Warning, the protected name Chi has been redefined and unprotected There all together, 103, different equivalence classes For the equivalence class of patterns, { {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, {[2, 1, 3], [3, 2, 1], [2, 3, 4, 1], [4, 1, 2, 3]}, {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [3, 2, 1, 4]}, {[1, 3, 2], [3, 2, 1], [2, 3, 4, 1], [4, 1, 2, 3]}} the member , {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 3, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], %9, {}], [[1, 3, 2], %9, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [ [2, 1, 1], {[0, 0, 2, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], %9, {}], [[2, 1, 3], {[0, 1, 3, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {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, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 3, 1], %7, {}], [[1, 3, 2, 1], %8, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], %7, {1}], [[2, 1, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 3, 1], %8, {2}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1}], [[3, 2, 4, 1], %7, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %8, {3, 4}], [[3, 4, 2, 1], %7, {}], [[3, 2, 1, 1], %8, {3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], %7, {}], [[2, 5, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %5, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %6, {1, 2, 3, 4}], [[2, 4, 3, 1, 1], %1, {4, 5}], [[3, 5, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 2, 5, 1, 3], %3, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], %5, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %6, {1, 2, 3, 4}], [[3, 2, 5, 1, 4], %3, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %3, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 1], %1, {4, 5}], [[3, 2, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %3, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], %5, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %6, {1, 2, 3, 4}], [[3, 5, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], %1, {4, 5}], [[3, 4, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], %6, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], %1, {4, 5}], [ [2, 4, 3, 2, 1], {[0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 4}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 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, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {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 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} %2 := {[0, 1, 0, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 1, 0, 1, 0]} %6 := {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]} %7 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %8 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} %9 := {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 21, 21, 21, 21, 21, 21, 21] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 96, 96, 96, 96] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [2, 1, 4, 3], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1], [3, 4, 1, 2]}, {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [2, 1, 4, 3]}, {[1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 1, 2, 3]}} the member , {[2, 3, 1], [3, 1, 2], [2, 1, 4, 3], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 0, 1], [2, 1, 0]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 3, 1]}, {1}], [[2, 1], {[0, 2, 0], [1, 1, 1]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {3}], [ [2, 1, 1], {[0, 0, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[3, 2, 4, 1], {[0, 1, 1, 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, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {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]}, {}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 1, 3, 5, 4], %2, {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, 2, 4, 5, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %2, {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]}, {3, 4}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[5, 4, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[3, 2, 1, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], { [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 30, 41, 52, 63, 74, 85, 96] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 160, 227, 294, 361] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [4, 1, 2, 3]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 3, 1, 2]}, {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4], [2, 3, 4, 1]}} the member , {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [4, 1, 2, 3]}, has a scheme of depth , 5 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, 2], {[1, 1, 0], [0, 2, 1]}, {}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {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, 4, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2}], [[1, 3, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2} ], [[1, 3, 2, 2], {[0, 2, 0, 2, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 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}], [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], { [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0]}, {}], [[3, 1, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {2}], [[4, 1, 2, 3], {[0, 1, 1, 1, 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, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 1], {[1, 0, 2, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 2, 1, 1, 0]}, {1, 2}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 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, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], { [0, 1, 1, 1, 1, 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]}, {1}], [ [1, 4, 3, 2, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1, 2}], [[1, 4, 3, 2, 1], %2, {1, 2, 3}], [[1, 4, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1], [0, 2, 0, 2, 1, 0], [0, 1, 0, 3, 1, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[1, 5, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], { [0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [1, 1, 1, 1, 1, 0]}, {2, 3}], [[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], %2, {1, 2, 3, 5}], [[5, 1, 4, 3, 2], {[0, 1, 1, 1, 1, 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]}, {3, 4}], [[4, 1, 3, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], %2, {1, 2, 3, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {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}], [[4, 3, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], { [0, 1, 1, 1, 1, 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]}, {1, 2, 4}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 7, 8, 9, 10, 11, 12] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 35, 51, 72, 97, 126, 159, 196] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 242, 475, 836, 1350] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [2, 4, 3, 1]}, {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [4, 2, 1, 3]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2, 4], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [4, 3, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[1, 2], {[1, 3, 0], [2, 2, 0], [0, 4, 0], [3, 1, 0], [0, 2, 1]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1], [2, 1, 0]}, {}], [ [1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 2], {[1, 3, 0, 0], [2, 2, 0, 0], [0, 4, 0, 0], [3, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[1, 3, 2], {[2, 1, 1, 0], [1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[1, 2, 3], {[0, 1, 2, 1], [0, 2, 1, 0], [3, 1, 1, 0], [2, 1, 2, 0], [1, 1, 3, 0], [0, 1, 4, 0]}, {}], [[2, 3, 1], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3} ], [ [2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 3} ], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], { [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [1, 1, 2, 1, 0], [2, 1, 1, 1, 0], [0, 1, 3, 1, 0]}, {2}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1]}, {2}], [ [1, 2, 3, 3], {[0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [3, 1, 1, 0, 0], [2, 1, 2, 0, 0], [1, 1, 3, 0, 0]}, {3, 4} ], [[1, 2, 3, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {1, 2} ], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {1, 2, 3}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {3, 4}], [[1, 3, 2, 3], { [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {1, 4}], [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[2, 4, 3, 1], %1, {1, 2, 3}], [[1, 4, 3, 2], %1, {1}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], %1, {1, 2, 3}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}]] %1 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 22, 22, 22, 22, 22, 22, 22] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 86, 86, 86, 86] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [4, 3, 1, 2]}, {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4], [3, 4, 2, 1]}} the member , {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 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, 2], {[1, 1, 0], [0, 2, 1]}, {}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[0, 2, 2, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 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], {[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, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {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, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 3, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[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, 3, 2, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[1, 3, 2, 2], {[0, 2, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 4, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[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}], [[3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {1}], [[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, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {2}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 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, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {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, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 44, 20, 20, 20, 20, 20, 20] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 430, 70, 70, 70] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}} the member , {[1, 2, 3], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 4], [5, 0], [3, 1]}, {}], [[1, 1], {[0, 2, 2], [0, 0, 4], [0, 1, 3], [0, 4, 0], [3, 1, 0], [5, 0, 0], [3, 0, 1], [0, 3, 1] }, {1, 2}], [[1, 2], {[1, 1, 0], [0, 1, 1], [0, 4, 0]}, {}], [[2, 1], {[0, 4, 0], [2, 1, 0], [0, 2, 1], [0, 1, 4]}, {}], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 4, 0], [1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 3, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 1], {[0, 0, 1, 4], [0, 0, 4, 0], [0, 1, 3, 0], [2, 0, 1, 0], [0, 1, 1, 2], [0, 2, 1, 0], [0, 0, 2, 1]}, {2, 3}], [ [2, 1, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[3, 2, 1], {[0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 4, 0]}, {}], [[3, 1, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}], [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {2, 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}], [[2, 4, 3, 1], {[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, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 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}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 2, 1, 1], {[0, 0, 1, 2, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 4, 0]}, {3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[4, 2, 1, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[2, 5, 4, 3, 1], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %5, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %5, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %2, {4, 5}], [[1, 4, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %4, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 3, 0, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 2], %2, {1, 3, 4}], [[2, 1, 5, 4, 3], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[2, 1, 5, 3, 4], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %3, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %5, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[5, 1, 4, 2, 3], %5, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %5, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %5, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %5, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %5, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], %3, {1, 2, 3, 4, 5}], [[5, 3, 2, 4, 1], %5, {1, 2, 3, 4, 5}], [[5, 2, 1, 3, 4], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 5], %5, {1, 2, 3, 4, 5}], [[5, 3, 1, 4, 2], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 3, 0, 1, 0]}, {4, 5}], [[4, 2, 1, 3, 4], %4, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], { [0, 1, 1, 1, 1, 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, 3}], [[4, 2, 1, 3, 1], %3, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 2], %2, {1, 2}], [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 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], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 3, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 14, 5, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 35, 7, 1, 0] For the equivalence class of patterns, { {[2, 1, 3], [3, 2, 1], [1, 3, 4, 2], [3, 4, 1, 2]}, {[1, 2, 3], [2, 3, 1], [2, 1, 4, 3], [4, 2, 1, 3]}, {[1, 3, 2], [3, 2, 1], [3, 1, 2, 4], [3, 4, 1, 2]}, {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3], [2, 4, 3, 1]}} the member , {[2, 1, 3], [3, 2, 1], [1, 3, 4, 2], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 0, 1], [2, 1, 0]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 1]}, {2}], [[1, 2], {[2, 1, 0], [0, 2, 1], [1, 2, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [ [1, 2, 2], {[2, 1, 0, 0], [0, 2, 1, 0], [1, 2, 0, 0], [0, 2, 0, 1]}, {2, 3} ], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 3], {[1, 1, 2, 0], [2, 1, 1, 0], [0, 1, 2, 1], [0, 2, 1, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [1, 1, 2, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {1, 2}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [2, 1, 1, 1, 0], [0, 1, 1, 2, 1], [1, 1, 1, 2, 0]}, {}], [[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], {[0, 1, 1, 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, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1}], [ [1, 2, 3, 4, 5], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 2, 1, 1, 1, 0]}, {2, 3}], [[1, 2, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3, 5, 4], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 1], [0, 1, 1, 2, 1, 0], [0, 1, 2, 1, 0, 0], [0, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0], [1, 1, 1, 2, 0, 0]}, {4, 5}], [ [2, 3, 4, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 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, 5, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 6, 7, 8, 9, 10, 11] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 30, 47, 68, 93, 122, 155, 192] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 223, 458, 819, 1333] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [3, 1, 2, 4], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1], [1, 3, 4, 2], [2, 3, 4, 1]}, {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [4, 2, 1, 3]}} the member , {[2, 3, 1], [3, 2, 1], [3, 1, 2, 4], [4, 1, 2, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[2, 1], [3, 0]}, {}], [[1, 2], {[1, 1, 0], [0, 4, 0], [0, 3, 1]}, {1}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 2, 1]}, {2}], [[1, 1], {[3, 0, 0], [2, 0, 1], [2, 1, 0]}, {1, 2}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 10, 16, 26, 42, 68, 110] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 70, 230, 716, 2282, 7198, 22808, 72126] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 924, 5950, 37564, 239246] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [2, 3, 1, 4], [4, 1, 2, 3]}, {[2, 1, 3], [3, 2, 1], [1, 4, 2, 3], [2, 3, 4, 1]}, {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [3, 2, 4, 1]}, {[1, 2, 3], [2, 3, 1], [3, 2, 1, 4], [4, 1, 3, 2]}} the member , {[2, 1, 3], [3, 2, 1], [1, 4, 2, 3], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 0, 2], [1, 2, 0]}, {1, 2}], [[1, 2], {[0, 2, 2], [0, 3, 0], [1, 1, 1], [1, 2, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[0, 2, 2, 0], [0, 2, 1, 1], [0, 2, 0, 2], [0, 3, 0, 0], [1, 1, 1, 0], [1, 2, 0, 0], [1, 1, 0, 1]}, {2, 3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [[2, 3, 1], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 1, 2, 2], [0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 2, 1, 1], [1, 1, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 2, 0, 0], [0, 3, 1, 0, 0], [0, 2, 1, 1, 0], [0, 2, 1, 0, 1], [0, 1, 2, 1, 1], [0, 1, 2, 0, 2], [1, 1, 1, 0, 0], [0, 1, 2, 2, 0]}, {3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[1, 2, 3, 4], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 3, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {}], [ [1, 3, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 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}], [[3, 4, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {3}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 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, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[1, 2, 3, 4, 4], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 3, 1, 0, 0], [0, 1, 2, 2, 0, 0], [0, 1, 1, 3, 0, 0], [0, 1, 2, 1, 0, 1]}, {4, 5}], [[1, 3, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {2}], [[2, 3, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [ [1, 2, 3, 4, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 4, 5, 3], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[1, 2, 3, 4, 5], {[0, 1, 2, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2}], [[1, 4, 5, 3, 2], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[1, 3, 5, 2, 4], %3, {1, 2, 3, 4, 5}], [[2, 4, 5, 3, 1], %3, {1, 2, 3, 4, 5}], [[1, 4, 5, 2, 3], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 2, 5], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1}], [[2, 3, 4, 2, 1], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 3, 1, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {1, 4, 5}], [ [1, 3, 4, 1, 2], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4}], [[1, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], {[0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 1, 0], [0, 2, 1, 0, 0, 0], [0, 1, 3, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 0, 1, 1, 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, 4, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 15, 14, 14, 14, 14, 14, 14] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 43, 41, 41, 41] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [2, 1, 4, 3]}, {[1, 2, 3], [1, 3, 2], [3, 4, 1, 2], [4, 3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 1, 4, 3]}} the member , {[2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [2, 1, 4, 3]}, has a scheme of depth , 2 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 0, 2], [1, 2, 0]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 2]}, {2}], [[1, 2], {[0, 2, 2], [1, 1, 0]}, {1}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 50, 84, 126, 176, 234, 300, 374] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 420, 890, 1612, 2640] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [3, 1, 2, 4]}, {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [4, 2, 3, 1]}, {[3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [1, 3, 4, 2]}} the member , {[1, 2, 3], [1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1]}, 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, 3, 0], [0, 2, 1], [0, 1, 2], [1, 2, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 2, 3}], [ [3, 2, 1], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 1, 2], [0, 1, 2, 0]}, {2} ], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 1, 1, 0], [1, 0, 2, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 66, 132, 222, 336, 474, 636, 822] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 798, 2510, 5824, 11280] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4], [4, 1, 2, 3]}, {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [3, 4, 2, 1]}, {[2, 1, 3], [3, 2, 1], [1, 2, 4, 3], [2, 3, 4, 1]}, {[1, 2, 3], [2, 3, 1], [3, 2, 1, 4], [4, 3, 1, 2]}} the member , {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4], [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], {[0, 3, 0], [1, 1, 0], [0, 1, 2]}, {}], [[1, 2], {[0, 2, 0], [3, 1, 0]}, {}], [[1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [3, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 1, 2], [1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[2, 1, 1], {[0, 3, 1, 0], [1, 0, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0], [0, 1, 1, 1, 2]}, {2}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [3, 1, 1, 0, 0]}, {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, 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, 2, 0], [0, 0, 1, 1, 2], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {}], [[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, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[3, 1, 2, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 2, 3], {[0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [[3, 1, 2, 5, 4], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 5, 2], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 2], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 1], %2, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2}], [[3, 5, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], { [0, 1, 1, 1, 1, 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]}, {1, 2}], [ [1, 2, 3, 1, 4], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [[1, 3, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1}], [ [2, 3, 1, 2, 2], {[0, 1, 0, 0, 1, 2], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0]}, {1}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 0, 2], [0, 1, 1, 2, 0, 0], [0, 1, 2, 0, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 1, 0, 1, 1], [0, 2, 1, 0, 0, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 0, 1, 1, 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, 4, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 17, 16, 16, 16, 16, 16, 16] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 49, 47, 47, 47] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}} the member , {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [1, 3], [0, 5], [3, 1]}, {}], [[1, 1], { [1, 1, 2], [1, 0, 3], [0, 0, 5], [4, 0, 0], [1, 3, 0], [3, 1, 0], [0, 4, 1], [0, 3, 2], [0, 2, 3], [0, 1, 4], [0, 5, 0], [1, 2, 1], [3, 0, 1]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 3], [0, 4, 0], [0, 3, 1]}, {}], [[1, 2], {[1, 1, 0], [0, 1, 3], [0, 4, 0], [0, 3, 1]}, {}], [[1, 2, 2], { [0, 1, 3, 0], [0, 4, 0, 0], [0, 3, 1, 0], [0, 3, 0, 1], [0, 1, 2, 1], [1, 1, 0, 0], [0, 1, 1, 2], [0, 1, 0, 3]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 4, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 0, 3, 1], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3]}, {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]}, {}] , [[1, 2, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[0, 1, 3, 0], [0, 4, 0, 0], [0, 3, 1, 0], [0, 3, 0, 1], [0, 1, 2, 1], [1, 1, 0, 0], [0, 1, 1, 2], [0, 1, 0, 3]}, {1, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 4, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 0, 3, 1], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 3], [0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %7, {3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2, 4}], [[1, 2, 4, 3], %6, {}], [[1, 3, 2, 3], %7, {2, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [0, 1, 0, 2, 1], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3]}, {3, 4} ], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], %6, {}], [[1, 3, 2, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %7, {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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[2, 1, 4, 3], %6, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], %7, {1, 4}], [[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}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [0, 1, 0, 2, 1], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3]}, {3, 4} ], [[3, 1, 2, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {}], [[4, 1, 2, 3], %6, {}], [[1, 2, 4, 3, 