"for patterns of lengths: ", [[5, 1]] There all together, 89, different equivalence classes For the equivalence class of patterns, { {[[2, 0], [4, 0], [5, 0], [1, 0], [3, 1]]}, {[[2, 0], [5, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [5, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [5, 1], [1, 0], [4, 0]]}, {[[3, 0], [4, 0], [1, 1], [5, 0], [2, 0]]}, {[[3, 1], [5, 0], [1, 0], [2, 0], [4, 0]]}, {[[4, 0], [1, 0], [5, 1], [2, 0], [3, 0]]}, {[[4, 0], [2, 0], [1, 0], [5, 0], [3, 1]]}} the member , {[[2, 0], [5, 0], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[1, 2, 3], {}, {2}, {}], [[2, 1], {}, {1}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {3}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 104, 532 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096, 32704759586810036, 367673428857985261, 4248441203547678973, 50404110322407327694, 613422482715518955984, 7651214934643864880660, 97729390389485866368687, 1277366713175414998967035, 17072416428147420401930622, 233171987305887240225320798] For the equivalence class of patterns, { {[[2, 0], [3, 0], [5, 1], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 0], [5, 0], [2, 0]]}, {[[3, 1], [5, 0], [2, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 0], [5, 0], [3, 1]]}, {[[4, 0], [1, 0], [5, 1], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 1], [5, 0], [2, 0]]}} the member , {[[2, 0], [5, 0], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[1, 2, 3], {}, {2}, {}], [[2, 1], {}, {1}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 104, 532 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096, 32704759586810036, 367673428857985261, 4248441203547678973, 50404110322407327694, 613422482715518955984, 7651214934643864880660, 97729390389485866368687, 1277366713175414998967035, 17072416428147420401930622, 233171987305887240225320798] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 0], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [3, 0], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [3, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 0], [4, 0], [5, 1]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 0], [4, 1], [5, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [3, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 0], [4, 1], [5, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [3, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1], [4, 0], [5, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 0], [5, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 0], [5, 0]]}, {[[2, 1], [1, 0], [3, 0], [4, 0], [5, 0]]}, {[[4, 0], [5, 1], [3, 0], [2, 0], [1, 0]]}, {[[4, 1], [5, 0], [3, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [3, 0], [1, 0], [2, 1]]}, {[[5, 0], [4, 0], [3, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 0], [5, 0], [4, 1]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 0], [5, 0]]}, {[[4, 0], [5, 0], [3, 1], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1], [5, 0], [4, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1, 2}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 0], [3, 1], [5, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 0], [5, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 0], [5, 0]]}, {[[5, 0], [3, 0], [4, 1], [2, 0], [1, 0]]}, {[[5, 0], [3, 1], [4, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [2, 0], [3, 1], [1, 0]]}, {[[5, 0], [4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [4, 0], [3, 1], [5, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 0], [5, 0], [3, 1]]}, {[[1, 0], [2, 0], [5, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 0], [5, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 0], [5, 0]]}, {[[3, 1], [5, 0], [4, 0], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [5, 1], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [1, 1], [3, 0], [2, 0]]}, {[[5, 0], [4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1], [4, 0], [5, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {}, {1}, {}], [[1, 3, 2], {}, {2}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 104, 532 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096, 32704759586810036, 367673428857985261, 4248441203547678973, 50404110322407327694, 613422482715518955984, 7651214934643864880660, 97729390389485866368687, 1277366713175414998967035, 17072416428147420401930622, 233171987305887240225320798] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 0], [5, 1], [3, 0]]}, {[[1, 0], [2, 0], [5, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0], [4, 0], [5, 0]]}, {[[3, 0], [1, 1], [2, 0], [4, 0], [5, 0]]}, {[[3, 0], [5, 1], [4, 0], [2, 0], [1, 0]]}, {[[4, 1], [3, 0], [5, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [1, 0], [3, 0], [2, 1]]}, {[[5, 0], [4, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [4, 0], [5, 1], [3, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {4}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 1], [5, 0], [3, 0]]}, {[[1, 0], [2, 0], [5, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 0], [5, 0]]}, {[[3, 0], [1, 0], [2, 1], [4, 0], [5, 0]]}, {[[3, 0], [5, 0], [4, 1], [2, 0], [1, 0]]}, {[[4, 0], [3, 1], [5, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [1, 0], [3, 1], [2, 0]]}, {[[5, 0], [4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [4, 1], [5, 0], [3, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {4}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [5, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [5, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1], [4, 0], [5, 0]]}, {[[3, 1], [2, 0], [1, 0], [4, 0], [5, 0]]}, {[[3, 0], [4, 0], [5, 1], [2, 0], [1, 0]]}, {[[3, 1], [4, 0], [5, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [1, 0], [2, 0], [3, 1]]}, {[[5, 0], [4, 0], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [5, 0], [4, 0], [3, 1]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {4}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [2, 0], [5, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 0], [5, 0]]}, {[[3, 0], [4, 1], [5, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [5, 0], [4, 1], [3, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {4}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1], [5, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 1], [5, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 0], [5, 0]]}, {[[4, 0], [5, 0], [2, 0], [3, 1], [1, 0]]}, {[[4, 0], [5, 0], [2, 1], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [4, 1], [1, 0], [2, 0]]}, {[[5, 