 3, 1], {[0, 1, 1, 1], [0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0]}, {1}], [[1, 2, 2], {[0, 1, 0, 1], [0, 1, 1, 0]}, {2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 3, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], {[0, 1, 1, 1], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 1], [0, 3, 1, 0]}, {1}], [[2, 1, 2], {[0, 1, 0, 1], [0, 1, 1, 0], [0, 3, 0, 0]}, {1, 3}], [[2, 1, 1], {[0, 3, 1, 0], [0, 0, 3, 0]}, {2, 3}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0]}, {2}], [[3, 1, 2], {[0, 1, 1, 1], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[1, 4, 3, 2], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 1, 1, 2, 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, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 3, 1, 0]}, {}], [[2, 4, 3, 1], {[0, 2, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0]}, {}], [[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, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 1, 0, 2, 0], [0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 2, 0], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[2, 5, 4, 1, 3], %1, {1, 2, 3}], [[3, 5, 4, 1, 2], %1, {1, 2, 3}], [ [2, 4, 3, 1, 2], {[0, 1, 0, 1, 1, 1], [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, 3}], [ [2, 4, 3, 1, 1], {[0, 1, 1, 1, 1, 0], [0, 0, 1, 3, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 3, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 5, 3, 1, 4], %2, {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, 3], {[0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 3}], [[2, 4, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], { [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {2, 3}], [[4, 2, 3, 1, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 3, 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, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {4}], [ [4, 2, 3, 1, 2], {[0, 1, 0, 1, 1, 1], [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, 3}], [[5, 3, 4, 1, 2], %1, {1, 2, 3}], [[1, 3, 2, 1, 2], {[0, 0, 2, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0]}, {1, 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, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 2, 1, 1, 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, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 3, 1, 0]}, {4, 5}], [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 2, 1], {[0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0], [0, 2, 0, 2, 1, 0], [0, 1, 0, 3, 1, 0], [0, 3, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0]}, {4}]] %1 := {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 32, 74, 163, 347, 722, 1480] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 248, 1161, 4942, 20231, 81588, 327253, 1310186] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 4287, 37956, 311692, 2508382] For the equivalence class of patterns, {{[1, 2, 3], [4, 3, 2, 1]}, {[3, 2, 1], [1, 2, 3, 4]}} the member , {[1, 2, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[5, 0], [0, 4]}, {}], [[1, 1], {[0, 4, 0], [0, 2, 2], [0, 3, 1], [0, 1, 3], [0, 0, 4], [5, 0, 0]}, {1, 2}] , [[1, 2], {[0, 4, 0], [0, 1, 1]}, {}], [[2, 1], {[3, 1, 0], [0, 4, 0], [0, 3, 2], [0, 2, 3], [0, 1, 4], [2, 3, 0]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 1, 1], [0, 1, 4, 0], [0, 2, 3, 0], [0, 4, 1, 0], [0, 3, 2, 0], [3, 1, 1, 0]}, {1}] , [[1, 2, 1], {[2, 0, 3, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 4, 0]}, {1} ], [[1, 2, 2], {[0, 1, 0, 1], [0, 1, 1, 0], [0, 4, 0, 0]}, {2, 3}], [ [1, 3, 2], {[0, 1, 1, 1], [0, 3, 1, 0], [0, 1, 2, 0], [3, 1, 1, 0], [2, 2, 1, 0]}, {}] , [[2, 1, 1], {[2, 0, 3, 0], [0, 0, 3, 2], [0, 0, 2, 3], [0, 0, 1, 4], [0, 1, 2, 1], [2, 1, 2, 0], [3, 0, 1, 0], [0, 3, 1, 0], [0, 2, 1, 1], [2, 1, 1, 1], [0, 2, 2, 0], [0, 1, 1, 2], [0, 1, 3, 0], [0, 