2], %5, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], %4, {4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], { [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[1, 3, 2, 4, 2], %5, {1, 2, 3, 4, 5}], [[1, 4, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [[1, 4, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %4, {2}], [[1, 4, 2, 3, 2], %5, {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}], [[1, 4, 2, 3, 5], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 4], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], %4, {4, 5}], [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %3, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], %5, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], %4, {4, 5}], [[2, 1, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [[3, 1, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], %5, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %4, {1}], [ [3, 1, 2, 4, 4], {[0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 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, 4, 5}], [[4, 1, 2, 3, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %5, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], %4, {4, 5}], [[5, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 0, 0]} %4 := {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]} %5 := {[0, 1, 0, 1, 1, 0]} %6 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %7 := {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 2, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 33, 6, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 182, 20, 0, 0] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1], [4, 3, 1, 2]}, {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 1, 3, 4]}, {[1, 2, 3], [2, 1, 3], [3, 4, 2, 1], [4, 3, 1, 2]}} the member , {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [2, 1, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3], [2, 2]}, {}], [[1, 1], { [1, 1, 2], [1, 0, 3], [2, 1, 1], [1, 3, 0], [2, 2, 0], [1, 2, 1], [2, 0, 2] }, {1, 2}], [[2, 1], {[0, 2, 2], [1, 1, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 2, 2], [1, 1, 0]}, {}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 2], {[0, 2, 2, 0], [0, 2, 1, 1], [1, 1, 0, 0], [0, 2, 0, 2]}, {2, 3} ], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 1], { [0, 2, 2, 0], [0, 1, 3, 0], [0, 2, 1, 1], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 2, 2], [0, 0, 1, 3]}, {2, 3}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3} ], [[3, 1, 2], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {2, 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, 3, 2, 3], {[0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {2, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 0, 1, 2], [1, 1, 0, 1, 0]}, {3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 2]}, {}], [[1, 3, 2, 4], %5, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [2, 1, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[2, 1, 4, 3], %5, {}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {1, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 0, 1, 2], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 1, 2]}, {}], [[3, 1, 2, 4], %5, {}], [[1, 2, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 5, 4], %3, {1, 2, 3, 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, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 4, 2, 5, 3], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %3, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %3, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [ [1, 5, 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, 3, 4}], [[1, 4, 2, 3, 5], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[1, 4, 2, 3, 4], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 2, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {2}], [[1, 4, 2, 3, 2], %2, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], { [0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 2, 0, 1, 0]}, {4, 5}], [[1, 4, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 5, 2], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], { [0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 2, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1}], [[4, 1, 2, 3, 2], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 5], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[4, 1, 2, 3, 3], {[0, 1, 1, 1, 1, 1], [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 2, 0, 1, 0]}, {4, 5}], [[5, 1, 2, 4, 3], %3, {1, 2, 3, 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]}, {2, 3, 4}], [[4, 1, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], { [1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], %2, {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], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 3, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {1, 2, 4, 5}], [[2, 1, 4, 2, 3], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4}], [[3, 2, 4, 3, 1], %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, 0, 1, 1, 1, 0]} %5 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 6, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 26, 19, 19, 19, 19, 19, 19] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 121, 69, 69, 69] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [4, 3, 1, 2]}, {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [2, 1, 3, 4]}, {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 3, 1, 4]}, {[1, 2, 3], [2, 1, 3], [3, 4, 2, 1], [4, 1, 3, 2]}} the member , {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [2, 1, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3]}, {}], [[1, 1], {[1, 1, 2], [1, 0, 3], [1, 3, 0], [1, 2, 1]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 2, 3]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 3, 1, 0], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3], [0, 0, 3, 0]}, {1}] , [[1, 2, 2], {[0, 2, 1, 2], [0, 2, 0, 3], [1, 1, 0, 0], [0, 3, 0, 0], [0, 2, 3, 0], [0, 2, 2, 1]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 0, 0], [0, 1, 1, 2], [0, 1, 0, 3], [0, 3, 0, 0]}, {3}] , [[2, 1, 1], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3]}, {2, 3}], [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 1, 3], [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, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 2], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3]}, {1, 2}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [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}], [[2, 1, 3, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}] , [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3], [0, 1, 1, 3, 0]}, {3, 4}], [[3, 1, 2, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {2, 3}], [[3, 1, 2, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [1, 1, 1, 0, 0], [0, 1, 1, 0, 3], [0, 1, 1, 3, 0]}, {}], [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[1, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 0, 1, 2, 1], [0, 1, 1, 1, 0, 2], [0, 1, 0, 1, 1, 2], [0, 1, 1, 1, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 2, 1, 0, 0], [0, 1, 0, 1, 0, 3]}, {1, 2, 3, 4, 5}], [ [3, 1, 2, 3, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 0, 1], [0, 2, 1, 0, 0, 0], [0, 1, 1, 1, 0, 2], [0, 1, 1, 0, 1, 2], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 1, 1, 0, 3, 0], [0, 1, 3, 0, 0, 0], [0, 1, 1, 0, 0, 3], [1, 1, 1, 0, 0, 0], [0, 1, 1, 3, 0, 0], [0, 1, 1, 0, 2, 1]}, {4, 5}], [[3, 1, 2, 3, 4], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 3, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 1, 1, 0]}, {2, 3, 4}], [ [4, 1, 2, 4, 3], {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 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, 4, 6, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 37, 39, 34, 34, 34, 34, 34] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 254, 218, 169, 169] For the equivalence class of patterns, { {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3], [0, 5], [3, 0]}, {}], [[1, 1], {[1, 1, 2], [1, 0, 3], [0, 0, 5], [3, 0, 0], [1, 3, 0], [0, 4, 1], [0, 3, 2], [0, 2, 3], [0, 1, 4], [0, 5, 0], [1, 2, 1]}, {1, 2}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {2}], [[1, 2], {[1, 1, 2], [0, 2, 2], [0, 1, 3], [0, 4, 0], [3, 1, 0], [1, 2, 0]}, {}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [[1, 2, 2], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 4, 0, 0], [3, 1, 0, 0], [1, 1, 1, 1], [0, 2, 1, 1], [0, 1, 2, 1], [1, 1, 0, 2], [0, 2, 0, 2], [0, 1, 1, 2], [0, 1, 0, 3], [1, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [1, 2, 1, 0], [0, 1, 1, 1], [0, 4, 1, 0], [3, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {2, 3}], [[1, 3, 4, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {1}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [1, 1, 2, 0, 0], [0, 2, 2, 0, 0], [1, 2, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 4, 1, 0, 0], [3, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[1, 2, 4, 3], %3, {}], [[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, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {4}], [[1, 3, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 4, 2, 3], %3, {}], [[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, 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, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], %3, {}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[1, 2, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %2, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[2, 3, 5, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 2], %1, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], %2, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 5], %2, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %2, {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, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 5, 2, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 12, 2, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 29, 2, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}} the member , {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[5, 0], [0, 3], [3, 2]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [3, 1, 1], [3, 0, 2], [0, 1, 2], [5, 0, 0], [3, 2, 0] }, {1, 2}], [[2, 1], {[0, 1, 1], [1, 3, 0], [0, 4, 0], [3, 1, 0]}, {}], [[1, 2], {[0, 3, 0], [0, 1, 1], [3, 2, 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}], [ [1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0], [3, 2, 0, 0]}, {2, 3} ], [[2, 3, 1], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 4, 1, 0], [3, 1, 1, 0], [1, 3, 1, 0]}, {}] , [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {3}], [[2, 1, 1], {[1, 0, 3, 0], [0, 0, 4, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}] , [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 4}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 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}], [[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}], [[2, 4, 3, 1], %5, {}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [1, 0, 3, 1, 0], [0, 0, 4, 1, 0], [3, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[3, 4, 2, 1], %5, {1, 2}], [[2, 3, 1, 2], { [0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {2, 4}], [[4, 1, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 3, 1], %5, {}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2, 4}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 5, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], { [0, 1, 1, 1, 1, 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]}, {1}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 4, 3, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %2, {2}], [[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, 3], %3, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], { [0, 1, 1, 1, 1, 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, 3}], [[4, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %3, {1, 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}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 0, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 5, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 31, 15, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 143, 45, 1, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [3, 1, 2, 4]}, {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [4, 3, 2, 1]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 3, 4, 2]}} the member , {[1, 2, 3], [1, 3, 2], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[5, 0], [0, 2]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {1}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2], [5, 0, 0]}, {1, 2}], [[2, 1], {[0, 3, 0], [3, 1, 0], [0, 2, 1], [0, 1, 2]}, {}], [[2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {3}], [[2, 1, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 1, 2], [1, 1, 1, 0], [0, 1, 2, 0]}, {}] , [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[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], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [3, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[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], { [3, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[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, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[3, 2, 1, 1], { [0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {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}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3}], [ [4, 3, 5, 1, 2], {[0, 1, 1, 1, 1, 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]}, {3}], [[3, 2, 4, 1, 2], %2, {1, 2, 3}], [ [3, 2, 4, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 2, 3, 1, 2], %2, {2}], [[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, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], { [0, 1, 1, 1, 1, 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, 3}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {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}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 4, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 33, 10, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 176, 26, 1, 0] For the equivalence class of patterns, { {[2, 1, 3], [3, 2, 1], [1, 2, 4, 3], [3, 4, 1, 2]}, {[1, 2, 3], [2, 3, 1], [2, 1, 4, 3], [4, 3, 1, 2]}, {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3], [3, 4, 2, 1]}, {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4], [3, 4, 1, 2]}} the member , {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 2]}, {}], [[1, 1], {[2, 1, 1], [2, 2, 0], [2, 0, 2]}, {1, 2}], [[1, 2], {[0, 1, 1], [2, 1, 0]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 2]}, {}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {2, 3}], [[1, 3, 2], {[2, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 2, 3}], [[2, 1, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[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, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {3, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {2, 3}], [[1, 3, 2, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 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], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {2, 3}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {}], [[2, 5, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[2, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 5}], [[4, 3, 1, 5, 2], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [[3, 2, 1, 5, 4], %3, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [0, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 2, 1, 4, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1}], [[2, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [2, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 1, 0]}, {4, 5}], [ [2, 1, 3, 2, 1], {[0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1}], [[3, 2, 1, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], {[0, 1, 1, 0, 1, 0], [2, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[4, 3, 1, 4, 2], {[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, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 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, 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], [2, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [ [2, 4, 3, 2, 1], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 0, 1, 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, 4, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 15, 14, 14, 14, 14, 14, 14] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 43, 41, 41, 41] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1], [4, 1, 2, 3]}} the member , {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 0, 1], [2, 1, 0]}, {1, 2}], [[2, 1], {[0, 2, 0], [1, 1, 1]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0]}, {}], [[1, 2, 2], {[1, 1, 0, 0], [0, 3, 0, 0]}, {2, 3}], [[2, 3, 1], {[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, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1]}, {2, 3} ], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 3, 0], [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, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {1, 4}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {2, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[2, 1, 3, 1], {[0, 0, 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, 3, 0]}, {1, 2}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 4, 3, 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, 4}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[1, 2, 5, 4, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4, 5}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %2, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4, 5}], [[2, 1, 4, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[2, 1, 4, 3, 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, 4}], [[5, 4, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[3, 2, 1, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], { [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 9, 14, 22, 35, 56, 90] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 54, 161, 518, 1622, 5151, 16268, 51514] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 663, 3816, 25403, 157774] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [4, 2, 3, 1]}, {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 3, 4, 1]}, {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [4, 2, 3, 1]}} the member , {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[2, 1], {[0, 3, 0], [2, 2, 0], [0, 2, 1], [0, 1, 2]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [2, 2, 1, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[2, 0, 2, 0], [0, 1, 1, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [3, 2, 1], {[1, 1, 2, 0], [0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 1, 1, 1], [2, 2, 1, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[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], %8, {3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[2, 3, 1, 3], %8, {2}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], %7, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [2, 0, 2, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 2, 1], { [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0]}, {}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], %8, {1}], [ [3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[4, 3, 1, 2], %7, {1, 2}], [ [3, 2, 1, 1], {[0, 0, 3, 1, 0], [1, 0, 1, 2, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [2, 0, 2, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4} ], [[4, 3, 2, 1], {[0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 1, 2, 1, 0], [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0]}, {}], [[4, 2, 1, 3], %7, {}], [[4, 2, 5, 1, 3], %5, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 1, 4], %5, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], %6, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %5, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 5, 1, 2], %3, {1, 2, 3}], [[4, 3, 5, 2, 1], %4, {1, 3}], [[3, 2, 4, 1, 2], %2, {1, 2, 3, 5}], [[3, 4, 2, 1, 5], %5, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %5, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 4], %6, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %3, {1, 2}], [[3, 4, 2, 1, 3], %1, {1}], [[4, 5, 3, 2, 1], %4, {1, 2}], [[4, 5, 3, 1, 2], %3, {1, 2, 3}], [[3, 4, 2, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [1, 0, 1, 2, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[3, 4, 2, 1, 2], %2, {1, 2, 3}], [[5, 3, 2, 4, 1], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], %1, {4, 5}], [[5, 2, 1, 3, 4], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 5], %5, {1, 2, 3, 4, 5}], [[5, 3, 1, 4, 2], %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, 4], %6, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], %5, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %6, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 2, 0], [1, 0, 1, 2, 1, 0], [0, 0, 2, 2, 1, 0], [0, 0, 1, 3, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[5, 4, 3, 2, 1], %4, {1, 2}], [[5, 4, 3, 1, 2], %3, {1, 2, 3}], [[5, 4, 2, 1, 3], %3, {1, 2}], [[4, 3, 2, 1, 2], %2, {1, 2, 3}], [[4, 3, 2, 1, 3], %1, {2}]] %1 := {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 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]} %4 := {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]} %5 := {[0, 1, 1, 1, 1, 0]} %6 := {[0, 1, 1, 1, 0, 0]} %7 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %8 := {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 9, 9, 9, 9, 9] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 57, 106, 120, 120, 120, 120, 120] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 677, 1791, 1932, 1932] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 1, 3, 2]}, {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 1, 3], [2, 3, 1], [1, 4, 2, 3], [4, 1, 2, 3]}} the member , {[1, 3, 2], [3, 1, 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], {[0, 2, 0]}, {}], [[1, 2], {[0, 2, 0], [1, 1, 1]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [1, 2, 1], {[0, 0, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1]}, {1, 3} ], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {1, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 1], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 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], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 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]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 0, 1], [0, 1, 2, 0, 0]}, {3, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 1, 3, 2], {[0, 1, 0, 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]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 0, 1], [0, 1, 2, 0, 0]}, {1}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [1, 1, 1, 1, 1]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}] , [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 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, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %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, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 35, 54, 77, 104, 135, 170, 209] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 242, 480, 844, 1361] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [2, 3, 1, 4], [3, 4, 1, 2]}, {[2, 1, 3], [3, 2, 1], [1, 4, 2, 3], [3, 4, 1, 2]}, {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3], [3, 2, 4, 1]}, {[1, 2, 3], [2, 3, 1], [2, 1, 4, 3], [4, 1, 3, 2]}} the member , {[1, 3, 2], [3, 2, 1], [2, 3, 1, 4], [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, 0]}, {}], [[2, 1], {[1, 1, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[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], {[0, 2, 0, 0], [2, 1, 0, 0]}, {2, 3}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[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, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {2, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}] , [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 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, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 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]}, {}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}] , [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [ [2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %5, {1}], [[1, 2, 3, 4, 3], %3, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [0, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0]}, {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], [0, 2, 1, 1, 1, 0]}, {2, 3, 4}], [[2, 1, 3, 5, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %3, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 