0], [3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1], [5, 0], [4, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[2, 3, 1], {}, {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {4}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 103, 513 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969] For the equivalence class of patterns, { {[[2, 0], [1, 0], [4, 0], [5, 0], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1], [5, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0], [5, 0], [4, 0]]}, {[[3, 1], [5, 0], [4, 0], [1, 0], [2, 0]]}, {[[4, 0], [3, 0], [5, 1], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 1], [3, 0], [2, 0]]}, {[[4, 0], [5, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1], [5, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {}, {1}, {}], [[1, 3, 2], {}, {2}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 23, 104, 532 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096, 32704759586810036, 367673428857985261, 4248441203547678973, 50404110322407327694, 613422482715518955984, 7651214934643864880660, 97729390389485866368687, 1277366713175414998967035, 17072416428147420401930622, 233171987305887240225320798] Out of a total of , 89, cases 15, were successful and , 74, failed Success Rate: , 0.169 Here are the failures {{{[[2, 0], [5, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [5, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [5, 0], [3, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [3, 0], [5, 0], [2, 1]]}, {[[4, 0], [1, 0], [3, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [3, 0], [5, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [5, 0], [2, 0]]}}, { {[[2, 0], [5, 0], [3, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [3, 1], [5, 0], [2, 0]]}}, { {[[2, 0], [1, 1], [5, 0], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [5, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [4, 0], [5, 0], [1, 0], [2, 1]]}, {[[3, 0], [4, 0], [5, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 0], [2, 0], [3, 0]]}, {[[4, 1], [5, 0], [1, 0], [2, 0], [3, 0]]}}, { {[[2, 0], [3, 0], [5, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 1], [2, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 0], [5, 1], [3, 0]]}, {[[4, 1], [1, 0], [5, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 0], [5, 0], [2, 1]]}}, { {[[2, 0], [4, 0], [5, 0], [1, 1], [3, 0]]}, {[[2, 1], [5, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [5, 0], [1, 0], [4, 1]]}, {[[3, 0], [4, 0], [1, 0], [5, 0], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [2, 0], [4, 0]]}, {[[4, 1], [1, 0], [5, 0], [2, 0], [3, 0]]}, {[[4, 0], [2, 0], [1, 0], [5, 1], [3, 0]]}}, { {[[1, 0], [4, 0], [3, 1], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 1], [4, 0], [1, 0]]}}, { {[[2, 1], [4, 0], [5, 0], [1, 0], [3, 0]]}, {[[2, 0], [5, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [5, 0], [1, 1], [4, 0]]}, {[[3, 0], [4, 0], [1, 0], [5, 1], [2, 0]]}, {[[3, 0], [5, 0], [1, 0], [2, 0], [4, 1]]}, {[[4, 0], [1, 1], [5, 0], [2, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [5, 0], [3, 0]]}}, { {[[2, 0], [3, 0], [5, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [5, 0], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [5, 0], [2, 1]]}, {[[3, 0], [5, 0], [2, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 0], [5, 0], [3, 0]]}, {[[4, 0], [1, 1], [5, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 0], [5, 1], [2, 0]]}}, { {[[1, 0], [4, 0], [5, 1], [3, 0], [2, 0]]}, {[[1, 0], [5, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 0], [5, 0], [1, 0]]}, {[[3, 1], [4, 0], [2, 0], [1, 0], [5, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [4, 0], [3, 1]]}, {[[5, 0], [2, 0], [1, 1], [3, 0], [4, 0]]}}, { {[[1, 0], [4, 1], [3, 0], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [3, 0], [4, 1], [1, 0]]}, {[[4, 0], [1, 0], [3, 0], [2, 1], [5, 0]]}, {[[4, 0], [2, 1], [3, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [3, 0], [4, 1], [2, 0]]}, {[[5, 0], [2, 1], [3, 0], [1, 0], [4, 0]]}}, { {[[2, 0], [4, 1], [5, 0], [1, 0], [3, 0]]}, {[[2, 0], [5, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [5, 0], [1, 0], [4, 0]]}, {[[3, 0], [4, 1], [1, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [1, 0], [2, 1], [4, 0]]}, {[[4, 0], [1, 0], [5, 0], [2, 1], [3, 0]]}, {[[4, 0], [2, 1], [1, 0], [5, 0], [3, 0]]}}, { {[[1, 0], [3, 0], [5, 1], [2, 0], [4, 0]]}, {[[1, 0], [4, 0], [2, 0], [5, 0], [3, 1]]}, {[[2, 0], [4, 0], [1, 1], [3, 0], [5, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0], [5, 0]]}, {[[3, 1], [5, 0], [2, 0], [4, 0], [1, 0]]}, {[[4, 0], [2, 0], [5, 1], [3, 0], [1, 0]]}, {[[5, 0], [2, 0], [4, 0], [1, 0], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [4, 0], [2, 0]]}}, { {[[2, 0], [3, 1], [5, 0], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [5, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [2, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 1], [5, 0], [3, 0]]}, {[[4, 0], [1, 0], [5, 0], [3, 1], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [5, 0], [2, 0]]}}, { {[[1, 0], [4, 0], [5, 0], [2, 0], [3, 1]]}, {[[1, 0], [4, 0], [5, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 0], [5, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [1, 0], [4, 0], [3, 1]]}, {[[5, 0], [2, 0], [1, 1], [4, 0], [3, 0]]}}, { {[[2, 1], [3, 0], [5, 0], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [5, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [5, 1], [2, 0]]}, {[[3, 0], [5, 0], [2, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 0], [5, 0], [3, 0]]}, {[[4, 0], [1, 0], [5, 0], [3, 0], [2, 1]]}, {[[4, 1], [3, 0], [1, 0], [5, 0], [2, 0]]}}, { {[[2, 0], [1, 0], [3, 0], [5, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0], [5, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 0], [1, 0], [2, 1]]}, {[[4, 0], [5, 0], [3, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [3, 0], [1, 0], [2, 0]]}, {[[4, 1], [5, 0], [3, 0], [1, 0], [2, 0]]}}, { {[[2, 0], [4, 0], [1, 0], [5, 0], [3, 1]]}, {[[2, 0], [4, 0], [1, 1], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [5, 0], [2, 0], [4, 0]]}, {[[3, 0], [5, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [5, 0], [1, 0], [4, 0], [2, 0]]}, {[[4, 0], [2, 0], [5, 0], [1, 0], [3, 1]]}, {[[4, 0], [2, 0], [5, 1], [1, 0], [3, 0]]}}, { {[[2, 0], [4, 0], [1, 0], [5, 1], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [5, 0], [2, 0], [4, 0]]}, {[[3, 0], [5, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [4, 0], [2, 0]]}, {[[4, 0], [2, 0], [5, 0], [1, 1], [3, 