0, 4, 0], [2, 2, 1, 0]}, {2, 3}], [[2, 1, 2], {[2, 3, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 4, 0, 0], [3, 1, 0, 0]}, {3} ], [[2, 1, 3], {[0, 1, 1, 1], [0, 1, 4, 0], [0, 2, 3, 0], [0, 4, 1, 0], [0, 3, 2, 0], [3, 1, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 4, 0], [0, 2, 3, 0], [0, 3, 1, 0], [1, 1, 1, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 1], [0, 3, 1, 0], [0, 1, 2, 0], [3, 1, 1, 0], [2, 2, 1, 0]}, {}] , [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %8, {3, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[1, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 3, 1, 0]}, {4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], %6, {}], [[2, 4, 3, 1], %7, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 3}], [[2, 1, 3, 3], {[0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 4, 1, 0, 0], [0, 2, 3, 0, 0], [0, 1, 4, 0, 0], [0, 3, 2, 0, 0], [3, 1, 1, 0, 0]}, {3, 4} ], [[2, 1, 4, 3], {[0, 2, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0]}, {1}], [[2, 1, 3, 2], %8, {1}], [ [2, 1, 3, 1], {[0, 1, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 3, 2, 0], [0, 0, 4, 1, 0], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0], [3, 0, 1, 1, 0]}, {1, 2, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 3, 1, 1, 0]}, {}], [[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, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], { [1, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 3, 1, 0]}, {4}], [[3, 1, 2, 2], %8, {3, 4}], [[4, 2, 3, 1], %7, {}], [[4, 1, 3, 2], %6, {}], [[4, 2, 1, 3], %7, {2}], [[3, 2, 1, 3], { [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 3, 1, 0, 0], [1, 1, 1, 0, 0], [0, 2, 3, 0, 0], [0, 1, 4, 0, 0]}, {4}], [[3, 2, 1, 1], {[0, 1, 1, 1, 1], [1, 0, 1, 1, 0], [0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 0, 3, 1, 0], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [0, 3, 0, 1, 0], [1, 1, 0, 1, 0]}, {2}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 3, 1, 1, 0]}, {}], [[4, 3, 1, 2], %6, {}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %3, {4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[2, 5, 4, 1, 3], %4, {1, 4}], [[2, 4, 3, 1, 3], %5, {1, 3, 5}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 1, 3, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[2, 4, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 2], %3, {1}], [[3, 5, 4, 1, 2], %4, {1}], [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}], [ [3, 2, 1, 4, 1], {[0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {3, 5}], [[3, 2, 1, 4, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [1, 1, 1, 1, 0, 0]}, {4, 5}], [[4, 2, 1, 5, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2, 4}], [ [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, 3], %5, {1, 2}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0]}, {1, 2, 4}], [[4, 3, 1, 5, 2], %4, {4}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [ [3, 2, 4, 1, 1], {[0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}], [[3, 2, 4, 1, 4], { [0, 1, 1, 1, 1, 0], [0, 3, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1], [1, 1, 1, 1, 0, 0]}, {3, 5}], [[4, 2, 5, 1, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2, 3}], [[4, 3, 5, 1, 2], %4, {3}], [[3, 2, 4, 1, 2], {[0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0]}, {1, 2, 3}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[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, 3], %5, {1, 2}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %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, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], %3, {4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %4, {2, 4}], [[5, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %3, {2}], [[4, 2, 3, 1, 3], %5, {2, 3, 5}], [[5, 3, 4, 1, 