3, 4}], [[2, 1, 3, 4, 1], %5, {2}], [[2, 3, 4, 1, 1], %5, {4, 5}], [[2, 3, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 2], %4, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], %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, 2], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 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]}, {4}], [[3, 1, 2, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[4, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 0, 1, 0]} %4 := {[0, 1, 0, 1, 1, 0]} %5 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 6, 7, 8, 9, 10, 11] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 14, 16, 18, 20, 22, 24, 26] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 41, 44, 47, 50] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [3, 4, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [4, 1, 3, 2]}, {[2, 1, 3], [2, 3, 1], [1, 4, 2, 3], [4, 3, 1, 2]}, {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4], [3, 2, 4, 1]}} the member , {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0], [2, 1, 0]}, {}], [[2, 1], {[0, 2, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0]}, {3}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {1}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[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, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 4}], [[1, 2, 3, 3], %3, {3, 4}], [[2, 3, 4, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 4], %4, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 1, 3, 3], %3, {3, 4}], [[2, 1, 3, 4], %4, {}], [[3, 2, 1, 4], %4, {1, 2}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], %3, {1}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}] , [[2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %2, {1}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [0, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0]}, {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], [0, 2, 1, 1, 1, 0]}, {2, 3, 4}], [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], %2, {2}], [ [3, 2, 4, 5, 1], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[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]}, {1, 3, 4}], [ [2, 1, 3, 4, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [0, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0]}, {4, 5}], [[2, 3, 4, 1, 1], %2, {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, 5, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %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}], [[3, 4, 5, 2, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} %3 := {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [2, 1, 1, 0, 0]} %4 := {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 26, 32, 38, 44, 50, 56, 62] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 94, 106, 118, 130] For the equivalence class of patterns, { {[1, 2, 3], [3, 2, 1], [3, 1, 4, 2], [3, 4, 1, 2]}, {[1, 2, 3], [3, 2, 1], [2, 1, 4, 3], [2, 4, 1, 3]}} the member , {[1, 2, 3], [3, 2, 1], [3, 1, 4, 2], [3, 4, 1, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 1], [3, 0], [0, 3]}, {}], [[1, 1], { [3, 0, 0], [0, 3, 0], [2, 0, 1], [2, 1, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2] }, {1, 2}], [[1, 2], {[0, 3, 0], [0, 1, 1], [2, 1, 0]}, {}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 1, 3], [0, 2, 1]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [ [1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0], [2, 1, 0, 0]}, {2, 3} ], [[2, 3, 1], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 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, 1], {[1, 0, 1, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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}], [[2, 4, 3, 1], {[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, 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, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 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, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 6, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 20, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [4, 2, 1, 3]}, {[3, 1, 2], [3, 2, 1], [1, 3, 4, 2], [2, 3, 1, 4]}, {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [4, 1, 3, 2]}, {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [3, 1, 2, 4]}} the member , {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 0, 2], [1, 2, 0]}, {1, 2}], [[1, 2], {[0, 1, 1], [1, 2, 0]}, {}], [[2, 1], {[0, 3, 0], [0, 1, 1]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0], [0, 0, 3, 0]}, {1, 3} ], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [1, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {2, 3}], [ [2, 1, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0], [1, 2, 0, 0]}, {1, 3} ], [[3, 2, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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}], [[2, 4, 3, 1], {[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, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[1, 3, 2, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 9, 14, 22, 35, 56, 90] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 57, 164, 521, 1625, 5154, 16271, 51517] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 677, 3830, 25417, 157788] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [4, 3, 1, 2]}} the member , {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 0, 1], [2, 1, 0]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2], {[2, 1, 0], [1, 2, 1], [0, 3, 1]}, {}], [[1, 3, 2], {[2, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 2], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 3, 0, 1], [1, 2, 0, 1], [2, 1, 0, 0]}, {2, 3}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[2, 1, 1, 0], [1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [ [2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 3} ], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[1, 2, 3, 3], {[1, 2, 1, 0, 0], [0, 3, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {3, 4}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[1, 3, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 2, 3, 2], {[0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {1, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 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, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[1, 2, 4, 3, 3], {[0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [2, 1, 1, 0, 1, 0], [1, 2, 1, 0, 1, 0], [0, 3, 1, 0, 1, 0]}, {4, 5}], [[1, 2, 5, 3, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[1, 2, 4, 3, 5], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 3, 4}], [ [1, 2, 4, 3, 2], {[0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [1, 2, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0], [2, 1, 0, 1, 1, 0]}, {1}], [[1, 2, 4, 3, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 5, 4, 2], {[0, 1, 1, 1, 1, 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]}, {1, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 19, 13, 13, 13, 13, 13, 13] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 54, 22, 22, 22] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [1, 4, 2, 3]}, {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [4, 2, 3, 1]}, {[1, 2, 3], [2, 1, 3], [4, 1, 3, 2], [4, 2, 3, 1]}, {[3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 3, 1, 4]}} the member , {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [1, 4, 2, 3]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 0]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 2, 1]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 2], {[1, 1, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3} ], [ [1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 1], [0, 0, 3, 0]}, {1, 3} ], [[1, 2, 3], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {1, 3} ], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[1, 2, 3, 3], %1, {3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], %2, {1, 2}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 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], %2, {1, 2}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %1, {3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[2, 1, 4, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}] , [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], %2, {2, 3}], [[3, 1, 2, 3], %1, {1}]] %1 := {[0, 1, 3, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]} %2 := {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 3, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 44, 56, 68, 80, 92, 104, 116] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 430, 490, 550, 610] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [3, 1, 2, 4]}, {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [1, 3, 4, 2]}, {[2, 1, 3], [3, 1, 2], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 3, 2], [2, 3, 1], [4, 2, 1, 3], [4, 3, 1, 2]}} the member , {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [3, 1, 2, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 0, 2], [1, 2, 0]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[1, 3, 0], [0, 2, 1], [0, 1, 2]}, {}], [[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], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[2, 1, 1], {[1, 0, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2]}, {2, 3}], [ [3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2], [1, 3, 1, 0]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 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], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[3, 2, 1, 1], { [0, 0, 2, 1, 1], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [1, 0, 3, 1, 0], [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [ [4, 3, 2, 1], {[0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 2, 1, 1, 1], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {1}], [[4, 3, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 22, 26, 30, 34, 38, 42, 46] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 86, 92, 98, 104] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 3, 2], [3, 1, 2], [2, 3, 4, 1], [3, 4, 2, 1]}, {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4], [3, 2, 1, 4]}, {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [1, 4, 3, 2]}} the member , {[2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {1}], [[2, 1], {[0, 1, 1], [1, 2, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[3, 1, 2, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[4, 1, 2, 3], {[0, 1, 1, 1, 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, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[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, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], { [0, 1, 1, 1, 1, 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]}, {2, 3, 4}], [[4, 1, 3, 2, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {2}], [[5, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {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, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 33, 42, 51, 60, 69, 78, 87] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 182, 216, 250, 284] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [3, 2, 1, 4]}, {[1, 3, 2], [3, 1, 2], [2, 3, 4, 1], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [1, 4, 3, 2]}} the member , {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 2]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1}], [ [1, 2, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 4], {[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], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[2, 3, 4, 1], %4, {1, 2}], [[3, 1, 4, 2], {[0, 1, 1, 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, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {2, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[2, 1, 3, 4], %4, {3}], [[3, 2, 4, 1], %4, {}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [0, 1, 2, 0, 0]}, {2, 4}], [[2, 3, 1, 4], %4, {1, 2}], [[3, 4, 2, 1], %4, {}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 4}], [[4, 3, 2, 1], %4, {}], [[4, 2, 5, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %3, {1, 2, 3, 4}], [[3, 2, 5, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 1], %1, {4, 5}], [[3, 2, 4, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %3, {1, 2, 3, 4}], [[3, 5, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], %1, {4, 5}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], %3, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], %1, {4, 5}]] %1 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 1], [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 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [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, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 38, 38, 38, 38, 38, 38, 38] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 231, 231, 231, 231] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [2, 3, 4, 1], [3, 1, 2, 4]}, {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [4, 2, 1, 3]}, {[2, 1, 3], [3, 2, 1], [1, 3, 4, 2], [4, 1, 2, 3]}, {[1, 2, 3], [3, 1, 2], [2, 4, 3, 1], [3, 2, 1, 4]}} the member , {[1, 3, 2], [3, 2, 1], [2, 3, 4, 1], [3, 1, 2, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 2]}, {}], [[1, 1], {[2, 1, 1], [2, 2, 0], [2, 0, 2]}, {1, 2}], [[1, 2], {[2, 1, 1], [0, 2, 0]}, {}], [[2, 1], {[1, 1, 0], [0, 2, 1]}, {}], [[1, 2, 2], {[2, 1, 1, 0], [2, 1, 0, 1], [0, 2, 0, 0]}, {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, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[0, 2, 1, 1], [1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 1]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[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], %6, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {4}], [[1, 2, 3, 4], %5, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [2, 1, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %6, {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], %5, {}], [ [3, 4, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2}], [[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, 3], %6, {2}], [ [2, 3, 1, 1], {[0, 0, 2, 1, 1], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1}], [[2, 3, 1, 4], %5, {}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 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, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %4, {4, 5}], [[1, 2, 3, 4, 5], %2, {1, 2, 3, 4}], [[1, 2, 3, 5, 4], %3, {1, 2, 3, 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, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], %4, {4, 5}], [[2, 1, 3, 4, 5], %2, {1, 2, 3, 4}], [[2, 3, 1, 4, 3], %1, {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], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], %4, {4, 5}], [[3, 4, 1, 5, 2], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %2, {1, 2, 3, 4}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], { [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %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, 1, 1, 1, 0]} %4 := {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %6 := {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 19, 19, 19, 19, 19, 19, 19] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 90, 90, 90, 90] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [3, 4, 1, 2]}, {[3, 1, 2], [3, 2, 1], [2, 1, 4, 3], [2, 3, 4, 1]}, {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [3, 4, 1, 2]}, {[2, 3, 1], [3, 2, 1], [2, 1, 4, 3], [4, 1, 2, 3]}} the member , {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[2, 1], {[0, 1, 1], [0, 4, 0]}, {1}], [[1, 2], {[0, 3, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 5, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], {[0, 1, 1, 1, 1, 1], [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}]] %1 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 46, 68, 90, 112, 134, 156, 178] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 348, 548, 748, 948] For the equivalence class of patterns, { {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [1, 3, 2, 4]}, {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [2, 1, 3, 4]}, {[1, 2, 3], [1, 3, 2], [4, 2, 3, 1], [4, 3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [3, 4, 2, 1], [4, 2, 3, 1]}} the member , {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [2, 1, 3, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 3]}, {}], [[1, 1], {[1, 1, 2], [1, 0, 3], [1, 3, 0], [1, 2, 1]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {}], [[2, 1], {[1, 1, 0], [0, 1, 3]}, {}], [[1, 2, 1], {[0, 1, 3, 0], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3], [0, 2, 1, 0], [0, 0, 2, 1]}, {1}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 0, 0], [0, 1, 1, 2], [0, 1, 0, 3], [0, 2, 1, 0], [0, 2, 0, 1]}, {3}], [[2, 1, 1], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3]}, {2, 3}], [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 1, 3], [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, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[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}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {1, 2}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1]}, {1, 2}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {4}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}] , [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3], [0, 1, 1, 3, 0]}, {3, 4}], [[3, 1, 2, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {2, 3}], [[3, 1, 2, 3], {[0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [1, 1, 1, 0, 0], [0, 1, 1, 0, 3], [0, 1, 1, 3, 0]}, {}], [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 3, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 1, 1, 0]}, {2, 3, 4}], [ [4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3, 2], {[1, 1, 0, 1, 0, 0], [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, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 0, 0, 1], [0, 1, 1, 2, 0, 1], [0, 2, 1, 0, 0, 0], [0, 1, 1, 1, 0, 2], [0, 1, 1, 0, 1, 2], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 1, 1, 0, 3, 0], [0, 1, 2, 0, 1, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 0, 0, 3], [1, 1, 1, 0, 0, 0], [0, 1, 1, 3, 0, 0], [0, 1, 1, 0, 2, 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, 6, 7, 8, 9, 10, 11, 12] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 41, 53, 74, 99, 128, 161, 198] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 299, 485, 846, 1360] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4], [1, 4, 3, 2]}, {[1, 3, 2], [2, 1, 3], [4, 1, 2, 3], [4, 2, 3, 1]}, {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1], [4, 2, 3, 1]}} the member , {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4], [1, 4, 3, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 2, 1]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 3, 1], {[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, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3} ], [[1, 2, 3], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 1, 3, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], %2, {1, 2}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 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, 4], %2, {1, 2}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 3, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2, 4}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}] , [[3, 2, 1, 4], %2, {2, 3}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %1, {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, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %1, {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, 1], {[0, 0, 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}], [[4, 3, 1, 4, 2], {[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, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [ [3, 2, 1, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 0, 3, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 1]}, {1, 2, 3, 4}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 3, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 42, 54, 66, 78, 90, 102, 114] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 418, 478, 538, 598] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [1, 4, 2, 3]}, {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 1, 4]}, {[1, 2, 3], [2, 1, 3], [4, 1, 3, 2], [4, 3, 2, 1]}} the member , {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [1, 4, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [2, 3], [0, 5], [3, 1]}, {}], [[1, 1], { [0, 0, 5], [4, 0, 0], [3, 1, 0], [0, 4, 1], [2, 1, 2], [0, 3, 2], [2, 0, 3], [0, 2, 3], [0, 1, 4], [2, 3, 0], [0, 5, 0], [3, 0, 1], [2, 2, 1]}, {1, 2}], [[2, 1], {[1, 1, 0], [0, 4, 0], [0, 2, 3], [0, 3, 1]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 1, 3]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 3, 1, 0], [0, 1, 2, 1], [1, 0, 1, 0], [0, 1, 1, 2], [0, 0, 1, 3], [0, 0, 3, 0]}, {3}] , [[1, 2, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 0, 0], [0, 1, 1, 2], [0, 1, 0, 3], [0, 3, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3], {[0, 1, 3, 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, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 0, 0], [0, 1, 1, 2], [0, 1, 0, 3], [0, 3, 0, 0]}, {1}] , [[2, 1, 1], {[0, 2, 1, 2], [0, 1, 2, 2], [0, 1, 1, 3], [0, 0, 2, 3], [0, 0, 4, 0], [0, 3, 1, 0], [0, 0, 3, 1], [1, 0, 1, 0], [0, 2, 3, 0], [0, 2, 2, 1]}, {2, 3}], [[3, 1, 2], {[0, 1, 1, 3], [0, 1, 3, 0], [0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[2, 1, 3], {[0, 1, 1, 3], [0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 4, 2, 3], {[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, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3]}, {3, 4}], [[1, 3, 2, 4], %5, {}], [[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, 4], %5, {1, 2}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3]}, {1}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 1, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [1, 1, 1, 0, 0], [0, 1, 1, 0, 3], [0, 1, 1, 3, 0]}, {3, 4} ], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 1, 0, 3, 0], [0, 1, 0, 2, 1], [1, 1, 0, 1, 0], [0, 1, 0, 1, 3]}, {3, 4}], [[3, 1, 2, 4], %5, {}], [ [4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 4, 3, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 5], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], %3, {4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 4], { [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {4, 5}], [[1, 3, 2, 4, 2], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %3, {2}], [ [1, 3, 2, 5, 4], {[0, 1, 1, 1, 1, 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, 3}], [[3, 1, 2, 5, 4], {[0, 1, 1, 1, 1, 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]}, {1}], [[3, 1, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %3, {1}], [ [3, 1, 2, 4, 4], {[0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 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, 4, 5}], [[4, 1, 2, 3, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %4, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], %3, {4, 5}], [[5, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 0, 1, 1, 0]} %5 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 4, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 24, 10, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 82, 26, 1, 0] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [4, 3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [3, 4, 2, 1]}, {[2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [2, 3, 4, 1]}} the member , {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3], [3, 1]}, {}], [[2, 1], {[0, 1, 1], [0, 4, 0], [3, 2, 0]}, {1}], [[1, 1], {[0, 3, 0], [3, 1, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2], [3, 0, 1]}, {1, 2}] , [[1, 2], {[0, 3, 0], [0, 1, 1], [3, 1, 0]}, {}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {2}], [[1, 2, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {3}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {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, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {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, 6, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 46, 59, 59, 59, 59, 59, 59] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 348, 484, 484, 484] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [1, 4, 2, 3]}, {[3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 1, 4]}, {[1, 2, 3], [2, 1, 3], [4, 1, 3, 2], [4, 3, 1, 2]}} the member , {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[2, 1], {[0, 3, 0], [0, 2, 1], [0, 1, 2]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 1], [3, 1, 