0]]}, {[[4, 1], [2, 0], [5, 0], [1, 0], [3, 0]]}}, { {[[2, 0], [4, 1], [1, 0], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [2, 1], [4, 0]]}, {[[3, 0], [5, 0], [1, 0], [4, 1], [2, 0]]}, {[[4, 0], [2, 1], [5, 0], [1, 0], [3, 0]]}}, { {[[2, 0], [4, 0], [5, 1], [1, 0], [3, 0]]}, {[[2, 0], [5, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [5, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [5, 0], [1, 0], [4, 0]]}, {[[3, 1], [4, 0], [1, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [1, 1], [2, 0], [4, 0]]}, {[[4, 0], [1, 0], [5, 0], [2, 0], [3, 1]]}, {[[4, 0], [2, 0], [1, 1], [5, 0], [3, 0]]}}, { {[[1, 0], [4, 0], [5, 0], [2, 1], [3, 0]]}, {[[1, 0], [4, 1], [5, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 1], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1], [5, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [1, 0], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [4, 0], [3, 0]]}}, { {[[1, 0], [2, 1], [3, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1], [5, 0]]}, {[[4, 0], [5, 0], [3, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 0], [1, 0], [2, 0]]}}, { {[[1, 1], [2, 0], [3, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 0], [5, 1]]}, {[[4, 0], [5, 0], [3, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [3, 0], [1, 0], [2, 0]]}}, { {[[1, 0], [2, 0], [4, 0], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 0], [5, 0]]}, {[[5, 1], [3, 0], [4, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [2, 0], [3, 0], [1, 1]]}}, { {[[1, 0], [2, 1], [4, 0], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1], [5, 0]]}, {[[5, 0], [3, 0], [4, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 0], [3, 0], [1, 0]]}}, { {[[1, 1], [2, 0], [4, 0], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 0], [5, 1]]}, {[[5, 0], [3, 0], [4, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 0], [3, 0], [1, 0]]}}, { {[[1, 0], [2, 1], [4, 0], [5, 0], [3, 0]]}, {[[1, 0], [2, 1], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 1], [5, 0]]}, {[[3, 0], [5, 0], [4, 0], [2, 1], [1, 0]]}, {[[4, 0], [3, 0], [5, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 0], [3, 0], [2, 0]]}, {[[5, 0], [4, 1], [2, 0], [1, 0], [3, 0]]}}, { {[[1, 1], [2, 0], [4, 0], [5, 0], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [1, 0], [2, 0], [4, 0], [5, 1]]}, {[[3, 0], [5, 0], [4, 0], [2, 0], [1, 1]]}, {[[4, 0], [3, 0], [5, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 0], [2, 0]]}, {[[5, 1], [4, 0], [2, 0], [1, 0], [3, 0]]}}, { {[[1, 0], [2, 1], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [4, 0], [5, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 0], [2, 0], [3, 0]]}}, { {[[1, 1], [2, 0], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [4, 0], [5, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [2, 0], [3, 0]]}}, { {[[1, 0], [3, 0], [2, 0], [5, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0], [5, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 0], [5, 0]]}, {[[4, 0], [5, 1], [2, 0], [3, 0], [1, 0]]}, {[[4, 1], [5, 0], [2, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [4, 0], [1, 0], [2, 1]]}, {[[5, 0], [3, 0], [4, 0], [1, 1], [2, 0]]}}, { {[[1, 1], [3, 0], [2, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 0], [5, 1]]}, {[[4, 0], [5, 0], [2, 0], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 0], [1, 0], [2, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [3, 0], [4, 0], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 0], [5, 0]]}, {[[5, 0], [2, 0], [4, 0], [3, 0], [1, 1]]}, {[[5, 1], [2, 0], [4, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [2, 0], [4, 0], [1, 1]]}, {[[5, 1], [3, 0], [2, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 0], [5, 0]]}, {[[5, 0], [2, 1], [4, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [2, 0], [4, 1], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 1], [5, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 0], [5, 0]]}, {[[5, 0], [2, 0], [4, 0], [3, 1], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [2, 1], [4, 0], [1, 0]]}, {[[5, 0], [3, 1], [2, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1], [5, 0]]}, {[[2, 1], [5, 0], [4, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0], [5, 0]]}, {[[4, 0], [3, 0], [2, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [4, 0], [3, 0], [2, 0]]}, {[[5, 0], [3, 0], [2, 0], [1, 0], [4, 1]]}}, { {[[1, 0], [3, 0], [4, 0], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [4, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [4, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 0], [5, 0]]}, {[[4, 1], [3, 0], [2, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 0], [3, 0], [2, 1]]}, {[[5, 0], [3, 0], [2, 0], [1, 1], [4, 0]]}}, { {[[1, 0], [3, 0], [4, 1], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [4, 1], [3, 0], [1, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 0], [5, 0]]}, {[[4, 0], [3, 1], [2, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 0], [3, 1], [2, 0]]}, {[[5, 0], [3, 0], [2, 1], [1, 0], [4, 0]]}}, { {[[1, 0], [3, 1], [4, 0], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [4, 0], [3, 1], [1, 0]]}, {[[4, 0], [1, 0], [2, 0], [3, 1], [5, 0]]}, {[[4, 0], [3, 0], [2, 1], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 1], [3, 0], [2, 0]]}, {[[5, 0], [3, 1], [2, 0], [1, 0], [4, 0]]}}, { {[[1, 1], [3, 0], [4, 0], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 0], [4, 0], [3, 0], [1, 1]]}, {[[4, 0], [1, 0], [2, 0], [3, 0], [5, 1]]}, {[[4, 0], [3, 0], [2, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [4, 0], [3, 0], [2, 0]]}, {[[5, 1], [3, 0], [2, 0], [1, 0], [4, 0]]}}, { {[[1, 0], [3, 0], [5, 0], [2, 0], [4, 1]]}, {[[1, 0], [4, 0], [2, 0], [5, 1], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0], [5, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0], [5, 0]]}, {[[3, 0], [5, 1], [2, 0], [4, 0], [1, 0]]}, {[[4, 1], [2, 0], [5, 0], [3, 0], [1, 0]]}, {[[5, 0], [2, 0], [4, 0], [1, 1], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [4, 0], [2, 1]]}}, { {[[1, 0], [3, 0], [5, 0], [2, 1], [4, 0]]}, {[[1, 0], [4, 1], [2, 0], [5, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0], [5, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1], [5, 0]]}, {[[3, 0], [5, 0], [2, 0], [4, 1], [1, 0]]}, {[[4, 0], [2, 1], [5, 0], [3, 0], [1, 0]]}, {[[5, 0], [2, 1], [4, 0], [1, 0], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [4, 1], [2, 0]]}}, { {[[1, 0], [3, 1], [5, 0], [2, 0], [4, 0]]}, {[[1, 0], [4, 0], [2, 1], [5, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 