2], %4, {2, 3}], [ [4, 2, 3, 1, 1], {[0, 1, 1, 1, 1, 0], [0, 0, 1, 3, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 3, 1, 1, 0], [1, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0]}, {4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %3, {4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 1, 1, 0, 0]} %3 := {[0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]} %4 := {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]} %5 := {[0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 3, 0, 1, 0], [0, 3, 1, 0, 1, 0], [0, 2, 2, 0, 1, 0], [1, 1, 1, 0, 1, 0]} %6 := {[0, 1, 1, 1, 1], [0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [1, 1, 1, 1, 0]} %7 := {[0, 2, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0], [1, 1, 1, 1, 0], [0, 3, 1, 1, 0]} %8 := {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [0, 3, 0, 1, 0], [3, 1, 0, 1, 0], [2, 2, 0, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 25, 25, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 214, 432, 265, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 3079, 6650, 3310, 0] For the equivalence class of patterns, {{[1, 3, 2], [1, 2, 3, 4]}, {[2, 1, 3], [1, 2, 3, 4]}, {[2, 3, 1], [4, 3, 2, 1]}, {[3, 1, 2], [4, 3, 2, 1]}} the member , {[1, 3, 2], [1, 2, 3, 4]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[2, 1], {[0, 4, 0], [0, 2, 2], [0, 3, 1], [0, 1, 3]}, {1}], [[1, 1], {[0, 1, 2], [0, 3, 0], [0, 2, 1], [0, 0, 3]}, {1, 2}], [[1, 2], {[0, 2, 0], [0, 1, 2]}, {2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 290, 1894, 12219, 78368, 501124, 3199594, 20413262] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 6078, 93879, 1419631, 21256044] For the equivalence class of patterns, {{[1, 3, 2], [2, 1, 3, 4]}, {[2, 1, 3], [1, 2, 4, 3]}, {[2, 3, 1], [4, 3, 1, 2]}, {[3, 1, 2], [3, 4, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[2, 1], {[0, 1, 2]}, {1}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[1, 2, 1], {[0, 1, 1, 1], [0, 0, 2, 0], [0, 2, 1, 0], [0, 0, 1, 2]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 2]}, {2}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {2}], [[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, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[1, 2, 3, 1], {[0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0]}, {}], [[2, 3, 4, 2, 1], {[0, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 2], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0]}, {2, 4}], [[1, 2, 3, 1, 4], { [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 2, 0, 0], [0, 0, 2, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 0, 1]}, {1, 2, 3, 4, 5}], [ [1, 2, 3, 1, 1], {[0, 0, 0, 2, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 2, 0]}, {4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], {[0, 0, 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, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 274, 1721, 10672, 65863, 405528, 2494257, 15333762] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5534, 80588, 1141097, 16081128] For the equivalence class of patterns, {{[1, 3, 2], [2, 3, 4, 1]}, {[2, 1, 3], [4, 1, 2, 3]}, {[2, 3, 1], [1, 4, 3, 2]}, {[3, 1, 2], [3, 2, 1, 4]}} the member , {[1, 3, 2], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[2, 1], {}, {}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 1, 2, 0]}, {}], [[3, 2, 1], {}, {1}], [[2, 1, 2], {[0, 2, 0, 0]}, {1}], [[3, 1, 2], {[0, 2, 1, 0]}, {1}], [[2, 1, 1], {}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 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], {[0, 2, 1, 0, 0], [0, 1, 2, 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], {[1, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 0, 2, 1, 0], [0, 1, 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, 1, 2, 0], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0]}, {4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[2, 1, 3, 4], %6, {}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {2}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 2, 0], [0, 2, 0, 1, 0], [0, 1, 2, 1, 0]}, {}], [[3, 4, 2, 1], {[0, 1, 1, 2, 0]}, {}], [[3, 4, 1, 2], {[0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 3, 1, 4], %6, {}], [[1, 2, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], %4, {1, 2, 3, 4}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %5, {4, 5}], [[2, 3, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], %4, {1, 2, 3, 4}], [[3, 2, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], %5, {4, 5}], [[2, 1, 3, 4, 2], %2, {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], %3, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %4, {1, 2, 3, 4}], [[2, 3, 1, 4, 2], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 5, 4], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], %5, {4, 5}], [[3, 4, 1, 5, 2], %3, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], %5, {1, 2, 4}], [ [4, 5, 1, 2, 3], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {1, 2}], [[3, 4, 1, 2, 3], { [0, 1, 1, 0, 2, 0], [0, 1, 1, 2, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2}], [[3, 4, 1, 2, 5], %4, {3, 4}], [[3, 4, 1, 2, 1], {[0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 2, 1, 1, 0]}, {5}], [[4, 5, 1, 3, 2], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], {[0, 1, 1, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0]}, {4, 5}], [[4, 5, 2, 3, 1], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 2}], [[3, 4, 2, 1, 1], {[0, 1, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0]}, {4, 5}], [ [3, 4, 2, 1, 3], {[0, 1, 1, 0, 2, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0]}, {1, 2}], [[3, 4, 2, 1, 5], %4, {3, 4}], [[4, 5, 2, 1, 3], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 2}], [ [3, 4, 2, 1, 2], {[0, 1, 1, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0]}, {3}], [[4, 5, 3, 2, 1], {[0, 1, 1, 1, 2, 0]}, {3}], [[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}], [[3, 5, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], {[0, 2, 1, 1, 1, 0], [0, 1, 1, 1, 2, 0]}, {3}], [ [2, 3, 1, 2, 3], {[1, 1, 0, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 2, 0, 1, 0, 0]}, {1, 2, 4}], [[2, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 2, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0]}, {1, 2}], [ [2, 3, 1, 2, 4], {[0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0]}, {4}], [ [2, 3, 1, 2, 1], {[0, 0, 2, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 2, 1, 0, 1, 0], [0, 0, 1, 2, 1, 0]}, {5}], [[2, 3, 1, 2, 2], { [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 0, 2, 1, 0]}, {4, 5}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 0, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 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 := {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 249, 1457, 8536, 50008, 292969, 1716342, 10055091] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 4331, 54492, 679220, 8473557] For the equivalence class of patterns, {{[1, 3, 2], [3, 4, 1, 2]}, {[2, 1, 3], [3, 4, 1, 2]}, {[2, 3, 1], [2, 1, 4, 3]}, {[3, 1, 2], [2, 1, 4, 3]}} the member , {[1, 3, 2], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[2, 1], {}, {}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {}, {1}], [[2, 1, 2], {[0, 2, 0, 0]}, {1}], [[3, 1, 2], {[0, 2, 1, 0]}, {1}], [[2, 1, 1], {}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 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, 4], %3, {2, 3}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0]}, {4}], [[2, 3, 4, 1], %3, {}], [[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, 1, 2, 0], [0, 0, 2, 1, 0], [0, 1, 1, 1, 