0]}, {}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {3}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3} ], [[2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {1}], [[3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[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, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], %2, {}], [[4, 3, 2, 1], {[0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0], [0, 2, 1, 1, 1], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {1}], [[4, 2, 1, 3], %2, {1, 2}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2} ], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[3, 2, 1, 1], { [0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 4], %2, {}], [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %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}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {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, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 6, 7, 8, 9, 10, 11, 12] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 31, 33, 35, 37, 39, 41, 43] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 170, 173, 176, 179] For the equivalence class of patterns, {{[1, 2, 3], [3, 2, 1], [2, 1, 4, 3], [3, 4, 1, 2]}} the member , {[1, 2, 3], [3, 2, 1], [2, 1, 4, 3], [3, 4, 1, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 2], [3, 0], [0, 3]}, {}], [[1, 1], {[2, 1, 1], [3, 0, 0], [0, 3, 0], [2, 2, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2], [2, 0, 2] }, {1, 2}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 1, 2]}, {}], [[1, 2], {[0, 3, 0], [0, 1, 1], [2, 1, 0]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [ [1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0], [2, 1, 0, 0]}, {2, 3} ], [[2, 3, 1], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 3} ], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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}], [[2, 4, 3, 1], {[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, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %1, {3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 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}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], %1, {1}], [ [3, 1, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 3}], [[2, 1, 3, 3], { [0, 3, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 3}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], %1, {1}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %1, {3, 4}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}]] %1 := {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 2, 0, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [4, 1, 3, 2]}, {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [3, 2, 4, 1]}, {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [4, 1, 2, 3]}, {[3, 1, 2], [3, 2, 1], [2, 3, 1, 4], [2, 3, 4, 1]}} the member , {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [4, 1, 3, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[1, 2], {[0, 3, 0], [0, 1, 1]}, {}], [[2, 1], {[0, 3, 0], [0, 1, 1]}, {}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3}], [[1, 3, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 3}], [[3, 2, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 10, 16, 26, 42, 68, 110] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 66, 222, 684, 2190, 6894, 21864, 69114] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 798, 5428, 33334, 215090] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [3, 2, 4, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 1, 3, 2]}, {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 4, 2, 3], [4, 3, 2, 1]}} the member , {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 2]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1}], [ [1, 2, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {3}], [[3, 2, 1], {[0, 1, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 4], {[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], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 3], {[0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {1, 2, 4}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 3]}, {3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [ [3, 2, 1, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {}], [[4, 3, 1, 5, 2], %2, {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], %2, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {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, 4], %1, {4, 5}], [[3, 2, 1, 4, 5], {[0, 1, 1, 1, 1, 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]}, {4}], [[4, 5, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %2, {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, 5], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [ [3, 4, 2, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 2]}, {4, 5}], [ [4, 5, 3, 2, 1], {[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}], [[3, 4, 2, 1, 4], %1, {2}], [[5, 4, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 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], [0, 2, 1, 1, 1, 0]}, {2, 3, 4}], [[4, 3, 2, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [ [4, 3, 2, 1, 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}], [[4, 3, 2, 1, 4], %1, {1}]] %1 := {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 2], [0, 1, 1, 1, 2, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 35, 23, 23, 23, 23, 23, 23] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 188, 78, 78, 78] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1], [4, 2, 1, 3]}, {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [4, 3, 1, 2]}, {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [3, 1, 2, 4]}, {[3, 1, 2], [3, 2, 1], [1, 3, 4, 2], [2, 1, 3, 4]}} the member , {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1], [4, 2, 1, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2]}, {1, 2}], [[2, 1], {[0, 3, 0], [0, 2, 1], [0, 1, 2], [3, 2, 0]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 1], [3, 1, 0]}, {}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {3}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 1], [0, 0, 1, 2], [3, 0, 2, 0], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 1, 2], [0, 1, 2, 0]}, {}], [[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], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [3, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[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, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[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, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[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, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 1], {[3, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[4, 2, 3, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [3, 1, 1, 0, 0]}, {1}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {2}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0], [0, 2, 1, 1, 1], [0, 1, 1, 1, 2]}, {2}], [[4, 2, 5, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 2], %1, {2}], [ [3, 2, 4, 1, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3}], [[3, 2, 4, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 5, 1, 2], { [0, 1, 1, 1, 1, 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]}, {1, 2}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], %1, {4, 5}], [[5, 2, 3, 1, 4], %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, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [ [5, 3, 4, 1, 2], {[0, 1, 1, 1, 1, 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]}, {1}], [[4, 2, 3, 1, 2], %1, {1, 2, 3, 5}]] %1 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 31, 33, 33, 33, 33, 33, 33] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 143, 146, 146, 146] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [4, 3, 1, 2]}, {[2, 1, 3], [3, 2, 1], [1, 2, 4, 3], [4, 1, 2, 3]}, {[1, 2, 3], [3, 1, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 4, 1]}} the member , {[1, 2, 3], [3, 1, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[3, 1]}, {}], [[1, 1], {[3, 1, 0], [3, 0, 1]}, {1, 2}], [[1, 2], {[0, 1, 1], [2, 1, 0]}, {}], [[2, 1], {[2, 1, 1], [0, 2, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [ [1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {2, 3}], [[1, 3, 2], {[2, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 2, 3}], [ [2, 1, 1], {[0, 0, 2, 0], [2, 1, 1, 0], [2, 0, 1, 1], [0, 2, 1, 0]}, {2, 3} ], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[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, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {3, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {2, 3}], [[1, 3, 2, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[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, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {2}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [ [3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {}], [[2, 5, 4, 1, 3], %4, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[2, 4, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %4, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %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, 3, 4, 5}], [[3, 5, 4, 2, 1], %4, {1, 2, 3, 4, 5}], [[4, 2, 5, 1, 3], %4, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 5, 1, 4], %4, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %4, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %4, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %4, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[5, 4, 2, 1, 3], %4, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[2, 1, 4, 2, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [2, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 1, 0]}, {4, 5}], [ [2, 1, 3, 2, 1], {[0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1}], [[3, 2, 4, 3, 1], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1, 4}], [[4, 3, 2, 4, 1], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 4}], [[3, 2, 1, 3, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], { [0, 1, 1, 0, 1, 0], [2, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[4, 3, 1, 4, 2], %1, {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, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [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, 4], {[0, 0, 1, 1, 1, 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, 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], [2, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [ [2, 4, 3, 2, 1], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 4}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 0, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 5, 5, 5, 5, 5, 5] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 12, 11, 11, 11, 11, 11, 11] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 21, 19, 19, 19] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [1, 4, 3, 2]}, {[2, 1, 3], [3, 1, 2], [2, 3, 4, 1], [3, 4, 2, 1]}, {[1, 3, 2], [2, 3, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [3, 2, 1, 4]}} the member , {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [1, 4, 3, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], %3, {1}], [[1, 2, 2], {[0, 3, 0, 0]}, {2, 3}], [[2, 3, 1], %3, {}], [[1, 2, 3], {[0, 3, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], %3, {}], [[1, 3, 4, 2], %1, {1}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], %2, {1}], [[1, 2, 3, 3], {[0, 3, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[2, 3, 4, 1], %1, {1, 2, 3}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %2, {3, 4}], [[3, 4, 2, 1], %1, {1, 2, 3}], [[3, 2, 1, 1], %2, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], %1, {1, 2, 3}], [[2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 5, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 2}], [[1, 2, 4, 5, 3], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4, 4], {[0, 1, 1, 2, 0, 0], [0, 3, 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], [0, 1, 1, 1, 2, 0]}, {3, 4}]] %1 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %2 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} %3 := {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 24, 30, 36, 42, 48, 54, 60] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 92, 104, 116, 128] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 4, 1, 2], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [2, 1, 4, 3]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 1, 4, 3]}} the member , {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [1, 3], [2, 2], [0, 4], [3, 1]}, {}], [[1, 1], { [1, 1, 2], [0, 2, 2], [1, 0, 3], [0, 0, 4], [2, 1, 1], [0, 1, 3], [4, 0, 0], [1, 3, 0], [2, 2, 0], [0, 4, 0], [3, 1, 0], [1, 2, 1], [3, 0, 1], [0, 3, 1], [2, 0, 2]}, {1, 2}], [[1, 2], {[0, 1, 1], [1, 3, 0], [2, 2, 0], [0, 4, 0], [3, 1, 0]}, {}], [[2, 1], {[0, 1, 1], [1, 3, 0], [2, 2, 0], [0, 4, 0], [3, 1, 0]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 3, 0], [0, 0, 4, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 2], {[1, 3, 0, 0], [2, 2, 0, 0], [0, 4, 0, 0], [3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3}], [[1, 3, 2], {[2, 1, 1, 0], [1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[2, 3, 1], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 3, 0], [0, 0, 4, 0], [3, 0, 1, 0], [2, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[2, 1, 2], {[1, 3, 0, 0], [0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 3}], [[3, 2, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[2, 1, 1, 0], [1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}] , [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], { [0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {3, 4}], [[1, 3, 2, 4], {[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], %7, {1, 4}], [[1, 4, 3, 2], %6, {}], [[2, 4, 3, 1], %6, {}], [[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], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {}], [[3, 4, 2, 1], %6, {}], [[3, 1, 2, 2], {[0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {3, 4} ], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[3, 1, 2, 1], %7, {2, 4}], [[4, 1, 3, 2], %6, {}], [[4, 2, 3, 1], %6, {}], [[3, 2, 1, 1], %7, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2, 4}], [[4, 3, 1, 2], %6, {}], [[2, 5, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %3, {4, 5}], [[1, 4, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 5, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], %5, {4, 5}], [[2, 5, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 2], %3, {1}], [[4, 5, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], %5, {4, 5}], [[4, 1, 3, 2, 2], %3, {4, 5}], [[5, 1, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %3, {2}], [[5, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], %5, {4, 5}], [[4, 2, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], %2, {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, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %3, {4, 5}], [[5, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4}], [ [2, 3, 1, 2, 2], {[2, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], {[0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} %6 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %7 := {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 26, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 121, 0, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, {[1, 2, 3], [2, 3, 1], [2, 1, 4, 3], [3, 2, 1, 4]}, {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [2, 1, 4, 3]}, {[2, 1, 3], [3, 2, 1], [2, 3, 4, 1], [3, 4, 1, 2]}} the member , {[1, 3, 2], [3, 2, 1], [3, 4, 1, 2], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[1, 2], {[0, 2, 0], [2, 1, 0]}, {}], [[2, 1], {[0, 3, 0], [1, 1, 0]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [1, 0, 1, 0], [0, 2, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {2, 3}], [[2, 3, 1], %2, {1}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 3], %2, {1}], [[2, 1, 1], {[0, 3, 1, 0], [1, 0, 1, 0], [0, 0, 3, 0]}, {2, 3}], [[3, 1, 2], %2, {}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {2, 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, 2, 1, 0, 0], [0, 1, 2, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {2, 3}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[3, 1, 2, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [ [2, 3, 4, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 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}], [[2, 3, 5, 1, 4], %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}], [[3, 4, 5, 2, 1], %1, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[3, 1, 2, 5, 4], %1, {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, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 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]}, {4}], [[3, 1, 2, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 6, 7, 8, 9, 10, 11] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 32, 49, 70, 95, 124, 157, 194] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 229, 464, 825, 1339] For the equivalence class of patterns, {{[1, 2, 3], [3, 2, 1], [2, 4, 1, 3], [3, 1, 4, 2]}} the member , {[1, 2, 3], [3, 2, 1], [2, 4, 1, 3], [3, 1, 4, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 2], [3, 0], [0, 3]}, {}], [[1, 1], {[2, 1, 1], [3, 0, 0], [0, 3, 0], [2, 2, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2], [2, 0, 2] }, {1, 2}], [[1, 2], {[0, 3, 0], [0, 1, 1], [3, 1, 0], [1, 2, 0]}, {}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 1, 3], [0, 2, 1]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [[1, 2, 2], {[3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0], [1, 2, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 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, 1], {[1, 0, 1, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 3, 0]}, {2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[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}], [[2, 4, 3, 1], {[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, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %1, {3, 4}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 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}], [[2, 1, 3, 2], %1, {1}], [ [2, 1, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 4], {[0, 1, 1, 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}], [[3, 4, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], %1, {1}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %1, {3, 4}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}]] %1 := {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 2, 0, 0, 0] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 3, 2], [3, 1, 2], [3, 2, 4, 1], [3, 4, 2, 1]}, {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4], [2, 3, 1, 4]}, {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [1, 4, 2, 3]}} the member , {[2, 1, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {1}], [[2, 1], {[0, 1, 1], [1, 2, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 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, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 1, 2, 3, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], {[0, 1, 1, 1, 1, 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, 3, 4}], [[5, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[4, 1, 2, 3, 4], { [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {2, 3, 5}], [[5, 4, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4}], [[3, 1, 2, 3, 2], { [1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0]}, {5}], [[3, 1, 2, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 1, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {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, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 39, 58, 81, 108, 139, 174, 213] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 287, 525, 889, 1406] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [1, 2, 4, 3]}} the member , {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[5, 0], [4, 1], [0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2], [5, 0, 0], [4, 1, 0], [4, 0, 1]}, {1, 2}] , [[1, 2], {[0, 2, 0], [0, 1, 1], [3, 1, 0]}, {}], [[2, 1], {[0, 3, 0], [3, 1, 0], [0, 2, 1], [0, 1, 2]}, {}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 2, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[2, 1, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2], [1, 1, 1, 0]}, {}], [[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], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [3, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[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, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[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, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], %3, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[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, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], %3, {1, 2}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[4, 2, 1, 3], %3, {1, 2}], [ [3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[3, 2, 1, 1], { [0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4} ], [[4, 3, 1, 2], %3, {}], [[4, 2, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {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}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 2], %2, {2}], [ [3, 2, 4, 1, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3}], [[4, 3, 5, 1, 2], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [[3, 2, 4, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], %2, {4, 5}], [[4, 2, 3, 1, 2], %2, {2}], [[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, 2, 1], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [ [5, 3, 4, 1, 2], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [[4, 2, 3, 1, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1, 2, 3}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {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}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 6, 2, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 20, 2, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 64, 2, 0, 0] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [1, 3, 4, 2]}, {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [3, 1, 2, 4]}, {[1, 3, 2], [2, 3, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [2, 4, 3, 1], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [1, 3, 4, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2], {[0, 2, 1]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 2], {[0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[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, 1], %2, {1}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[2, 3, 4, 1], %1, {1, 2, 3}], [[1, 2, 4, 3], {[0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[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, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[2, 4, 3, 1], %1, {1, 2, 3}], [[1, 3, 2, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {1}], [[1, 3, 2, 1], %2, {1}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %2, {3, 4}], [[3, 4, 2, 1], %1, {1, 2, 3}], [[3, 2, 1, 1], %2, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], %1, {1, 2, 3}], [[1, 3, 5, 4, 2], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3, 5], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 5, 4, 3], {[0, 1, 1, 1, 1, 1], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3, 3], {[0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [ [1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 2}]] %1 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %2 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 24, 30, 36, 42, 48, 54, 60] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 92, 104, 116, 128] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [4, 2, 3, 1]}, {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [4, 2, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [0, 1, 2]}, {}], [[2, 1], {[0, 1, 1], [0, 4, 0], [1, 2, 0]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3} ], [[2, 3, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 4, 1, 0]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[0, 0, 4, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3} ], [[3, 2, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 4, 1, 0]}, {}], [[3, 1, 2], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[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], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 4, 1], %4, {2, 3}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], { [1, 0, 2, 1, 0], [0, 0, 4, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 2, 1], %4, {1, 