1], [5, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0], [5, 0]]}, {[[3, 0], [5, 0], [2, 1], [4, 0], [1, 0]]}, {[[4, 0], [2, 0], [5, 0], [3, 1], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [1, 0], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [4, 0], [2, 0]]}}, { {[[1, 1], [3, 0], [5, 0], [2, 0], [4, 0]]}, {[[1, 1], [4, 0], [2, 0], [5, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [1, 0], [4, 0], [2, 0], [5, 1]]}, {[[3, 0], [5, 0], [2, 0], [4, 0], [1, 1]]}, {[[4, 0], [2, 0], [5, 0], [3, 0], [1, 1]]}, {[[5, 1], [2, 0], [4, 0], [1, 0], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 0], [2, 0]]}}, { {[[1, 0], [3, 0], [5, 0], [4, 0], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [4, 0], [5, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 1], [5, 0]]}, {[[3, 0], [4, 0], [2, 0], [5, 1], [1, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0], [5, 0]]}, {[[5, 0], [1, 1], [4, 0], [2, 0], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [2, 0], [4, 1]]}}, { {[[1, 0], [3, 0], [5, 0], [4, 1], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [4, 1], [5, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 0], [5, 0]]}, {[[3, 0], [4, 1], [2, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 0], [5, 0]]}, {[[5, 0], [1, 0], [4, 0], [2, 1], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [2, 1], [4, 0]]}}, { {[[1, 0], [3, 0], [5, 1], [4, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [4, 0], [5, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 0], [5, 0]]}, {[[3, 1], [4, 0], [2, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 0], [5, 0]]}, {[[5, 0], [1, 0], [4, 0], [2, 0], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [2, 0], [4, 0]]}}, { {[[1, 0], [3, 1], [5, 0], [4, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [4, 0], [5, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0], [5, 0]]}, {[[3, 0], [4, 0], [2, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1], [5, 0]]}, {[[5, 0], [1, 0], [4, 1], [2, 0], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [2, 0], [4, 0]]}}, { {[[1, 1], [3, 0], [5, 0], [4, 0], [2, 0]]}, {[[1, 1], [5, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [4, 0], [5, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [4, 0], [1, 0], [5, 1]]}, {[[3, 0], [4, 0], [2, 0], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [1, 0], [3, 0], [5, 1]]}, {[[5, 1], [1, 0], [4, 0], [2, 0], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [2, 0], [4, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [3, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 0], [4, 0], [1, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 0], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 1], [5, 0]]}, {[[2, 1], [5, 0], [3, 0], [4, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 0], [5, 0]]}, {[[4, 0], [2, 0], [3, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 0], [4, 0], [2, 0]]}, {[[5, 0], [2, 0], [3, 0], [1, 0], [4, 1]]}}, { {[[1, 0], [4, 0], [3, 0], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [3, 0], [4, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0], [5, 0]]}, {[[4, 1], [2, 0], [3, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [3, 0], [4, 0], [2, 1]]}, {[[5, 0], [2, 0], [3, 0], [1, 1], [4, 0]]}}, { {[[1, 0], [4, 0], [3, 1], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [3, 1], [4, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 0], [5, 0]]}, {[[4, 0], [2, 0], [3, 1], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [3, 1], [4, 0], [2, 0]]}, {[[5, 0], [2, 0], [3, 1], [1, 0], [4, 0]]}}, { {[[1, 1], [4, 0], [3, 0], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 0], [3, 0], [4, 0], [1, 1]]}, {[[4, 0], [1, 0], [3, 0], [2, 0], [5, 1]]}, {[[4, 0], [2, 0], [3, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 0], [4, 0], [2, 0]]}, {[[5, 1], [2, 0], [3, 0], [1, 0], [4, 0]]}}, { {[[1, 1], [4, 0], [5, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [4, 0], [1, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 0], [4, 0], [3, 0]]}}, { {[[1, 0], [4, 0], [5, 0], [3, 0], [2, 1]]}, {[[1, 0], [5, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 0], [5, 1], [1, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1], [5, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [1, 1], [2, 0], [4, 0], [3, 0]]}, {[[5, 0], [2, 0], [1, 0], [3, 0], [4, 1]]}}, { {[[1, 0], [4, 0], [5, 0], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 1], [5, 0], [1, 0]]}, {[[3, 0], [4, 0], [2, 1], [1, 0], [5, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 1], [4, 0], [3, 0]]}, {[[5, 0], [2, 0], [1, 0], [3, 1], [4, 0]]}}, { {[[1, 0], [4, 1], [5, 0], [3, 0], [2, 0]]}, {[[1, 0], [5, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 1], [4, 0], [5, 0], [1, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 0], [5, 0]]}, {[[4, 0], [3, 0], [1, 0], [2, 1], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [3, 0], [4, 0]]}}, { {[[1, 1], [4, 0], [5, 0], [3, 0], [2, 0]]}, {[[1, 1], [5, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [4, 0], [5, 0], [1, 1]]}, {[[3, 0], [4, 0], [2, 0], [1, 0], [5, 1]]}, {[[4, 0], [3, 0], [1, 0], [2, 0], [5, 1]]}, {[[5, 1], [1, 0], [2, 0], [4, 0], [3, 0]]}, {[[5, 1], [2, 0], [1, 0], [3, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [5, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 0], [5, 1], [1, 0]]}, {[[2, 1], [4, 0], [3, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1], [5, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [3, 0], [2, 0], [4, 1]]}, {[[5, 0], [1, 1], [3, 0], [2, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [4, 1], [3, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [3, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [3, 0], [2, 1], [4, 0]]}}, { {[[1, 0], [5, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [3, 1], [2, 0], [4, 0]]}}, { {[[1, 1], [5, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 0], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [3, 0], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [3, 0], [2, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [5, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [5, 1], [1, 0]]}, {[[2, 1], [3, 0], [4, 0], [5, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 0], [1, 1], [5, 0]]}, {[[4, 1], [3, 0], [2, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [3, 0], [4, 1]]}, {[[5, 0], [1, 1], [2, 0], [3, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 1], [5, 0], [1, 0]]}, {[[2, 0], [3, 1], [4, 