0]}, {4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[2, 1, 3, 4], %3, {1, 3}], [[3, 2, 4, 1], %3, {}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {2}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], %3, {1, 2}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 2, 1, 0], [0, 2, 1, 1, 0]}, {3, 4}] , [[2, 3, 1, 2], {[0, 1, 0, 2, 0], [0, 2, 0, 1, 0], [0, 1, 2, 1, 0]}, {4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], %3, {3}], [[2, 4, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[3, 4, 5, 1, 2], %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, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %2, {1, 2, 3}], [[2, 3, 5, 1, 4], %1, {1, 2, 3, 4, 5}], [ [2, 3, 4, 1, 4], {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {1, 2, 3, 5}] , [[3, 4, 5, 2, 1], %2, {4}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %2, {4}], [[3, 2, 4, 1, 5], %2, {1, 2, 3}], [[4, 3, 5, 1, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {1, 2, 3, 5}] , [[3, 2, 5, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 1], { [0, 1, 1, 1, 1, 0], [0, 0, 1, 1, 2, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0]}, {4, 5}], [[4, 2, 5, 1, 3], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]} %3 := {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 256, 1472, 8398, 47810, 272009, 1547247, 8800499] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 4554, 53476, 625442, 7313539] For the equivalence class of patterns, {{[1, 3, 2], [4, 1, 2, 3]}, {[2, 1, 3], [2, 3, 4, 1]}, {[2, 3, 1], [3, 2, 1, 4]}, {[3, 1, 2], [1, 4, 3, 2]}} the member , {[1, 3, 2], [4, 1, 2, 3]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 3, 0]}, {}], [[1, 2], {[0, 2, 0]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {2}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {1, 3}], [[2, 1, 1], {[0, 3, 1, 0], [0, 0, 3, 0]}, {2, 3}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 2, 0], [0, 1, 3, 0]}, {2}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0]}, {3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[2, 1, 2], {[0, 2, 0, 0]}, {1, 3}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 43, 286, 1872, 12171, 78885, 510576, 3302611, 21356691] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 374, 5952, 93180, 1439380, 22153962] Out of a total of , 24, cases 9, were successful and , 15, failed Success Rate: , 0.375 Here are the failures {{{[1, 2, 3], [2, 4, 1, 3]}, {[3, 2, 1], [3, 1, 4, 2]}}, { {[1, 2, 3], [2, 4, 3, 1]}, {[1, 2, 3], [4, 2, 1, 3]}, {[3, 2, 1], [1, 3, 4, 2]}, {[3, 2, 1], [3, 1, 2, 4]}}, {{[1, 2, 3], [3, 1, 4, 2]}, {[3, 2, 1], [2, 4, 1, 3]}}, {{[1, 2, 3], [3, 4, 1, 2]}, {[3, 2, 1], [2, 1, 4, 3]}}, { {[1, 2, 3], [3, 4, 2, 1]}, {[1, 2, 3], [4, 3, 1, 2]}, {[3, 2, 1], [1, 2, 4, 3]}, {[3, 2, 1], [2, 1, 3, 4]}}, {{[1, 2, 3], [4, 2, 3, 1]}, {[3, 2, 1], [1, 3, 2, 4]}}, { {[1, 3, 2], [2, 3, 1, 4]}, {[2, 1, 3], [1, 4, 2, 3]}, {[2, 3, 1], [4, 1, 3, 2]}, {[3, 1, 2], [3, 2, 4, 1]}}, { {[1, 3, 2], [3, 1, 2, 4]}, {[2, 1, 3], [1, 3, 4, 2]}, {[2, 3, 1], [4, 2, 1, 3]}, {[3, 1, 2], [2, 4, 3, 1]}}, { {[1, 3, 2], [3, 2, 1, 4]}, {[2, 1, 3], [1, 4, 3, 2]}, {[2, 3, 1], [4, 1, 2, 3]}, {[3, 1, 2], [2, 3, 4, 1]}}, { {[1, 3, 2], [3, 2, 4, 1]}, {[2, 1, 3], [4, 1, 3, 2]}, {[2, 3, 1], [1, 4, 2, 3]}, {[3, 1, 2], [2, 3, 1, 4]}}, { {[1, 3, 2], [3, 4, 2, 1]}, {[2, 1, 3], [4, 3, 1, 2]}, {[2, 3, 1], [1, 2, 4, 3]}, {[3, 1, 2], [2, 1, 3, 4]}}, { {[1, 3, 2], [4, 2, 1, 3]}, {[2, 1, 3], [2, 4, 3, 1]}, {[2, 3, 1], [3, 1, 2, 4]}, {[3, 1, 2], [1, 3, 4, 2]}}, { {[1, 3, 2], [4, 2, 3, 1]}, {[2, 1, 3], [4, 2, 3, 1]}, {[2, 3, 1], [1, 3, 2, 4]}, {[3, 1, 2], [1, 3, 2, 4]}}, { {[1, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3], [3, 4, 2, 1]}, {[2, 3, 1], [2, 1, 3, 4]}, {[3, 1, 2], [1, 2, 4, 3]}}, { {[1, 3, 2], [4, 3, 2, 1]}, {[2, 1, 3], [4, 3, 2, 1]}, {[2, 3, 1], [1, 2, 3, 4]}, {[3, 1, 2], [1, 2, 3, 4]}}}