2}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {2, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[3, 1, 2, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[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, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[4, 1, 2, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[4, 3, 2, 1], %4, {1, 2}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [1, 0, 2, 1, 0], [0, 0, 4, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[3, 4, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 3, 1, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[4, 5, 2, 3, 1], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %3, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], { [0, 1, 1, 1, 1, 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]}, {1, 2}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %3, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 3], %2, {1}], [ [3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3}], [[4, 1, 2, 3, 5], %3, {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], %2, {4, 5}], [[5, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[5, 3, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %3, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 0, 3, 1, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 4, 1, 3, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3}], [[4, 3, 1, 2, 3], %2, {2}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [[2, 3, 4, 2, 1], { [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [1, 2, 0, 1, 1, 0], [0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4}]] %1 := {[0, 0, 1, 1, 1, 0]} %2 := {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 2, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 9, 9, 9, 9, 9] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 44, 61, 64, 64, 64, 64, 64] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 430, 523, 529, 529] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 4, 1, 2], [4, 2, 1, 3]}, {[3, 1, 2], [3, 2, 1], [1, 3, 4, 2], [2, 1, 4, 3]}, {[2, 3, 1], [3, 2, 1], [2, 1, 4, 3], [3, 1, 2, 4]}, {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [3, 4, 1, 2]}} the member , {[2, 3, 1], [3, 2, 1], [2, 1, 4, 3], [3, 1, 2, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 0, 1], [2, 1, 0]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 3, 1]}, {1}], [[2, 1], {[1, 1, 0], [0, 2, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {2}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 1]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[3, 2, 4, 1], {[0, 1, 1, 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, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {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]}, {}], [[2, 1, 3, 5, 4], %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, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {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]}, {3, 4}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 46, 72, 102, 136, 174, 216, 262] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 348, 647, 1072, 1650] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [4, 3, 1, 2]}, {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [3, 4, 2, 1]}} the member , {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 0, 2], [1, 2, 0]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[1, 3, 0], [0, 1, 2], [1, 2, 1]}, {}], [[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], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {1}], [ [2, 1, 1], {[1, 0, 3, 0], [1, 0, 2, 1], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 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], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [ [3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 0, 1, 2], [0, 1, 0, 2, 1], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {1, 4}], [[3, 2, 1, 1], {[0, 0, 1, 3, 0], [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 1, 1, 3, 0]}, {}], [[4, 3, 2, 1, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1, 2}], [[5, 4, 2, 1, 3], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[5, 4, 3, 1, 2], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 1], [0, 0, 1, 1, 3, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 2]}, {4, 5}], [ [5, 3, 2, 1, 4], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[5, 4, 3, 2, 1], {[0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}], [ [4, 3, 2, 1, 5], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 18, 10, 10, 10, 10, 10, 10] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 50, 14, 14, 14] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [2, 1, 4, 3]}, {[2, 3, 1], [3, 1, 2], [2, 1, 3, 4], [2, 1, 4, 3]}, {[1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}, {[1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}} the member , {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [2, 1, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0]}, {}], [[1, 2], {[1, 1, 0]}, {}], [[2, 3, 1], {[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]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %8, {3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[1, 2, 3, 4], %7, {}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], %8, {2}], [[1, 3, 2, 2], {[0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {3, 4}] , [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[1, 3, 2, 4], %7, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[3, 2, 4, 1], {[0, 1, 1, 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, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %8, {3, 4}], [[2, 1, 3, 4], %7, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}] , [[3, 2, 1, 3], %8, {}], [[3, 2, 1, 4], %7, {}], [[1, 2, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %1, {4, 5}], [[1, 2, 3, 4, 5], %6, {1, 2, 3, 4}], [[1, 2, 3, 5, 4], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %5, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], %5, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 2], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %6, {1, 2, 3, 4}], [[1, 3, 2, 4, 4], %1, {4, 5}], [[2, 1, 3, 5, 4], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], %5, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], %1, {4, 5}], [[2, 1, 3, 4, 5], %6, {1, 2, 3, 4}], [[4, 3, 1, 5, 2], %4, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %6, {1, 2, 3, 4}], [[3, 2, 1, 4, 1], %5, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %4, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4], %1, {4, 5}], [[4, 3, 2, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 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}], [[4, 3, 1, 4, 2], {[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, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {1, 4}], [[3, 2, 1, 3, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}]] %1 := {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 0, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[0, 0, 1, 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 := {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %8 := {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 25, 31, 37, 43, 49, 55, 61] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 105, 117, 129, 141] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, {[1, 2, 3], [1, 3, 2], [4, 2, 3, 1], [4, 3, 2, 1]}, {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4], [1, 3, 2, 4]}, {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4], [1, 3, 2, 4]}} the member , {[1, 2, 3], [2, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [1, 3], [0, 4], [3, 2]}, {}], [[1, 1], { [1, 1, 2], [0, 2, 2], [1, 0, 3], [0, 0, 4], [0, 1, 3], [4, 0, 0], [1, 3, 0], [0, 4, 0], [3, 1, 1], [3, 0, 2], [3, 2, 0], [1, 2, 1], [0, 3, 1]}, {1, 2}], [[1, 2], {[0, 1, 1], [1, 3, 0], [0, 4, 0], [4, 1, 0], [3, 2, 0]}, {}], [[2, 1], {[0, 1, 1], [0, 4, 0], [3, 1, 0], [1, 2, 0]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[1, 3, 0, 0], [0, 4, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [4, 1, 0, 0], [3, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 4, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {1} ], [[1, 3, 2], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}] , [[2, 3, 1], {[1, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 4, 1, 0], [3, 1, 1, 0]}, {}] , [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 4, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {2, 3}], [[2, 1, 2], {[0, 4, 0, 0], [3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [1, 2, 0, 0]}, {3} ], [[3, 1, 2], {[0, 3, 1, 0], [1, 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], [0, 1, 1, 1]}, {}], [[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, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], %7, {1, 4}], [[1, 3, 2, 2], {[0, 3, 0, 1, 0], [1, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[2, 4, 3, 1], %8, {}], [[1, 4, 3, 2], %5, {}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], %8, {1, 2}], [[2, 3, 1, 2], %6, {1}], [[3, 4, 1, 2], %8, {1, 2}], [[2, 3, 1, 1], { [1, 0, 2, 1, 0], [0, 0, 4, 1, 0], [3, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %6, {3, 4}], [[4, 2, 3, 1], {[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, 1], %7, {2, 4}], [[4, 1, 3, 2], %5, {}], [[3, 2, 1, 1], %7, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], %6, {2, 4}], [[4, 3, 1, 2], %5, {}], [[2, 5, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], {[0, 0, 1, 1, 1, 0]}, {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, 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, 2], %2, {4, 5}], [[1, 4, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[2, 5, 4, 1, 3], %1, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}], [[3, 5, 4, 1, 2], { [0, 1, 1, 1, 1, 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]}, {1}], [[2, 4, 3, 1, 2], %2, {1}], [[2, 4, 3, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 1, 3, 2, 2], %2, {4, 5}], [[5, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %3, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], {[0, 0, 1, 1, 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, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %3, {1, 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}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %2, {4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 0, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %6 := {[0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]} %7 := {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]} %8 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 3, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 31, 7, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 170, 21, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [3, 4, 2, 1]}, {[2, 3, 1], [3, 2, 1], [2, 1, 3, 4], [3, 1, 2, 4]}, {[1, 2, 3], [1, 3, 2], [4, 2, 1, 3], [4, 3, 1, 2]}, {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3], [1, 3, 4, 2]}} the member , {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2], [3, 1]}, {}], [[2, 1], {[0, 1, 1], [1, 3, 0], [3, 2, 0]}, {1}], [[1, 1], {[3, 1, 0], [1, 1, 1], [1, 0, 2], [3, 0, 1], [1, 2, 0]}, {1, 2}], [[1, 2], {[0, 1, 1], [3, 1, 0], [1, 2, 0]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0]}, {3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [1, 2, 0, 0]}, {2, 3} ], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {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, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {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, 6, 7, 8, 9, 10, 11, 12] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 46, 63, 84, 109, 138, 171, 208] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 348, 583, 944, 1458] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [2, 3, 4, 1], [3, 2, 1, 4]}, {[2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 1, 2, 3]}} the member , {[1, 3, 2], [3, 1, 2], [2, 3, 4, 1], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 2]}, {}], [[1, 1], {[2, 1, 1], [2, 2, 0], [2, 0, 2]}, {1, 2}], [[2, 1], {[1, 1, 2], [0, 2, 0]}, {}], [[1, 2], {[2, 1, 1], [0, 2, 0]}, {}], [[1, 2, 2], {[2, 1, 1, 0], [2, 1, 0, 1], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1]}, {1, 3} ], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[1, 1, 1, 1], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[0, 0, 2, 0], [1, 0, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {2, 3} ], [[2, 1, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {1, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 1], [0, 2, 1, 0], [0, 1, 2, 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], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 4}], [[1, 2, 3, 4], %9, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 0, 1], [0, 1, 2, 0, 0]}, {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[1, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {2, 4}], [[3, 2, 4, 1], %8, {}], [[2, 1, 3, 4], %9, {}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[1, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 0, 1], [0, 1, 2, 0, 0]}, {2, 4}], [[3, 4, 2, 1], %8, {}], [[2, 3, 1, 4], %9, {}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 4}], [[4, 3, 2, 1], %8, {}], [[1, 2, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %7, {4, 5}], [[1, 2, 3, 4, 5], %6, {1, 2, 3, 4}], [[1, 2, 3, 5, 4], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 5, 4], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], %7, {4, 5}], [[2, 1, 3, 4, 5], %6, {1, 2, 3, 4}], [[2, 3, 1, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 2], %2, {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, 4, 1, 5, 3], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], %7, {4, 5}], [[3, 4, 1, 5, 2], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %3, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 5], %6, {1, 2, 3, 4}], [[4, 2, 5, 1, 3], %3, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], %4, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %5, {1, 2, 3, 4}], [[3, 2, 5, 1, 4], %3, {1, 2, 3, 4, 5}], [[4, 3, 5, 1, 2], %3, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 1], %1, {4, 5}], [[3, 2, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %3, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], %4, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %5, {1, 2, 3, 4}], [[3, 5, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], %1, {4, 5}], [[3, 4, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], %5, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], %1, {4, 5}]] %1 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} %2 := {[0, 1, 0, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 0, 1, 0]} %5 := {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 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 := {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]} %8 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %9 := {[0, 1, 2, 1, 0], [1, 1, 1, 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, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 30, 30, 30, 30, 30, 30, 30] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 168, 168, 168, 168] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1], [3, 4, 1, 2]}, {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [2, 1, 4, 3]}, {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [4, 1, 3, 2]}, {[3, 1, 2], [3, 2, 1], [2, 1, 4, 3], [2, 3, 1, 4]}} the member , {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3], [2, 1, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 0]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0]}, {}], [[1, 2, 2], {[1, 1, 0, 0], [0, 3, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 1], {[0, 3, 1, 0], [1, 0, 1, 0], [0, 0, 3, 0]}, {1}], [[1, 2, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 3, 0, 0]}, {3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 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, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], %2, {1, 2}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {1, 2}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[3, 2, 4, 1], {[0, 1, 1, 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, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[2, 1, 3, 4], %2, {}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}] , [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], %2, {2, 3}], [[3, 1, 2, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {}], [[2, 1, 3, 5, 4], %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, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {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]}, {3, 4}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {2, 3, 4}], [[3, 1, 2, 3, 3], {[0, 2, 1, 0, 0, 0], [0, 1, 3, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [ [3, 1, 2, 3, 2], {[1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 0], [1, 1, 1, 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, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 41, 56, 71, 86, 101, 116, 131] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 299, 399, 499, 599] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 3, 1, 2]}, {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3], [4, 3, 2, 1]}, {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4], [4, 3, 2, 1]}} the member , {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [3, 4, 2, 1]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 2, 0], [2, 1, 0], [0, 1, 2]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[2, 3, 1], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 2], {[0, 2, 0, 0], [2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[2, 1, 3], {[2, 1, 1, 0], [0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 4], {[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, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 4}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2} ], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[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], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [0, 1, 2, 0, 0], [2, 1, 1, 0, 0]}, {3, 4}], [[3, 2, 4, 1], { [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {1, 2}], [[2, 1, 3, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {1, 3}], [[2, 1, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1, 2, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [0, 1, 2, 0, 0], [2, 1, 1, 0, 0]}, {1}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0], [0, 1, 1, 1, 2]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 3]}, {3, 4}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 57, 35, 35, 35, 35, 35, 35] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 677, 210, 210, 210] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [1, 3, 2, 4]}, {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1], [4, 2, 3, 1]}, {[1, 2, 3], [2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]}, {[3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 1, 3, 4]}} the member , {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [1, 3, 2, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 0]}, {}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 1]}, {3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {1}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 3], {[0, 1, 2, 1], [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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[1, 2, 3, 4], %6, {}], [[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, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 4, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {1, 2}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1}], [[2, 1, 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, 1, 3, 4], %6, {1, 2}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {1}], [[3, 1, 2, 4], %6, {}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {}], [[1, 2, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %2, {4, 5}], [[1, 2, 3, 4, 5], %1, {1, 2, 3, 4}], [[1, 2, 3, 5, 4], %3, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 2], %5, {1, 2, 3, 4, 5}], [[1, 5, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {2}], [[1, 4, 2, 3, 5], %3, {1, 2, 3, 4, 5}], [[2, 5, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[1, 5, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 2, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[1, 5, 2, 3, 4], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[3, 1, 2, 5, 4], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 1], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 2], %5, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 3, 5, 2], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %1, {1, 4}], [[3, 1, 2, 4, 4], %2, {4, 5}], [[4, 1, 2, 3, 2], %5, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %2, {1}], [[4, 1, 2, 3, 5], %1, {1, 2, 3, 4}], [[4, 1, 2, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 2, 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}]] %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, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 0, 1, 1, 1, 0]} %5 := {[0, 1, 0, 1, 1, 0]} %6 := {[0, 1, 2, 1, 0], [1, 1, 1, 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, 4, 6, 7, 8, 9, 10, 11, 12] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 24, 23, 25, 27, 29, 31, 33] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 82, 69, 72, 75] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 4, 2, 3], [4, 1, 3, 2]}, {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [3, 2, 4, 1]}} the member , {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [3, 2, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0]}, {}], [[1, 2], {[0, 2, 0]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1]}, {1, 3} ], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [1, 1, 1, 0], [1, 1, 0, 1]}, {1, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[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, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [ [2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[2, 1, 3, 2], {[0, 1, 0, 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]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}] , [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [ [1, 2, 3, 4, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[2, 3, 4, 5, 1], %8, {1, 2, 3, 4}], [[1, 2, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %6, {1, 2, 3, 4, 5}], [[1, 2, 3, 5, 4], %6, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %7, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %6, {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], [0, 2, 1, 1, 1, 0]}, {2, 3, 4}], [[1, 2, 3, 4, 1], %9, {1}], [[2, 1, 3, 5, 4], %6, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 3], %7, {1, 2, 3, 4, 5}], [[3, 2, 4, 5, 1], %6, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %6, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %6, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], %3, {4, 5}], [[2, 1, 3, 4, 5], %4, {1, 3, 4}], [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {2}], [[2, 3, 4, 1, 3], %7, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 3, 5, 1, 4], %6, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %6, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 2], %5, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], %6, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %6, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], %9, {4, 5}], [[3, 4, 5, 2, 1], %8, {4}], [[4, 3, 1, 5, 2], %6, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 2, 1, 5, 4], %6, {1, 2, 3, 4, 5}], [[4, 2, 1, 5, 3], %6, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %6, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], %5, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 3], %7, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %4, {4}], [[3, 2, 1, 4, 4], %3, {4, 5}], [[4, 5, 3, 1, 2], %6, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %6, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %6, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], %7, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %6, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], %9, {4, 5}], [[3, 4, 2, 1, 2], %5, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %8, {1, 3, 4}], [ [3, 4, 2, 1, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {2}], [[5, 4, 2, 1, 3], %6, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %6, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 3], %7, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %6, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], %5, {1, 2, 3, 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], [0, 2, 1, 1, 1, 0]}, {2, 3, 4}], [[4, 3, 2, 1, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[4, 3, 2, 1, 5], %4, {1, 2, 3, 4}], [[4, 3, 2, 1, 4], %3, {1}], [[1, 3, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [ [2, 3, 4, 2, 1], {[0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %1, {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, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [ [3, 2, 1, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]} %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]} %5 := {[0, 1, 0, 1, 1, 0]} %6 := {[0, 1, 1, 1, 1, 0]} %7 := {[0, 1, 1, 0, 1, 0]} %8 := {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]} %9 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 22, 26, 30, 34, 38, 42, 46] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 74, 80, 86, 92] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [4, 1, 2, 3]}} the member , {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[1, 2], {[0, 3, 0], [1, 1, 0]}, {}], [[2, 1], {[0, 2, 0], [2, 1, 0]}, {}], [[1, 2, 2], {[1, 1, 0, 0], [0, 3, 0, 0]}, {2, 3}], [[2, 3, 1], {[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, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 3], {[0, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0]}, {2, 3}], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[0, 1, 3, 0], [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, 3, 4], %2, {1, 2}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {1, 4}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {2, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {3, 4}] , [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], %2, {1, 2}], [[2, 1, 4, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 4], %2, {2, 3}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [ [1, 2, 4, 3, 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, 4}], [[1, 2, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[1, 2, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[1, 2, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4, 5}], [[1, 2, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {4, 5}], [[2, 1, 4, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[2, 1, 4, 3, 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, 4}], [[4, 3, 2, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 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}], [[4, 3, 1, 4, 2], {[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, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [ [3, 2, 1, 3, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 3, 0], [0, 1, 2, 0, 1, 0]}, {1, 2, 3, 4}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 10, 16, 26, 42, 68, 110] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 61, 192, 609, 1925, 6094, 19279, 61009] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 707, 4148, 27382, 170760] For the equivalence class of patterns, { {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, {[3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2], [4, 3, 1, 2]}, {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [4, 1, 2, 3]}} the member , {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 1], [0, 2]}, {}], [[1, 1], {[0, 2, 0], [0, 1, 1], [0, 0, 2], [4, 1, 0], [4, 0, 1]}, {1, 2}], [[1, 2], {[0, 2, 0], [0, 1, 1], [3, 1, 0]}, {}], [[2, 1], {[0, 3, 0], [0, 2, 1], [3, 1, 1], [0, 1, 2]}, {}], [ [1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {3}], [[2, 3, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 2, 1], [0, 0, 1, 2], [3, 0, 1, 1], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {1}], [[3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[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], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [3, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {[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, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[3, 2, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[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, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 2, 5, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {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}], [[3, 2, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 5], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 1, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {2}], [ [3, 2, 4, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 5, 1, 2], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {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, 6, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 33, 35, 35, 35, 35, 35, 35] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 176, 179, 179, 179] For the equivalence class of patterns, { {[1, 2, 3], [3, 2, 1], [2, 1, 4, 3], [3, 1, 4, 2]}, {[1, 2, 3], [3, 2, 1], [2, 4, 1, 3], [3, 4, 1, 2]}} the member , {[1, 2, 3], [3, 2, 1], [2, 1, 4, 3], [3, 1, 4, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 2], [3, 0], [0, 3]}, {}], [[1, 1], {[2, 1, 1], [3, 0, 0], [0, 3, 0], [2, 2, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2], [2, 0, 2] }, {1, 2}], [[1, 2], {[0, 3, 0], [0, 1, 1], [2, 2, 0], [3, 1, 0]}, {}], [[2, 1], {[0, 3, 0], [1, 1, 0], [0, 2, 1], [0, 1, 2]}, {}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 3} ], [[1, 2, 2], {[2, 2, 0, 0], [3, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {2, 3}], [[2, 3, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {}] , [[1, 3, 2], %2, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], %2, {1}], [[2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 3} ], [[3, 1, 2], %2, {}], [[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}], [[2, 4, 3, 1], {[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, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %1, {3, 4}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 3}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 1], { [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], %1, {1}], [ [2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %1, {3, 4}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}]] %1 := {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]} %2 := {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 2, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 2, 0, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [3, 2, 1, 4]}, {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [1, 4, 3, 2]}, {[1, 3, 2], [2, 3, 1], [4, 1, 2, 3], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [2, 3, 4, 1], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [3, 2, 1, 4]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {[2, 2], [0, 3], [3, 1]}, {}], [[1, 1], {[2, 1, 1], [0, 3, 0], [2, 2, 0], [3, 1, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2], [3, 0, 1], [2, 0, 2]}, {1, 2}], [[2, 1], { [0, 2, 2], [0, 1, 3], [0, 4, 0], [1, 1, 1], [2, 3, 0], [3, 2, 0], [0, 3, 1] }, {}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 2]}, {}], [[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], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[3, 2, 1], {[1, 1, 2, 0], [0, 1, 1, 1], [0, 4, 1, 0], [0, 2, 3, 0], [0, 1, 4, 0], [0, 3, 2, 0]}, {1}], [[2, 1, 1], {[0, 0, 4, 0], [0, 0, 3, 1], [0, 0, 2, 2], [0, 0, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [1, 0, 1, 1], [0, 1, 1, 1], [3, 0, 2, 0], [2, 0, 3, 0]}, {2, 3}], [[3, 1, 2], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0]}, {}] , [[2, 1, 3], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[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], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 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, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[2, 1, 3, 4], %1, {1, 2, 3}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], %1, {1, 2, 3}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 1, 2, 1], {[0, 0, 1, 3, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 4}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 0, 1, 2], [0, 1, 0, 2, 1], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 1, 2, 3], %1, {1}]] %1 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 6, 6, 6, 6, 6, 6, 6] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 22, 22, 22, 22, 22, 22, 22] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 86, 86, 86, 86] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [1, 2, 4, 3]}, {[2, 1, 3], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [2, 1, 3, 4]}, {[1, 3, 2], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [1, 2, 4, 3]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2], {[0, 1, 2]}, {}], [[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]}, {1}], [[1, 2, 3], {[0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 2], {[0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 30, 42, 54, 66, 78, 90, 102] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 140, 200, 260, 320] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[5, 0], [4, 1], [0, 3], [3, 2]}, {}], [[1, 1], { [0, 3, 0], [0, 2, 1], [0, 0, 3], [3, 1, 1], [3, 0, 2], [0, 1, 2], [5, 0, 0], [4, 1, 0], [3, 2, 0], [4, 0, 1]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0], [0, 1, 2]}, {}], [[2, 1], {[0, 2, 2], [0, 1, 3], [0, 4, 0], [3, 1, 1], [2, 1, 2], [2, 3, 0], [4, 1, 0], [3, 2, 0], [0, 3, 1], [2, 2, 1]}, {}], [[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], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[2, 1, 1], {[2, 0, 1, 2], [0, 0, 4, 0], [2, 1, 1, 0], [0, 0, 3, 1], [0, 0, 2, 2], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 0, 2, 0], [2, 0, 3, 0], [4, 0, 1, 0], [3, 0, 1, 1], [2, 0, 2, 1]}, {2, 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} ], [[2, 1, 3], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 2, 1, 2], [0, 1, 2, 2], [0, 1, 1, 3], [1, 1, 1, 0], [0, 4, 1, 0], [0, 2, 3, 0], [0, 1, 4, 0], [0, 2, 2, 1], [0, 1, 3, 1], [0, 3, 1, 1], [0, 3, 2, 0]}, {}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[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], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 1, 0, 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, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[2, 1, 3, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [0, 0, 4, 1, 0], [0, 0, 3, 1, 1], [0, 0, 2, 2, 1], [0, 0, 1, 3, 1], [0, 0, 2, 1, 2], [0, 0, 1, 2, 2], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 3], [0, 0, 3, 2, 0], [0, 0, 2, 3, 0], [0, 0, 1, 4, 0]}, {3, 4} ], [[4, 2, 1, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 1, 1, 3, 0]}, {1}], [[3, 2, 1, 4], { [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {1, 2, 3}], [[3, 2, 1, 3], {[0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {1}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 0, 1, 2], [0, 1, 0, 2, 1], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {1, 2} ], [[4, 3, 1, 2], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 3, 1, 0], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {}], [[4, 3, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %1, {1, 2}], [[4, 3, 1, 2, 3], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1, 2}], [[5, 4, 2, 3, 1], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %1, {1, 2}], [[5, 4, 1, 3, 2], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 1, 2, 1], [0, 1, 0, 2, 1, 1], [0, 1, 0, 1, 1, 2], [0, 1, 0, 3, 1, 0], [0, 1, 0, 2, 2, 0], [0, 1, 0, 1, 3, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [ [4, 3, 1, 2, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4}]] %1 := {[0, 1, 1, 1, 1, 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]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 6, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 18, 6, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 50, 6, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [3, 1, 2, 4], [4, 1, 2, 3]}, {[2, 1, 3], [3, 2, 1], [1, 3, 4, 2], [2, 3, 4, 1]}, {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 2, 3], [2, 3, 1], [3, 2, 1, 4], [4, 2, 1, 3]}} the member , {[1, 3, 2], [3, 2, 1], [3, 1, 2, 4], [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], {[0, 3, 0], [1, 1, 0], [0, 2, 1]}, {}], [[1, 2], {[0, 2, 0], [3, 1, 0]}, {}], [[1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [1, 0, 1, 0], [0, 2, 1, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [3, 1, 1, 0]}, {}], [[2, 3, 1], {[0, 3, 1, 0], [0, 2, 1, 1], [1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [ [2, 1, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 1], [0, 0, 3, 0]}, {2, 3} ], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [3, 1, 1, 0, 0]}, {3, 4}] , [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {2, 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, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0], [0, 2, 1, 1, 1]}, {}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {1, 2}] , [[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, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[2, 3, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 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, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[2, 3, 4, 1, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3}], [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 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}], [[2, 3, 5, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 5, 1, 2], { [0, 1, 1, 1, 1, 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]}, {1, 2, 3}], [ [2, 3, 4, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1}], [[2, 3, 4, 1, 1], {[0, 0, 2, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[4, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 6, 7, 8, 9, 10, 11] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 30, 47, 68, 93, 122, 155, 192] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 223, 458, 819, 1333] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [1, 2, 4, 3]}, {[1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [2, 1, 3, 4]}} the member , {[1, 3, 2], [2, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 2, 0]}, {}], [[2, 1], {[0, 1, 1], [2, 1, 0]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[1, 2, 2], {[0, 2, 0, 0]}, {2, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 3, 1], {[2, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [2, 1, 0, 0]}, {1, 3} ], [[2, 1, 1], {[2, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[3, 1, 2], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[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, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 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}], [ [2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {2, 3}], [[1, 2, 3, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 3, 1, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {2}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {}], [[3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {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, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [2, 1, 0, 1, 0]}, {3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [2, 1, 1, 1, 0]}, {}], [[4, 2, 3, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {}], [[4, 1, 2, 3, 5], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 2], %1, {1, 2, 3, 4, 5}], [[5, 1, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2}], [[5, 1, 2, 4, 3], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [0, 2, 1, 1, 0, 0], [2, 1, 1, 1, 0, 0]}, {3, 4}], [ [5, 1, 2, 3, 4], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 2, 1, 1, 1, 0]}, {3, 4}], [[5, 2, 3, 4, 1], { [0, 1, 1, 1, 1, 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, 3, 4}], [ [4, 1, 2, 3, 3], {[0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 1, 1, 0], [2, 1, 1, 0, 1, 0]}, {4, 5}], [[5, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[4, 2, 3, 1, 5], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {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, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 2, 1], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [2, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 2], {[2, 1, 0, 0, 1, 0], [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 1, 2, 1], { [0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 3, 1], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {1}], [[4, 1, 3, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0]}, {1}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 1, 0], [2, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [ [4, 2, 3, 4, 1], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 21, 27, 33, 39, 45, 51, 57] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 58, 70, 82, 94] For the equivalence class of patterns, { {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [4, 1, 2, 3]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 3, 1, 2]}, {[2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [3, 4, 2, 1]}, {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [2, 3, 4, 1]}} the member , {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [4, 1, 2, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2]}, {}], [[1, 1], {[1, 1, 1], [1, 0, 2], [1, 2, 0]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 0]}, {}], [[2, 1], {[0, 3, 0], [0, 1, 2], [1, 2, 1]}, {}], [[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], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[2, 1, 1], {[0, 3, 1, 0], [1, 0, 2, 1], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 1, 2], [0, 0, 3, 0]}, {2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 1, 2, 1], [0, 1, 1, 2], [1, 2, 1, 1]}, {}], [[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 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], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 4, 3], {[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, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[3, 2, 1, 1], { [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [1, 0, 2, 1, 1], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2, 3}], [ [3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {1, 4}], [[4, 3, 2, 1], { [0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {2}], [[4, 3, 1, 2], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 1, 1, 2]}, {}], [[4, 3, 1, 2, 1], {[0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 1, 1, 2]}, {2, 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}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[5, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 2], [0, 1, 1, 1, 1, 0]}, {4, 5}], [ [4, 3, 1, 2, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2, 5], {[0, 1, 1, 1, 1, 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]}, {1, 2, 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, 4, 6, 7, 8, 9, 10, 11, 12] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 22, 23, 25, 27, 29, 31, 33] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 86, 87, 90, 93] For the equivalence class of patterns, { {[1, 3, 2], [2, 1, 3], [4, 1, 2, 3], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [3, 2, 1, 4]}, {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [1, 4, 3, 2]}, {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1], [4, 3, 2, 1]}} the member , {[1, 3, 2], [2, 1, 3], [4, 1, 2, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[5, 0]}, {}], [[1, 1], {[5, 0, 0]}, {1, 2}], [[2, 1], {[0, 3, 0], [0, 1, 1], [3, 1, 0]}, {}], [[1, 2], {[0, 2, 0]}, {}], [[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], [3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1}], [[2, 3, 1], {[0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[3, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {2, 3} ], [[3, 2, 1], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {}], [[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, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 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}], [ [2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {2, 3}], [[1, 2, 3, 1], {[3, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {}], [[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, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 2, 1], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[2, 3, 1, 1], {[0, 0, 3, 1, 0], [3, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {}], [[3, 4, 1, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 1, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1, 2}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[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, 2], { [0, 2, 0, 1, 0], [3, 1, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {}], [[3, 1, 2, 3], { [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [3, 1, 1, 0, 0]}, {}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 4, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [ [3, 4, 1, 2, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 5}], [[4, 5, 1, 2, 3], %4, {1, 2, 3, 4, 5}], [[4, 5, 2, 3, 1], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[3, 4, 1, 2, 5], %4, {1, 2, 3, 4, 5}], [[3, 5, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 1, 2, 2], { [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[3, 4, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 5, 1, 3, 2], %4, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {2}], [[5, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %4, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %4, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %4, {1, 2, 3, 4, 5}], [[5, 3, 4, 1, 2], { [0, 1, 1, 1, 1, 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, 3}], [[4, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[4, 3, 1, 2, 1], %3, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %4, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %4, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %4, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 4, 1, 3, 2], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[1, 2, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {[0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 1, 1, 1], [3, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {4, 5}], [ [2, 3, 4, 2, 1], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0], [0, 3, 0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1, 2, 1], {[0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 4, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2], {[0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [3, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [ [3, 4, 2, 3, 1], {[1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 3, 1, 0, 1, 0]}, {1}], [[4, 1, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [ [4, 2, 3, 4, 1], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 3, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0]}, {4}], [[4, 1, 2, 4, 3], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], { [0, 0, 1, 2, 0, 0], [0, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0]}, {1}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [3, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0]}, {4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 1, 1, 0, 0]} %3 := {[0, 0, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 23, 21, 20, 20, 20, 20, 20] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 72, 55, 53, 53] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [2, 3, 1, 4]}, {[1, 2, 3], [3, 1, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[1, 2, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [1, 4, 2, 3]}} the member , {[1, 2, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [0, 4], [3, 1]}, {}], [[1, 1], {[0, 2, 2], [0, 0, 4], [0, 1, 3], [4, 0, 0], [0, 4, 0], [3, 1, 0], [3, 0, 1], [0, 3, 1] }, {1, 2}], [[2, 1], {[2, 1, 1], [0, 3, 0], [2, 2, 0], [3, 1, 0], [0, 2, 1], [0, 1, 4]}, {}], [[1, 2], {[1, 1, 0], [0, 1, 1], [0, 4, 0]}, {}], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 3, 0]}, {1, 2, 3}], [[1, 3, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 0, 1, 4], [2, 1, 1, 0], [3, 0, 1, 0], [2, 0, 2, 0], [2, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 0], [0, 0, 2, 1], [0, 0, 3, 0]}, {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], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}], [[3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 2, 1], [1, 1, 1, 0]}, {}], [[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}], [[2, 4, 3, 1], {[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, 2], { [0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}], [[1, 4, 3, 2], %7, {}], [[1, 3, 2, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[3, 2, 1, 1], {[0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 0, 1, 2, 1], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[3, 2, 1, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[4, 3, 1, 2], %7, {}], [[4, 2, 1, 3], %7, {}], [[2, 5, 4, 3, 1], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %5, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %5, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %6, {4, 