0], [5, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 0], [5, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [3, 1], [4, 0]]}, {[[5, 0], [1, 0], [2, 1], [3, 0], [4, 0]]}}, { {[[1, 1], [5, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [5, 0], [1, 1]]}, {[[4, 0], [3, 0], [2, 0], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [2, 0], [3, 0], [4, 0]]}}, { {[[2, 0], [1, 0], [3, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 1], [1, 0], [2, 0]]}}, { {[[2, 0], [1, 0], [4, 0], [5, 1], [3, 0]]}, {[[2, 0], [1, 0], [5, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0], [5, 0], [4, 0]]}, {[[3, 0], [5, 1], [4, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [3, 0], [2, 1]]}, {[[4, 0], [5, 0], [2, 0], [1, 1], [3, 0]]}}, { {[[2, 0], [1, 0], [4, 1], [5, 0], [3, 0]]}, {[[2, 0], [1, 0], [5, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1], [5, 0], [4, 0]]}, {[[3, 0], [5, 0], [4, 1], [1, 0], [2, 0]]}, {[[4, 0], [3, 1], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [3, 1], [2, 0]]}, {[[4, 0], [5, 0], [2, 1], [1, 0], [3, 0]]}}, { {[[2, 0], [1, 1], [4, 0], [5, 0], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [5, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 0], [5, 1], [4, 0]]}, {[[3, 0], [5, 0], [4, 0], [1, 1], [2, 0]]}, {[[4, 0], [3, 0], [5, 0], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [1, 0], [3, 0], [2, 0]]}, {[[4, 0], [5, 1], [2, 0], [1, 0], [3, 0]]}}, { {[[2, 1], [1, 0], [4, 0], [5, 0], [3, 0]]}, {[[2, 0], [1, 1], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 0], [5, 0], [4, 1]]}, {[[3, 0], [5, 0], [4, 0], [1, 0], [2, 1]]}, {[[4, 0], [3, 0], [5, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 0], [3, 0], [2, 0]]}, {[[4, 1], [5, 0], [2, 0], [1, 0], [3, 0]]}}, { {[[2, 0], [1, 0], [5, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1], [5, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [4, 0], [5, 1], [1, 0], [2, 0]]}, {[[3, 1], [4, 0], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [2, 0], [3, 1]]}, {[[4, 0], [5, 0], [1, 1], [2, 0], [3, 0]]}}, { {[[2, 0], [1, 0], [5, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [4, 1], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [2, 1], [3, 0]]}}} {{{[[2, 0], [5, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [5, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [5, 0], [3, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [3, 0], [5, 0], [2, 1]]}, {[[4, 0], [1, 0], [3, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [3, 0], [5, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [5, 0], [2, 0]]}}, { {[[2, 0], [5, 0], [3, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [3, 1], [5, 0], [2, 0]]}}, { {[[2, 0], [1, 1], [5, 0], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [5, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [4, 0], [5, 0], [1, 0], [2, 1]]}, {[[3, 0], [4, 0], [5, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 0], [2, 0], [3, 0]]}, {[[4, 1], [5, 0], [1, 0], [2, 0], [3, 0]]}}, { {[[2, 0], [3, 0], [5, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 1], [2, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 0], [5, 1], [3, 0]]}, {[[4, 1], [1, 0], [5, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 0], [5, 0], [2, 1]]}}, { {[[2, 0], [4, 0], [5, 0], [1, 1], [3, 0]]}, {[[2, 1], [5, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [5, 0], [1, 0], [4, 1]]}, {[[3, 0], [4, 0], [1, 0], [5, 0], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [2, 0], [4, 0]]}, {[[4, 1], [1, 0], [5, 0], [2, 0], [3, 0]]}, {[[4, 0], [2, 0], [1, 0], [5, 1], [3, 0]]}}, { {[[1, 0], [4, 0], [3, 1], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 1], [4, 0], [1, 0]]}}, { {[[2, 1], [4, 0], [5, 0], [1, 0], [3, 0]]}, {[[2, 0], [5, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [5, 0], [1, 1], [4, 0]]}, {[[3, 0], [4, 0], [1, 0], [5, 1], [2, 0]]}, {[[3, 0], [5, 0], [1, 0], [2, 0], [4, 1]]}, {[[4, 0], [1, 1], [5, 0], [2, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [5, 0], [3, 0]]}}, { {[[2, 0], [3, 0], [5, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [5, 0], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [5, 0], [2, 1]]}, {[[3, 0], [5, 0], [2, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 0], [5, 0], [3, 0]]}, {[[4, 0], [1, 1], [5, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 0], [5, 1], [2, 0]]}}, { {[[1, 0], [4, 0], [5, 1], [3, 0], [2, 0]]}, {[[1, 0], [5, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 0], [5, 0], [1, 0]]}, {[[3, 1], [4, 0], [2, 0], [1, 0], [5, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [4, 0], [3, 1]]}, {[[5, 0], [2, 0], [1, 1], [3, 0], [4, 0]]}}, { {[[1, 0], [4, 1], [3, 0], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [3, 0], [4, 1], [1, 0]]}, {[[4, 0], [1, 0], [3, 0], [2, 1], [5, 0]]}, {[[4, 0], [2, 1], [3, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [3, 0], [4, 1], [2, 0]]}, {[[5, 0], [2, 1], [3, 0], [1, 0], [4, 0]]}}, { {[[2, 0], [4, 1], [5, 0], [1, 0], [3, 0]]}, {[[2, 0], [5, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [5, 0], [1, 0], [4, 0]]}, {[[3, 0], [4, 1], [1, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [1, 0], [2, 1], [4, 0]]}, {[[4, 0], [1, 0], [5, 0], [2, 1], [3, 0]]}, {[[4, 0], [2, 1], [1, 0], [5, 0], [3, 0]]}}, { {[[1, 0], [3, 0], [5, 1], [2, 0], [4, 0]]}, {[[1, 0], [4, 0], [2, 0], [5, 0], [3, 1]]}, {[[2, 0], [4, 0], [1, 1], [3, 0], [5, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0], [5, 0]]}, {[[3, 1], [5, 0], [2, 0], [4, 0], [1, 0]]}, {[[4, 0], [2, 0], [5, 1], [3, 0], [1, 0]]}, {[[5, 0], [2, 0], [4, 0], [1, 0], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [4, 0], [2, 0]]}}, { {[[2, 0], [3, 1], [5, 0], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [5, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [2, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 1], [5, 0], [3, 0]]}, {[[4, 0], [1, 0], [5, 0], [3, 1], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [5, 0], [2, 0]]}}, { {[[1, 0], [4, 0], [5, 0], [2, 0], [3, 1]]}, {[[1, 0], [4, 0], [5, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 0], [5, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [1, 0], [4, 0], [3, 1]]}, {[[5, 0], [2, 0], [1, 1], [4, 0], [3, 0]]}}, { {[[2, 1], [3, 0], [5, 0], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [5, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [5, 1], [2, 0]]}, {[[3, 0], [5, 0], [2, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 0], [5, 0], [3, 0]]}, {[[4, 0], [1, 0], [5, 0], [3, 0], [2, 1]]}, {[[4, 1], [3, 0], [1, 0], [5, 0], [2, 0]]}}, { {[[2, 0], [1, 0], [3, 0], [5, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0], [5, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 0], [1, 0], [2, 1]]}, {[[4, 0], [5, 0], [3, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [3, 0], [1, 0], [2, 0]]}, {[[4, 1], [5, 0], [3, 0], [1, 0], [2, 0]]}}, { {[[2, 0], [4, 0], [1, 0], [5, 0], [3, 1]]}, {[[2, 0], [4, 0], [1, 1], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [5, 0], [2, 0], [4, 0]]}, {[[3, 0], [5, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [5, 0], [1, 0], [4, 0], [2, 0]]}, {[[4, 0], [2, 0], [5, 0], [1, 0], [3, 1]]}, {[[4, 0], [2, 0], [5, 1], [1, 0], [3, 0]]}}, { {[[2, 0], [4, 0], [1, 0], [5, 1], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [5, 0], [2, 0], [4, 0]]}, {[[3, 0], [5, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [4, 0], [2, 0]]}, {[[4, 0], [2, 0], [5, 0], [1, 1], [3, 0]]}, {[[4, 1], [2, 0], [5, 0], [1, 0], [3, 0]]}}, { {[[2, 0], [4, 1], [1, 0], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [2, 1], [4, 0]]}, {[[3, 0], [5, 0], [1, 0], [4, 1], [2, 0]]}, {[[4, 0], [2, 1], [5, 0], [1, 0], [3, 0]]}}, { {[[2, 0], [4, 0], [5, 1], [1, 0], [3, 0]]}, {[[2, 0], [5, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [5, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [5, 0], [1, 0], [4, 0]]}, {[[3, 1], [4, 0], [1, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [1, 1], [2, 0], [4, 0]]}, {[[4, 0], [1, 0], [5, 0], [2, 0], [3, 1]]}, {[[4, 0], [2, 0], [1, 1], [5, 0], [3, 0]]}}, { {[[1, 0], [4, 0], [5, 0], [2, 1], [3, 0]]}, {[[1, 0], [4, 1], [5, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 1], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1], [5, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [1, 0], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [4, 0], [3, 0]]}}, { {[[1, 0], [2, 1], [3, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1], [5, 0]]}, {[[4, 0], [5, 0], [3, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 0], [1, 0], [2, 0]]}}, { {[[1, 1], [2, 0], [3, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 0], [5, 1]]}, {[[4, 0], [5, 0], [3, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [3, 0], [1, 0], [2, 0]]}}, { {[[1, 0], [2, 0], [4, 0], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 0], [5, 0]]}, {[[5, 1], [3, 0], [4, 0], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [2, 0], [3, 0], [1, 1]]}}, { {[[1, 0], [2, 1], [4, 0], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1], [5, 0]]}, {[[5, 0], [3, 0], [4, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 0], [3, 0], [1, 0]]}}, { {[[1, 1], [2, 0], [4, 0], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 0], [5, 1]]}, {[[5, 0], [3, 0], [4, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 0], [3, 0], [1, 0]]}}, { {[[1, 0], [2, 1], [4, 0], [5, 0], [3, 0]]}, {[[1, 0], [2, 1], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 1], [5, 0]]}, {[[3, 0], [5, 0], [4, 0], [2, 1], [1, 0]]}, {[[4, 0], [3, 0], [5, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 0], [3, 0], [2, 0]]}, {[[5, 0], [4, 1], [2, 0], [1, 0], [3, 0]]}}, { {[[1, 1], [2, 0], [4, 0], [5, 0], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [1, 0], [2, 0], [4, 0], [5, 1]]}, {[[3, 0], [5, 0], [4, 0], [2, 0], [1, 1]]}, {[[4, 0], [3, 0], [5, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 0], [2, 0]]}, {[[5, 1], [4, 0], [2, 0], [1, 0], [3, 0]]}}, { {[[1, 0], [2, 1], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [4, 0], [5, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 0], [2, 0], [3, 0]]}}, { {[[1, 1], [2, 0], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [4, 0], [5, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [2, 0], [3, 0]]}}, { {[[1, 0], [3, 0], [2, 0], [5, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0], [5, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 0], [5, 0]]}, {[[4, 0], [5, 1], [2, 0], [3, 0], [1, 0]]}, {[[4, 1], [5, 0], [2, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [4, 0], [1, 0], [2, 1]]}, {[[5, 0], [3, 0], [4, 0], [1, 1], [2, 0]]}}, { {[[1, 1], [3, 0], [2, 0], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 0], [5, 1]]}, {[[4, 0], [5, 0], [2, 0], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 0], [1, 0], [2, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [3, 0], [4, 0], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 0], [5, 0]]}, {[[5, 0], [2, 0], [4, 0], [3, 0], [1, 1]]}, {[[5, 1], [2, 0], [4, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [2, 0], [4, 0], [1, 1]]}, {[[5, 1], [3, 0], [2, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 0], [5, 0]]}, {[[5, 0], [2, 1], [4, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [2, 0], [4, 1], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 1], [5, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 0], [5, 0]]}, {[[5, 0], [2, 0], [4, 0], [3, 1], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [2, 1], [4, 0], [1, 0]]}, {[[5, 0], [3, 1], [2, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1], [5, 0]]}, {[[2, 1], [5, 0], [4, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0], [5, 0]]}, {[[4, 0], [3, 0], [2, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [4, 0], [3, 0], [2, 0]]}, {[[5, 0], [3, 0], [2, 0], [1, 0], [4, 1]]}}, { {[[1, 0], [3, 0], [4, 0], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [4, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [4, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 0], [5, 0]]}, {[[4, 1], [3, 0], [2, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 0], [3, 0], [2, 1]]}, {[[5, 0], [3, 0], [2, 0], [1, 1], [4, 0]]}}, { {[[1, 0], [3, 0], [4, 1], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [4, 1], [3, 0], [1, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 0], [5, 0]]}, {[[4, 0], [3, 1], [2, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 0], [3, 1], [2, 0]]}, {[[5, 0], [3, 0], [2, 1], [1, 0], [4, 0]]}}, { {[[1, 0], [3, 1], [4, 0], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [4, 0], [3, 1], [1, 0]]}, {[[4, 0], [1, 0], [2, 0], [3, 1], [5, 0]]}, {[[4, 0], [3, 0], [2, 1], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 1], [3, 0], [2, 0]]}, {[[5, 0], [3, 1], [2, 0], [1, 0], [4, 0]]}}, { {[[1, 1], [3, 0], [4, 0], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 0], [4, 0], [3, 0], [1, 1]]}, {[[4, 0], [1, 0], [2, 0], [3, 0], [5, 1]]}, {[[4, 0], [3, 0], [2, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [4, 0], [3, 0], [2, 0]]}, {[[5, 1], [3, 0], [2, 0], [1, 0], [4, 0]]}}, { {[[1, 