5}], [[1, 4, 3, 2, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %3, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 3, 0, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 2], %6, {1, 3, 4}], [[2, 1, 5, 4, 3], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[2, 1, 5, 3, 4], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %5, {1, 2, 3, 4, 5}], [[5, 3, 2, 4, 1], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 2, 1, 3, 4], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 5], %5, {1, 2, 3, 4, 5}], [[5, 3, 1, 4, 2], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 4], %3, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %3, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %4, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %5, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %6, {4, 5}], [[5, 4, 1, 3, 2], %5, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], %1, {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], %4, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[3, 2, 1, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4}], [[4, 3, 2, 4, 1], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %3, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 2], { [1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 0, 1, 0, 1], [0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 1, 0]}, {1}], [ [3, 2, 1, 3, 3], {[0, 1, 1, 0, 1, 0], [0, 2, 1, 0, 0, 0], [0, 1, 3, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[1, 3, 2, 1, 2], {[0, 1, 1, 0, 1, 0], [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [1, 0, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 4], %2, {1, 2, 3, 4, 5}], [[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}], [[1, 4, 3, 1, 2], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 4}], [[2, 4, 3, 2, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], { [0, 0, 0, 1, 2, 0], [0, 0, 0, 3, 1, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0]}, {2, 4, 5}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[0, 0, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 0, 0]} %4 := {[0, 1, 1, 0, 1, 0]} %5 := {[0, 1, 1, 1, 1, 0]} %6 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %7 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 5, 2, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 9, 3, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 13, 4, 1, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [1, 3, 4, 2]}, {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [3, 1, 2, 4]}, {[1, 2, 3], [3, 1, 2], [2, 4, 3, 1], [4, 3, 2, 1]}} the member , {[1, 2, 3], [2, 3, 1], [4, 2, 1, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [0, 4], [3, 1]}, {}], [[1, 1], {[0, 2, 2], [0, 0, 4], [0, 1, 3], [4, 0, 0], [0, 4, 0], [3, 1, 0], [3, 0, 1], [0, 3, 1] }, {1, 2}], [[1, 2], {[1, 1, 0], [0, 1, 1], [0, 4, 0]}, {}], [[2, 1], {[2, 1, 1], [0, 4, 0], [3, 1, 0], [0, 2, 1], [0, 1, 4], [1, 2, 0]}, {}], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 4, 0], [1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 3, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[2, 1, 1], {[0, 0, 1, 4], [0, 0, 4, 0], [2, 1, 1, 0], [0, 1, 3, 0], [3, 0, 1, 0], [2, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 0], [1, 0, 2, 0], [0, 0, 2, 1]}, {2, 3}], [[3, 1, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}], [[3, 2, 1], {[0, 3, 1, 0], [0, 2, 1, 1], [1, 1, 1, 0], [0, 1, 2, 0]}, {}], [[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}], [[2, 4, 3, 1], {[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, 2], %7, {3, 4}], [[1, 3, 2, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[1, 4, 3, 2], %6, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %7, {3, 4}], [[4, 2, 3, 1], {[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, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[4, 1, 3, 2], %6, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}], [[3, 2, 1, 2], %7, {2}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 1], {[0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0]}, {3, 4}], [[4, 3, 1, 2], %6, {}], [[2, 5, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %3, {4, 5}], [[1, 4, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %4, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 3, 0, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 2], %3, {1, 3, 4}], [[2, 1, 5, 4, 3], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[2, 1, 5, 3, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %5, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], %3, {4, 5}], [[5, 1, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %3, {4, 5}], [[5, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 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], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 0, 1, 1, 1, 0]} %6 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %7 := {[0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 2, 1, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 19, 3, 1, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 90, 4, 1, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}, {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [4, 1, 2, 3]}} the member , {[1, 2, 3], [2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1], [0, 4], [5, 0]}, {}], [[1, 1], {[0, 2, 2], [0, 0, 4], [2, 0, 1], [0, 1, 3], [0, 4, 0], [2, 1, 0], [5, 0, 0], [0, 3, 1] }, {1, 2}], [[1, 2], {[1, 1, 0], [0, 1, 1], [0, 4, 0]}, {}], [[2, 1], {[2, 2, 0], [0, 4, 0], [3, 1, 0], [1, 1, 1], [0, 2, 1], [0, 1, 4]}, {}], [ [1, 2, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [1, 2, 1], {[0, 0, 4, 0], [1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3} ], [[1, 3, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [ [2, 1, 2], {[0, 4, 0, 0], [1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3} ], [[2, 1, 1], {[0, 0, 1, 4], [0, 0, 4, 0], [0, 1, 3, 0], [3, 0, 1, 0], [2, 0, 2, 0], [0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1], [0, 0, 2, 1]}, {2, 3}], [[3, 1, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}], [[3, 2, 1], {[0, 2, 2, 0], [0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0]}, {}] , [[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}], [[2, 4, 3, 1], {[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, 2], %7, {3, 4}], [[1, 3, 2, 1], {[0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[1, 4, 3, 2], %6, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %7, {3, 4}], [[4, 2, 3, 1], {[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, 1], { [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {4}], [[4, 1, 3, 2], %6, {}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], %7, {2}], [ [3, 2, 1, 3], {[0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 1], {[0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 4, 0]}, {3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[4, 3, 1, 2], %6, {}], [[2, 5, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 1], %5, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[1, 5, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 2], %3, {4, 5}], [[1, 4, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 5], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], %4, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 3, 0, 1, 0]}, {4, 5}], [[2, 1, 4, 3, 2], %3, {1, 3, 4}], [[2, 1, 5, 4, 3], {[0, 1, 1, 1, 1, 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]}, {1, 2}], [[2, 1, 5, 3, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 1], %5, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], %3, {4, 5}], [[5, 1, 4, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 5], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 1], %5, {1, 2, 3, 4, 5}], [[5, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[5, 2, 1, 3, 4], %2, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 5], %2, {1, 2, 3, 4, 5}], [[5, 3, 1, 4, 2], %2, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [0, 1, 3, 0, 1, 0]}, {4, 5}], [[4, 2, 1, 3, 4], %4, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], { [0, 1, 1, 1, 1, 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, 3}], [[4, 2, 1, 3, 1], %5, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 2], %3, {1, 2}], [[4, 3, 1, 2, 1], %5, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 3], %1, {1, 2, 3, 4, 5}], [[5, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %2, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %3, {4, 5}], [[5, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 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], %1, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}]] %1 := {[0, 1, 1, 0, 1, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 0, 1, 1, 1, 0]} %6 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %7 := {[0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 5, 2, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 21, 3, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 96, 4, 0, 0] For the equivalence class of patterns, { {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[1, 3, 2], [3, 1, 2], [3, 2, 1, 4], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 4, 3, 2], [4, 3, 2, 1]}} the member , {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 3]}, {}], [[1, 2], {[0, 2, 0], [0, 1, 2]}, {}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {2}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {3}], [ [1, 2, 2], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3} ], [[2, 3, 1], {[0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 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], {[0, 1, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], %3, {1, 2}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {2, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %2, {3, 4}], [[2, 1, 3, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[0, 0, 1, 2, 0], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], %2, {2, 4}], [[3, 4, 2, 1], %3, {3}], [[2, 3, 1, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[3, 2, 1, 4], %3, {1, 2}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 3]}, {3, 4}], [[3, 2, 1, 3], %2, {1}], [[2, 1, 3, 5, 4], %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, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], %1, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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}], [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 3, 1, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[3, 4, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 5, 1], %1, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 2, 1, 0, 0], [0, 1, 1, 2, 0], [0, 1, 2, 0, 0]} %3 := {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 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, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 42, 72, 110, 156, 210, 272, 342] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 303, 674, 1270, 2145] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [3, 2, 1, 4]}, {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2], [2, 1, 3, 4]}, {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1], [4, 3, 1, 2]}, {[1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 1, 2, 3]}} the member , {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [3, 2, 1, 4]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[2, 1]}, {}], [[1, 1], {[2, 0, 1], [2, 1, 0]}, {1, 2}], [[2, 1], {[0, 2, 0], [1, 1, 1]}, {}], [[1, 2], {[1, 1, 0], [0, 3, 1]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[0, 3, 1, 0], [0, 3, 0, 1], [1, 1, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [1, 0, 1, 0], [0, 2, 1, 0]}, {3}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 3, 2], {[0, 2, 1, 1], [1, 1, 1, 0], [0, 1, 2, 0]}, {}], [ [2, 1, 1], {[0, 0, 2, 0], [1, 1, 1, 0], [0, 2, 1, 0], [1, 0, 1, 1]}, {2, 3} ], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {1}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 3, 1]}, {}], [[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[1, 2, 3, 4], %5, {}], [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [ [1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 3, 2, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {2}], [ [1, 3, 2, 2], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 0, 2, 0], [0, 2, 0, 1, 1], [1, 1, 0, 1, 0]}, {3, 4}], [[1, 3, 2, 4], %5, {}], [[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, 2, 1, 0, 0], [0, 1, 3, 1, 0], [0, 1, 3, 0, 1], [1, 1, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 4], %5, {1, 2}], [[2, 1, 4, 3], {[1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [0, 1, 2, 1, 1]}, {2}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3], { [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[1, 2, 3, 4, 2], %3, {1, 2, 3, 4, 5}], [[1, 3, 4, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {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, 5, 4], %4, {1, 2, 3, 4, 5}], [[2, 3, 4, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 2], %3, {1, 2, 3, 4, 5}], [[1, 4, 2, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %2, {1, 2, 3, 4, 5}], [[2, 4, 3, 5, 1], %4, {1, 2, 3, 4, 5}], [[1, 4, 3, 5, 2], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 5, 4], %4, {1, 2, 3, 4, 5}], [[1, 3, 2, 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]}, {2, 3, 4}], [[1, 3, 2, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[5, 4, 2, 1, 3], %4, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], { [0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[2, 1, 4, 2, 3], %3, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], { [1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 1, 1, 1, 0]}, {1}], [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}], [[3, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], { [0, 1, 0, 2, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 2, 0, 1, 0], [1, 1, 0, 0, 1, 0]}, {4, 5}], [[2, 1, 3, 2, 3], { [1, 1, 0, 1, 0, 0], [0, 2, 0, 1, 0, 0], [0, 1, 0, 2, 0, 0], [0, 1, 2, 1, 0, 0]}, {1, 3, 5}], [[3, 2, 1, 3, 4], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3], { [0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 0, 1, 0]} %3 := {[0, 1, 0, 1, 1, 0]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[0, 1, 2, 1, 0], [1, 1, 1, 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, 4, 6, 7, 7, 7, 7, 7, 7] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 26, 26, 25, 25, 25, 25, 25] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 115, 112, 110, 110] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4], [4, 1, 2, 3]}, {[2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]}} the member , {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4], [2, 3, 4, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[1, 1, 1]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 2], {[1, 1, 1, 0], [1, 1, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[1, 1, 1, 0], [0, 1, 1, 1]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {[1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}] , [[1, 2, 3, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {1}], [[1, 3, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 2, 4, 3], {[0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[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, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[2, 4, 3, 1], %1, {1, 2, 3}], [[1, 3, 2, 3], {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {1}], [[1, 3, 2, 1], %2, {1}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %2, {3, 4}], [[3, 4, 2, 1], %1, {1, 2, 3}], [[3, 2, 1, 1], %2, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], %1, {1, 2, 3}], [[1, 2, 4, 3, 3], {[1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [ [1, 2, 4, 3, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 2}], [[1, 2, 5, 3, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 5, 4, 2], {[0, 1, 1, 1, 1, 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]}, {1, 2, 3, 4}], [[1, 2, 4, 3, 5], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 5, 4, 1], {[0, 1, 1, 1, 1, 0]}, {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, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 5, 4, 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}]] %1 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %2 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 24, 30, 36, 42, 48, 54, 60] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 92, 104, 116, 128] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 1, 3, 2]}, {[2, 1, 3], [2, 3, 1], [1, 4, 2, 3], [1, 4, 3, 2]}, {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [3, 2, 1, 4]}, {[1, 3, 2], [3, 1, 2], [2, 3, 4, 1], [3, 2, 4, 1]}} the member , {[2, 1, 3], [2, 3, 1], [4, 1, 2, 3], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 1]}, {}], [[1, 1], {[1, 1, 0], [1, 0, 1]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {1}], [[2, 1], {[0, 3, 0], [0, 1, 1], [1, 2, 0]}, {}], [ [3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1, 2} ], [[2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [ [2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [1, 0, 2, 0], [0, 0, 3, 0]}, {2, 3} ], [[3, 2, 1], {[1, 2, 1, 0], [0, 3, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], { [1, 0, 2, 1, 0], [0, 0, 3, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}], [[3, 2, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 2, 1, 1, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[4, 3, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 3, 1, 2, 4], {[0, 1, 1, 1, 0, 0]}, {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}], [[5, 3, 1, 2, 4], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 5], %1, {1, 2, 3, 4, 5}], [[5, 4, 2, 3, 1], %1, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 1], { [0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 5}], [[4, 3, 1, 2, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 4, 1, 3, 2], %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, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 33, 42, 51, 60, 69, 78, 87] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 182, 216, 250, 284] For the equivalence class of patterns, { {[2, 3, 1], [3, 1, 2], [2, 1, 4, 3], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [3, 4, 1, 2]}} the member , {[2, 3, 1], [3, 1, 2], [2, 1, 4, 3], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[1, 2], {[1, 1, 0], [0, 4, 0]}, {1}], [[2, 1], {[0, 2, 0], [2, 1, 0]}, {}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0]}, {3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0]}, {2, 3}], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 2, 1, 0], [0, 1, 0, 2, 0], [1, 1, 0, 1, 0]}, {4}], [[3, 2, 4, 1], {[0, 1, 1, 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, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {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]}, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {}], [ [3, 2, 1, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[2, 1, 3, 5, 4], %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, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {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]}, {3, 4}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 3, 1, 5, 2], %1, {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], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[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}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {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, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 3, 2, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1], {[0, 0, 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}], [[4, 3, 1, 4, 2], {[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, 4], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {1, 4}], [[3, 2, 1, 3, 3], {[0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]}, {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, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 32, 45, 58, 71, 84, 97, 110] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 166, 239, 312, 385] For the equivalence class of patterns, { {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, {[3, 1, 2], [3, 2, 1], [2, 1, 3, 4], [2, 1, 4, 3]}, {[1, 2, 3], [1, 3, 2], [3, 4, 1, 2], [3, 4, 2, 1]}, {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3], [2, 1, 4, 3]}} the member , {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 1, 1]}, {}], [[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]}, {1, 3}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 3, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[2, 1, 2], {[0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 2], {[0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[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, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], %8, {1, 4}], [[2, 4, 3, 1], %7, {}], [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {}], [[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], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %8, {3, 4}], [[2, 3, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 4}], [[3, 4, 2, 1], %7, {}], [[3, 1, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}] , [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], %8, {2, 4}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {}], [[4, 2, 3, 1], %7, {}], [[3, 2, 1, 1], %8, {3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {2, 4}], [[4, 3, 2, 1], %7, {}], [[1, 4, 3, 2, 5], %3, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[1, 5, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[1, 5, 4, 2, 3], %3, {1, 2, 3, 4, 5}], [[1, 4, 3, 2, 3], %5, {1, 2, 3, 4, 5}], [[2, 5, 4, 3, 1], %6, {1, 2, 3, 4}], [[1, 4, 3, 2, 1], %1, {1}], [[1, 4, 3, 2, 2], {[0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [ [1, 5, 4, 3, 2], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 2, 3, 4}], [[2, 5, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 5, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 5], %3, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 3], %5, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %6, {1, 2, 3, 4}], [[2, 4, 3, 1, 1], %1, {4, 5}], [[3, 5, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 5, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 5], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], %5, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %6, {1, 2, 3, 4}], [[3, 5, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], %1, {4, 5}], [[3, 4, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], %2, {1, 2, 3, 4, 5}], [[5, 1, 4, 2, 3], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 3], %5, {1, 2, 3, 4, 5}], [[5, 2, 4, 3, 1], %6, {1, 2, 3, 4}], [[4, 1, 3, 2, 5], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}], [[5, 1, 3, 2, 4], %3, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], { [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[4, 1, 3, 2, 1], %1, {2}], [[5, 1, 4, 3, 2], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 2, 3, 4}], [[5, 2, 3, 1, 4], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 5], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 3], %5, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 2], %2, {1, 2, 3, 4, 5}], [[5, 2, 4, 1, 3], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 3, 4, 2, 1], %6, {1, 2, 3, 4}], [[5, 3, 4, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 2, 3, 1, 1], %1, {4, 5}], [[5, 4, 2, 1, 3], %3, {1, 2, 3, 4, 5}], [[5, 3, 2, 1, 4], %3, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], %6, {1, 2, 3, 4}], [[4, 3, 2, 1, 3], %5, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], %4, {1, 2, 3, 4, 5}], [[5, 4, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 5], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 2], %2, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], %1, {4, 5}]] %1 := {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]} %2 := {[0, 1, 0, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 0]} %4 := {[0, 1, 1, 1, 0, 0]} %5 := {[0, 1, 1, 0, 1, 0]} %6 := {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]} %7 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %8 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 33, 42, 51, 60, 69, 78, 87] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 182, 216, 250, 284] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [1, 4, 3, 2]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2, 4], [3, 2, 1, 4]}, {[2, 1, 3], [3, 1, 2], [2, 3, 4, 1], [2, 4, 3, 1]}, {[1, 3, 2], [2, 3, 1], [4, 1, 2, 3], [4, 2, 1, 3]}} the member , {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [1, 4, 3, 2]}, has a scheme of depth , 4 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[1, 2], {[0, 3, 0], [0, 2, 1]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 3, 2], %3, {1}], [[1, 2, 2], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], %3, {}], [[1, 2, 3], {[0, 1, 3, 0], [0, 1, 2, 1], [0, 2, 1, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], %3, {}], [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], %2, {1}], [[1, 2, 3, 3], {[0, 1, 3, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0]}, {3, 4}], [[1, 2, 4, 3], %1, {2}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1], [0, 1, 1, 3, 0]}, {2}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[2, 3, 4, 1], %1, {1, 2, 3}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %2, {3, 4}], [[3, 4, 2, 1], %1, {1, 2, 3}], [[3, 2, 1, 1], %2, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], %1, {1, 2, 3}]] %1 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %2 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} %3 := {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 30, 42, 54, 66, 78, 90, 102] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 140, 200, 260, 320] For the equivalence class of patterns, { {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]}, {[1, 2, 3], [2, 3, 1], [2, 1, 4, 3], [4, 3, 2, 1]}, {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]}, {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3], [4, 3, 2, 1]}} the member , {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[4, 0], [2, 2], [0, 3], [3, 1]}, {}], [[1, 1], { [2, 1, 1], [0, 3, 0], [4, 0, 0], [2, 2, 0], [3, 1, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2], [3, 0, 1], [2, 0, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [2, 1, 0], [0, 1, 2]}, {}], [[2, 1], {[0, 2, 2], [1, 1, 0], [0, 1, 3], [0, 4, 0], [0, 3, 1]}, {}], [ [1, 2, 1], {[0, 0, 2, 0], [1, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 3, 1], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[1, 2, 2], {[0, 2, 0, 0], [2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 3], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[2, 1, 3], {[0, 1, 1, 2], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[2, 1, 1], {[0, 0, 4, 0], [0, 0, 3, 1], [1, 0, 1, 0], [0, 0, 2, 2], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {2, 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, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [2, 1, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 4], {[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, 1], { [0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]}, {2, 4}], [[2, 3, 4, 1], %3, {}], [[4, 2, 3, 1], {[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, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 3, 0], [0, 1, 0, 1, 2], [0, 1, 0, 2, 1], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[3, 1, 2, 4], %3, {}], [[4, 1, 2, 3], %3, {}], [[3, 1, 2, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {}], [[2, 3, 4, 1, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 5, 1, 4], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 5], %2, {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], %2, {1, 2, 3, 4, 5}], [[2, 4, 5, 1, 3], %2, {1, 2, 3, 4, 5}], [[3, 4, 5, 2, 1], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 5}], [[3, 1, 2, 5, 4], %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, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 5, 2], %2, {1, 2, 3, 4, 5}], [[4, 2, 3, 5, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 5], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 5, 3], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 5], %2, {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], {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]}, {4, 5}], [[5, 1, 3, 4, 2], %2, {1, 2, 3, 4, 5}], [[5, 1, 2, 4, 3], %2, {1, 2, 3, 4, 5}], [[5, 1, 2, 3, 4], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 2, 3, 4, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 4, 2], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 3, 4, 1], %1, {1, 2, 3, 4, 5}], [[4, 1, 2, 4, 3], %1, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 1, 0, 1, 0], [0, 1, 2, 0, 0, 0], [0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 1, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}]] %1 := {[0, 1, 1, 1, 0, 0]} %2 := {[0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 5, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 18, 0, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 88, 0, 0, 0] For the equivalence class of patterns, { {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [2, 1, 4, 3]}, {[1, 2, 3], [1, 3, 2], [3, 4, 1, 2], [4, 2, 3, 1]}, {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2], [4, 2, 3, 1]}, {[3, 1, 2], [3, 2, 1], [1, 3, 2, 4], [2, 1, 4, 3]}} the member , {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4], [2, 1, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[1, 1, 0]}, {}], [[1, 2], {[1, 1, 0], [0, 2, 1]}, {}], [[1, 3, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {2, 3}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 2, 1, 0], [0, 0, 2, 1]}, {1}], [[1, 2, 3], {[0, 1, 2, 1], [1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[3, 2, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[1, 0, 1, 0]}, {2, 3}], [[2, 1, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1]}, {3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 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, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[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}], [[1, 2, 4, 3], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {1, 2}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 1]}, {1, 2}], [[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, 4, 3], {[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, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}] , [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 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]}, {}], [[3, 1, 2, 2], {[0, 2, 0, 1, 0], [1, 1, 0, 1, 0]}, {3, 4}], [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0]}, {2, 3}] , [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4], {[0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}], [[3, 1, 2, 3], {[0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0]}, {}], [[2, 1, 3, 5, 4], %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, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 4, 5, 2], %1, {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]}, {3, 4}], [[2, 1, 3, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 1, 3, 4, 2], {[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}], [[4, 2, 3, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 2, 3, 3], {[0, 1, 2, 0, 0, 1], [0, 2, 1, 0, 0, 0], [0, 1, 2, 0, 1, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 0, 0, 0]}, {4, 5}], [[3, 1, 2, 3, 4], { [1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0]}, {2, 3, 4}], [[4, 1, 2, 4, 3], { [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3, 2], { [1, 1, 0, 1, 0, 0], [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, 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, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 37, 56, 79, 106, 137, 172, 211] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 254, 492, 856, 1373] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 2, 1]}, {[1, 3, 2], [3, 1, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [1, 4, 2, 3]}, {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [2, 3, 1, 4]}} the member , {[1, 3, 2], [3, 1, 2], [3, 2, 4, 1], [4, 3, 2, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[3, 0]}, {}], [[1, 1], {[3, 0, 0]}, {1, 2}], [[1, 2], {[0, 2, 0], [3, 1, 0]}, {}], [[2, 1], {[0, 2, 0], [2, 1, 0]}, {}], [[1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0]}, {1}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [3, 1, 1, 0]}, {}], [[2, 3, 1], {[2, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[2, 1, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0]}, {2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [2, 1, 0, 0]}, {3}], [[3, 2, 1], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {}], [[1, 2, 3, 3], {[0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [3, 1, 1, 0, 0]}, {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, 4], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}] , [[1, 2, 3, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {1}], [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0], [2, 1, 1, 1, 0]}, {1, 2}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {[2, 0, 1, 1, 0], [0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 4], %2, {1, 2}], [[2, 3, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {1, 2, 4}], [[3, 4, 2, 1], %2, {}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], {[0, 0, 1, 2, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0]}, {3, 4}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0]}, {4}], [[3, 2, 1, 4], %2, {}], [[4, 3, 1, 5, 2], %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}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {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], [1, 1, 1, 1, 1, 0], [0, 2, 1, 1, 1, 0]}, {4}], [[3, 2, 1, 4, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[4, 5, 3, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 5, 2, 1, 3], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 5, 2, 1, 4], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %1, {1, 2, 3, 4, 5}], [[3, 4, 2, 1, 1], { [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [1, 0, 1, 1, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {4, 5}], [[3, 4, 2, 1, 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, 4], { [0, 1, 1, 2, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {2}]] %1 := {[0, 1, 1, 1, 1, 0]} %2 := {[0, 1, 2, 1, 0], [1, 1, 1, 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, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 41, 62, 87, 116, 149, 186, 227] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 293, 537, 907, 1430] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [2, 1, 4, 3]}, {[1, 3, 2], [3, 2, 1], [2, 3, 4, 1], [3, 4, 1, 2]}, {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3], [3, 2, 1, 4]}, {[2, 1, 3], [3, 2, 1], [3, 4, 1, 2], [4, 1, 2, 3]}} the member , {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [2, 1, 4, 3]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[1, 2], [0, 3]}, {}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {2}], [[1, 1], { [0, 3, 0], [1, 1, 1], [0, 2, 1], [1, 0, 2], [0, 0, 3], [0, 1, 2], [1, 2, 0] }, {1, 2}], [[2, 1], {[1, 3, 0], [0, 4, 0], [0, 2, 1], [0, 1, 2]}, {}], [ [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 3, 0, 0]}, {1, 3} ], [[3, 1, 2], {[0, 3, 1, 0], [1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[1, 0, 3, 0], [0, 0, 4, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 1, 2]}, {2, 3}], [ [3, 2, 1], {[0, 2, 2, 0], [0, 1, 3, 0], [0, 2, 1, 1], [0, 1, 2, 1], [0, 1, 1, 2], [0, 4, 1, 0], [1, 3, 1, 0]}, {}], [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 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}], [[2, 1, 4, 3], {[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, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {3, 4}], [[2, 1, 3, 2], {[0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[4, 2, 1, 3], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[3, 2, 1, 2], {[0, 3, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[3, 2, 1, 3], {[0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[4, 3, 2, 1], {[0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 2, 1, 1, 1], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 1, 1, 1, 2], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {1}], [[4, 3, 1, 2], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0], [0, 3, 1, 1, 0]}, {1, 2}], [[3, 2, 1, 1], {[0, 0, 2, 1, 1], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [1, 0, 3, 1, 0], [0, 0, 4, 1, 0], [0, 0, 1, 2, 1], [0, 0, 1, 1, 2], [0, 1, 1, 1, 0]}, {3, 4}], [[3, 2, 1, 4], { [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], %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}], [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}], [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {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, 4], {[0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0]}, {4, 5}], [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 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}], [[3, 2, 4, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], {[0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {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, 5, 6, 7, 8, 9, 10, 11] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 21, 23, 25, 27, 29, 31, 33] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 96, 99, 102, 105] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, {[2, 1, 3], [2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}, {[1, 3, 2], [3, 1, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [2, 1, 3, 4]}} the member , {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [1, 2, 4, 3]}, has a scheme of depth , 3 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, 1], [0, 1, 2]}, {}], [[2, 3, 1], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 1], {[1, 0, 1, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 2, 3}], [[1, 3, 2], {[0, 2, 2, 0], [0, 1, 3, 0], [1, 1, 1, 0], [0, 1, 1, 1]}, {2}], [[1, 2, 3], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[1, 2, 2], {[1, 1, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 2, 0, 1], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 66, 132, 222, 336, 474, 636, 822] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 798, 2510, 5824, 11280] For the equivalence class of patterns, { {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4], [4, 3, 2, 1]}, {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}} the member , {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}, has a scheme of depth , 3 here it is: [[[], {}, {}], [[1], {[3, 0], [0, 3]}, {}], [[1, 1], {[3, 0, 0], [0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[1, 2], {[0, 2, 0], [3, 1, 0], [0, 1, 2]}, {}], [[2, 1], {[0, 2, 0], [0, 1, 3], [2, 1, 0]}, {}], [[1, 3, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[1, 2, 2], {[3, 1, 0, 0], [0, 2, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {2, 3}], [[1, 2, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1], [0, 0, 1, 2]}, {1, 3}], [[1, 2, 3], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [3, 1, 1, 0]}, {2}], [[2, 3, 1], {[2, 1, 1, 0], [0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[3, 2, 1], {[0, 1, 1, 3], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {2}], [[2, 1, 1], {[0, 0, 2, 0], [2, 0, 1, 0], [0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 1, 1]}, {2, 3}], [[2, 1, 2], {[0, 2, 0, 0], [2, 1, 0, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 1, 0, 2]}, {1, 3}], [[2, 1, 3], {[2, 1, 1, 0], [0, 1, 1, 2], [0, 2, 1, 0], [0, 1, 2, 0]}, {1}]] Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 6, 0, 0, 0, 0, 0] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 24, 70, 70, 0, 0, 0, 0, 0] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 148, 924, 924, 0, 0] For the equivalence class of patterns, { {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [4, 1, 3, 2]}, {[2, 1, 3], [3, 2, 1], [1, 4, 2, 3], [4, 1, 2, 3]}, {[1, 3, 2], [3, 2, 1], [2, 3, 1, 4], [2, 3, 4, 1]}, {[1, 2, 3], [3, 1, 2], [3, 2, 1, 4], [3, 2, 4, 1]}} the member , {[1, 2, 3], [2, 3, 1], [1, 4, 3, 2], [4, 1, 3, 2]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {[0, 3]}, {}], [[1, 1], {[0, 3, 0], [0, 2, 1], [0, 0, 3], [0, 1, 2]}, {1, 2}], [[1, 2], {[0, 3, 0], [1, 1, 0], [0, 1, 1]}, {2}], [[2, 1], {[0, 3, 0], [0, 1, 3], [0, 2, 1]}, {}], [[3, 1, 2], {[1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 1, 1], {[0, 0, 1, 3], [0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1], [0, 0, 2, 1], [0, 0, 3, 0]}, {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, 1, 3, 0], [1, 1, 1, 0], [0, 2, 1, 0], [0, 1, 1, 1]}, {}], [[3, 2, 1], {[0, 1, 1, 3], [0, 2, 2, 0], [0, 1, 3, 0], [0, 3, 1, 0], [0, 2, 1, 1], [0, 1, 2, 1]}, {}], [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], { [0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {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}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {}], [[2, 1, 4, 3], %5, {}], [[3, 2, 1, 2], { [0, 2, 0, 1, 0], [0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2}], [[4, 3, 1, 2], %5, {1, 2}], [[3, 2, 1, 1], { [0, 0, 2, 1, 1], [0, 0, 3, 1, 0], [0, 0, 2, 2, 0], [0, 0, 1, 3, 0], [0, 0, 1, 2, 1], [0, 1, 1, 1, 0], [0, 0, 1, 1, 3]}, {3, 4}], [[3, 2, 1, 3], {[0, 1, 3, 0, 0], [0, 2, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1]}, {1}], [[3, 2, 1, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 2, 1, 1, 0], [0, 1, 1, 3, 0]}, {2, 3}], [[4, 2, 1, 3], %5, {}], [[4, 3, 2, 1], {[0, 2, 2, 1, 0], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0], [0, 2, 1, 1, 1], [0, 1, 2, 1, 1], [0, 1, 1, 2, 1], [0, 2, 1, 2, 0], [0, 1, 2, 2, 0], [0, 1, 1, 3, 0]}, {}], [[2, 1, 4, 3, 5], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 5, 4, 1], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 5, 4, 3], %4, {1, 2, 3, 4, 5}], [[2, 1, 5, 3, 4], %4, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3], %2, {4, 5}], [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 1, 5, 4, 2], %4, {1, 2, 3, 4, 5}], [[5, 3, 2, 4, 1], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], %2, {4, 5}], [[5, 2, 1, 3, 4], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 5], %4, {1, 2, 3, 4, 5}], [[5, 3, 1, 4, 2], %4, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 2], %1, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], %4, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 4], { [0, 1, 1, 1, 0, 1], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 2, 1, 1, 0, 0], [0, 1, 1, 3, 0, 0]}, {1, 3, 4}], [[5, 3, 2, 1, 4], %3, {2, 3, 4}], [[5, 4, 3, 1, 2], %3, {1, 2, 3}], [[5, 4, 2, 1, 3], %3, {1, 2}], [[4, 3, 2, 1, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 2, 3}], [[4, 3, 2, 1, 3], %2, {2}], [[4, 3, 2, 1, 5], {[0, 1, 1, 1, 1, 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, 3, 4}], [[4, 3, 2, 1, 1], {[0, 0, 2, 1, 1, 1], [0, 0, 1, 2, 1, 1], [0, 0, 1, 1, 2, 1], [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, 0, 1, 1, 3, 0], [0, 1, 1, 1, 1, 0], [0, 0, 3, 1, 1, 0]}, {4, 5}], [[5, 4, 3, 2, 1], {}, {3}], [[2, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 4], %1, {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}], [[3, 2, 4, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], {[0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 2, 0], [0, 2, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}]] %1 := {[0, 1, 0, 1, 1, 0]} %2 := {[1, 1, 1, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1], [0, 1, 2, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0]} %3 := {[0, 1, 1, 1, 1, 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]} %4 := {[0, 1, 1, 1, 1, 0]} %5 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 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, 4, 5, 6, 7, 8, 9, 10, 11] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 19, 14, 16, 18, 20, 22, 24, 26] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 93, 35, 38, 41, 44] For the equivalence class of patterns, { {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [2, 4, 3, 1]}, {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [3, 4, 2, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2, 4], [4, 3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4], [4, 2, 1, 3]}} the member , {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3], [2, 4, 3, 1]}, has a scheme of depth , 5 here it is: [[[], {}, {}], [[1], {}, {}], [[1, 1], {}, {1, 2}], [[2, 1], {[0, 2, 0], [0, 1, 1]}, {}], [[1, 2], {[1, 2, 0]}, {}], [[1, 2, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {1, 3}], [[1, 2, 2], {[1, 2, 0, 0]}, {2, 3}], [[1, 3, 2], {[1, 1, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {1}], [[2, 3, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3], {[1, 2, 1, 0], [0, 1, 2, 0]}, {}], [[2, 1, 2], {[0, 2, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1]}, {1, 3}], [[3, 1, 2], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 3], {[0, 1, 1, 0]}, {1, 2, 3}], [[2, 1, 1], {[0, 0, 2, 0], [0, 1, 1, 0], [0, 0, 1, 1]}, {2, 3}], [[3, 2, 1], {[0, 2, 1, 0], [0, 1, 2, 0], [0, 1, 1, 1]}, {}], [[1, 2, 3, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 0, 1, 1]}, {1, 2, 4}], [[1, 2, 3, 3], {[1, 2, 1, 0, 0], [0, 1, 2, 0, 0]}, {3, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1], %2, {1}], [[2, 3, 4, 1], %1, {1, 2, 3}], [[1, 3, 4, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1}], [[1, 2, 3, 4], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [1, 2, 1, 1, 0]}, {}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %2, {3, 4}], [[3, 4, 2, 1], %1, {1, 2, 3}], [[3, 2, 1, 1], %2, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4], {[0, 1, 1, 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, 1, 0, 0]}, {1, 2, 3, 4}], [[4, 3, 2, 1], %1, {1, 2, 3}], [[2, 3, 4, 5, 1], {[0, 1, 1, 1, 1, 1], [0, 1, 2, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0], [0, 2, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 5, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[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, 0, 0], [1, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0]}, {4, 5}], [ [1, 2, 3, 4, 2], {[1, 1, 0, 1, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 1, 1], [0, 1, 1, 1, 1, 0]}, {1, 2}], [ [1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 1], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 4, 5, 2], {[0, 1, 1, 1, 1, 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]}, {1, 2, 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 := {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 2, 1, 1, 0], [0, 1, 1, 2, 0]} %2 := {[0, 0, 1, 2, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1]} Using the scheme, the first, , 10, terms for , 1, copies of each letter are [1, 2, 4, 6, 8, 10, 12, 14, 16, 18] Using the scheme, the first, , 10, terms for , 2, copies of each letter are [1, 6, 18, 24, 30, 36, 42, 48, 54, 60] Using the scheme, the first, , 7, terms for , 3, copies of each letter are [1, 20, 80, 92, 104, 116, 128] Out of a total of , 103, cases 89, were successful and , 14, failed Success Rate: , 0.864 Here are the failures {{{[1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [2, 1, 4, 3]}}, { {[1, 2, 3], [2, 3, 1], [4, 1, 3, 2], [4, 2, 1, 3]}, {[1, 3, 2], [3, 2, 1], [2, 3, 1, 4], [3, 1, 2, 4]}, {[2, 1, 3], [3, 2, 1], [1, 3, 4, 2], [1, 4, 2, 3]}, {[1, 2, 3], [3, 1, 2], [2, 4, 3, 1], [3, 2, 4, 1]}}, { {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [4, 3, 2, 1]}}, { {[1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 1, 2, 3]}, {[2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [2, 3, 4, 1]}}, { {[1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 2, 3, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [1, 3, 2, 4]}, {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4], [2, 1, 3, 4]}, {[1, 3, 2], [2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2]}}, { {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [2, 4, 3, 1]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2, 4], [4, 2, 1, 3]}}, { {[1, 2, 3], [2, 3, 1], [4, 2, 1, 3], [4, 3, 1, 2]}, {[2, 1, 3], [3, 2, 1], [1, 2, 4, 3], [1, 3, 4, 2]}, {[1, 2, 3], [3, 1, 2], [2, 4, 3, 1], [3, 4, 2, 1]}, {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4], [3, 1, 2, 4]}}, { {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [4, 3, 2, 1]}, {[2, 3, 1], [3, 1, 2], [2, 1, 3, 4], [4, 3, 2, 1]}, {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [4, 3, 1, 2]}, {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4], [3, 4, 2, 1]}}, { {[2, 3, 1], [3, 1, 2], [2, 1, 3, 4], [3, 2, 1, 4]}, {[1, 3, 2], [2, 1, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1], [3, 4, 2, 1]}, {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [1, 4, 3, 2]}}, { {[1, 3, 2], [2, 3, 1], [3, 1, 2, 4], [4, 1, 2, 3]}, {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2], [2, 3, 4, 1]}, {[2, 1, 3], [3, 1, 2], [1, 4, 3, 2], [2, 4, 3, 1]}, {[1, 3, 2], [2, 3, 1], [3, 2, 1, 4], [4, 2, 1, 3]}}, { {[2, 3, 1], [3, 1, 2], [1, 2, 3, 4], [1, 3, 2, 4]}, {[1, 3, 2], [2, 1, 3], [4, 2, 3, 1], [4, 3, 2, 1]}}, { {[2, 1, 3], [3, 2, 1], [1, 2, 4, 3], [1, 4, 2, 3]}, {[1, 2, 3], [2, 3, 1], [4, 1, 3, 2], [4, 3, 1, 2]}, {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4], [2, 3, 1, 4]}, {[1, 2, 3], [3, 1, 2], [3, 2, 4, 1], [3, 4, 2, 1]}}, { {[1, 3, 2], [2, 1, 3], [3, 4, 2, 1], [4, 3, 1, 2]}, {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3], [2, 1, 3, 4]}}, { {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4], [2, 1, 4, 3]}, {[1, 3, 2], [2, 1, 3], [3, 4, 1, 2], [4, 2, 3, 1]}}}