0], [3, 0], [5, 0], [2, 0], [4, 1]]}, {[[1, 0], [4, 0], [2, 0], [5, 1], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0], [5, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0], [5, 0]]}, {[[3, 0], [5, 1], [2, 0], [4, 0], [1, 0]]}, {[[4, 1], [2, 0], [5, 0], [3, 0], [1, 0]]}, {[[5, 0], [2, 0], [4, 0], [1, 1], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [4, 0], [2, 1]]}}, { {[[1, 0], [3, 0], [5, 0], [2, 1], [4, 0]]}, {[[1, 0], [4, 1], [2, 0], [5, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0], [5, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1], [5, 0]]}, {[[3, 0], [5, 0], [2, 0], [4, 1], [1, 0]]}, {[[4, 0], [2, 1], [5, 0], [3, 0], [1, 0]]}, {[[5, 0], [2, 1], [4, 0], [1, 0], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [4, 1], [2, 0]]}}, { {[[1, 0], [3, 1], [5, 0], [2, 0], [4, 0]]}, {[[1, 0], [4, 0], [2, 1], [5, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 1], [5, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0], [5, 0]]}, {[[3, 0], [5, 0], [2, 1], [4, 0], [1, 0]]}, {[[4, 0], [2, 0], [5, 0], [3, 1], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [1, 0], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [4, 0], [2, 0]]}}, { {[[1, 1], [3, 0], [5, 0], [2, 0], [4, 0]]}, {[[1, 1], [4, 0], [2, 0], [5, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [1, 0], [4, 0], [2, 0], [5, 1]]}, {[[3, 0], [5, 0], [2, 0], [4, 0], [1, 1]]}, {[[4, 0], [2, 0], [5, 0], [3, 0], [1, 1]]}, {[[5, 1], [2, 0], [4, 0], [1, 0], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 0], [2, 0]]}}, { {[[1, 0], [3, 0], [5, 0], [4, 0], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [4, 0], [5, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 1], [5, 0]]}, {[[3, 0], [4, 0], [2, 0], [5, 1], [1, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0], [5, 0]]}, {[[5, 0], [1, 1], [4, 0], [2, 0], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [2, 0], [4, 1]]}}, { {[[1, 0], [3, 0], [5, 0], [4, 1], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [4, 1], [5, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 0], [5, 0]]}, {[[3, 0], [4, 1], [2, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 0], [5, 0]]}, {[[5, 0], [1, 0], [4, 0], [2, 1], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [2, 1], [4, 0]]}}, { {[[1, 0], [3, 0], [5, 1], [4, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [4, 0], [5, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 0], [5, 0]]}, {[[3, 1], [4, 0], [2, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 0], [5, 0]]}, {[[5, 0], [1, 0], [4, 0], [2, 0], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [2, 0], [4, 0]]}}, { {[[1, 0], [3, 1], [5, 0], [4, 0], [2, 0]]}, {[[1, 0], [5, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [4, 0], [5, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0], [5, 0]]}, {[[3, 0], [4, 0], [2, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1], [5, 0]]}, {[[5, 0], [1, 0], [4, 1], [2, 0], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [2, 0], [4, 0]]}}, { {[[1, 1], [3, 0], [5, 0], [4, 0], [2, 0]]}, {[[1, 1], [5, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [4, 0], [5, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [4, 0], [1, 0], [5, 1]]}, {[[3, 0], [4, 0], [2, 0], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [1, 0], [3, 0], [5, 1]]}, {[[5, 1], [1, 0], [4, 0], [2, 0], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [2, 0], [4, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [3, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 0], [4, 0], [1, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 0], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 0], [4, 0], [1, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 1], [5, 0]]}, {[[2, 1], [5, 0], [3, 0], [4, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 0], [5, 0]]}, {[[4, 0], [2, 0], [3, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 0], [4, 0], [2, 0]]}, {[[5, 0], [2, 0], [3, 0], [1, 0], [4, 1]]}}, { {[[1, 0], [4, 0], [3, 0], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [3, 0], [4, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0], [5, 0]]}, {[[4, 1], [2, 0], [3, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [3, 0], [4, 0], [2, 1]]}, {[[5, 0], [2, 0], [3, 0], [1, 1], [4, 0]]}}, { {[[1, 0], [4, 0], [3, 1], [5, 0], [2, 0]]}, {[[1, 0], [5, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [3, 1], [4, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 0], [5, 0]]}, {[[4, 0], [2, 0], [3, 1], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [3, 1], [4, 0], [2, 0]]}, {[[5, 0], [2, 0], [3, 1], [1, 0], [4, 0]]}}, { {[[1, 1], [4, 0], [3, 0], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 0], [3, 0], [4, 0], [1, 1]]}, {[[4, 0], [1, 0], [3, 0], [2, 0], [5, 1]]}, {[[4, 0], [2, 0], [3, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 0], [4, 0], [2, 0]]}, {[[5, 1], [2, 0], [3, 0], [1, 0], [4, 0]]}}, { {[[1, 1], [4, 0], [5, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [4, 0], [1, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 0], [4, 0], [3, 0]]}}, { {[[1, 0], [4, 0], [5, 0], [3, 0], [2, 1]]}, {[[1, 0], [5, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 0], [5, 1], [1, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1], [5, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [1, 1], [2, 0], [4, 0], [3, 0]]}, {[[5, 0], [2, 0], [1, 0], [3, 0], [4, 1]]}}, { {[[1, 0], [4, 0], [5, 0], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 1], [5, 0], [1, 0]]}, {[[3, 0], [4, 0], [2, 1], [1, 0], [5, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 1], [4, 0], [3, 0]]}, {[[5, 0], [2, 0], [1, 0], [3, 1], [4, 0]]}}, { {[[1, 0], [4, 1], [5, 0], [3, 0], [2, 0]]}, {[[1, 0], [5, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 1], [4, 0], [5, 0], [1, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 0], [5, 0]]}, {[[4, 0], [3, 0], [1, 0], [2, 1], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [3, 0], [4, 0]]}}, { {[[1, 1], [4, 0], [5, 0], [3, 0], [2, 0]]}, {[[1, 1], [5, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [4, 0], [5, 0], [1, 1]]}, {[[3, 0], [4, 0], [2, 0], [1, 0], [5, 1]]}, {[[4, 0], [3, 0], [1, 0], [2, 0], [5, 1]]}, {[[5, 1], [1, 0], [2, 0], [4, 0], [3, 0]]}, {[[5, 1], [2, 0], [1, 0], [3, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [5, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 0], [5, 1], [1, 0]]}, {[[2, 1], [4, 0], [3, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1], [5, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [3, 0], [2, 0], [4, 1]]}, {[[5, 0], [1, 1], [3, 0], [2, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [4, 1], [3, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [3, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [3, 0], [2, 1], [4, 0]]}}, { {[[1, 0], [5, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [3, 1], [2, 0], [4, 0]]}}, { {[[1, 1], [5, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 0], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [3, 0], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [3, 0], [2, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [5, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [5, 1], [1, 0]]}, {[[2, 1], [3, 0], [4, 0], [5, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 0], [1, 1], [5, 0]]}, {[[4, 1], [3, 0], [2, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [3, 0], [4, 1]]}, {[[5, 0], [1, 1], [2, 0], [3, 0], [4, 0]]}}, { {[[1, 0], [5, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 1], [5, 0], [1, 0]]}, {[[2, 0], [3, 1], [4, 0], [5, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 0], [5, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 0], [3, 1], [4, 0]]}, {[[5, 0], [1, 0], [2, 1], [3, 0], [4, 0]]}}, { {[[1, 1], [5, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [5, 0], [1, 1]]}, {[[4, 0], [3, 0], [2, 0], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [2, 0], [3, 0], [4, 0]]}}, { {[[2, 0], [1, 0], [3, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 1], [1, 0], [2, 0]]}}, { {[[2, 0], [1, 0], [4, 0], [5, 1], [3, 0]]}, {[[2, 0], [1, 0], [5, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0], [5, 0], [4, 0]]}, {[[3, 0], [5, 1], [4, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [3, 0], [2, 1]]}, {[[4, 0], [5, 0], [2, 0], [1, 1], [3, 0]]}}, { {[[2, 0], [1, 0], [4, 1], [5, 0], [3, 0]]}, {[[2, 0], [1, 0], [5, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1], [5, 0], [4, 0]]}, {[[3, 0], [5, 0], [4, 1], [1, 0], [2, 0]]}, {[[4, 0], [3, 1], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [3, 1], [2, 0]]}, {[[4, 0], [5, 0], [2, 1], [1, 0], [3, 0]]}}, { {[[2, 0], [1, 1], [4, 0], [5, 0], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [5, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 0], [5, 1], [4, 0]]}, {[[3, 0], [5, 0], [4, 0], [1, 1], [2, 0]]}, {[[4, 0], [3, 0], [5, 0], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [1, 0], [3, 0], [2, 0]]}, {[[4, 0], [5, 1], [2, 0], [1, 0], [3, 0]]}}, { {[[2, 1], [1, 0], [4, 0], [5, 0], [3, 0]]}, {[[2, 0], [1, 1], [5, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 0], [5, 0], [4, 1]]}, {[[3, 0], [5, 0], [4, 0], [1, 0], [2, 1]]}, {[[4, 0], [3, 0], [5, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 0], [3, 0], [2, 0]]}, {[[4, 1], [5, 0], [2, 0], [1, 0], [3, 0]]}}, { {[[2, 0], [1, 0], [5, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1], [5, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [4, 0], [5, 1], [1, 0], [2, 0]]}, {[[3, 1], [4, 0], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [2, 0], [3, 1]]}, {[[4, 0], [5, 0], [1, 1], [2, 0], [3, 0]]}}, { {[[2, 0], [1, 0], [5, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [5, 0], [4, 0]]}, {[[3, 0], [4, 1], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [2, 1], [3, 0]]}}} "for patterns of lengths: ", [[5, 2]] There all together, 172, different equivalence classes For the equivalence class of patterns, { {[[3, 1], [5, 1], [1, 0], [4, 0], [2, 0]]}, {[[4, 0], [2, 0], [5, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [5, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 1], [5, 0], [2, 0], [4, 0]]}, {[[2, 1], [4, 0], [1, 1], [5, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [5, 1], [3, 1]]}, {[[4, 1], [2, 0], [5, 1], [1, 0], [3, 0]]}, {[[3, 0], [5, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[3, 0], [1, 0], [5, 1], [2, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [1, 0], [4, 0], [2, 1]]}, {[[4, 1], [2, 0], [5, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [5, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [5, 0], [2, 0], [4, 1]]}, {[[2, 0], [4, 0], [1, 1], [5, 1], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [5, 0], [3, 1]]}, {[[4, 0], [2, 0], [5, 1], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [1, 1], [5, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [4, 0], [3, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [3, 1], [4, 0], [1, 0]]}, {[[5, 0], [2, 0], [3, 1], [1, 1], [4, 0]]}, {[[1, 0], [4, 0], [3, 1], [5, 1], [2, 0]]}, {[[4, 1], [2, 0], [3, 1], [5, 0], [1, 0]]}, {[[1, 0], [5, 0], [3, 1], [2, 0], [4, 1]]}, {[[5, 0], [1, 0], [3, 1], [4, 0], [2, 1]]}, {[[4, 0], [1, 1], [3, 1], [2, 0], [5, 0]]}} the member , {[[5, 0], [2, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [4, 1], [3, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 0], [3, 1], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [4, 1], [3, 1], [5, 0], [2, 0]]}, {[[4, 0], [2, 1], [3, 1], [5, 0], [1, 0]]}, {[[1, 0], [5, 0], [3, 1], [2, 1], [4, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 1], [5, 0]]}, {[[5, 0], [1, 0], [3, 1], [4, 1], [2, 0]]}} the member , {[[5, 0], [2, 1], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [2, 0], [4, 1], [3, 0], [1, 0]]}, {[[5, 0], [2, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 0], [3, 0], [4, 1], [2, 0], [5, 1]]}, {[[1, 1], [3, 1], [4, 0], [2, 0], [5, 0]]}, {[[1, 1], [4, 0], [2, 1], [3, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 1], [5, 1]]}, {[[5, 0], [3, 0], [2, 1], [4, 0], [1, 1]]}, {[[5, 1], [3, 1], [2, 0], [4, 0], [1, 0]]}} the member , {[[5, 0], [2, 0], [4, 0], [3, 1], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [4, 1], [2, 1], [5, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 1], [5, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 0], [5, 0]]}, {[[5, 0], [3, 0], [2, 1], [4, 1], [1, 0]]}, {[[5, 0], [3, 1], [2, 0], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [4, 0], [3, 1], [1, 0]]}} the member , {[[5, 0], [2, 1], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [2, 0], [4, 0], [3, 1], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 1], [5, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [2, 1], [4, 0], [1, 0]]}, {[[5, 0], [3, 1], [2, 0], [4, 0], [1, 1]]}} the member , {[[5, 0], [2, 0], [4, 1], [3, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [4, 0], [1, 1], [5, 0]]}, {[[1, 0], [3, 0], [5, 1], [4, 0], [2, 1]]}, {[[5, 0], [3, 0], [1, 1], [2, 0], [4, 1]]}, {[[1, 0], [5, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [4, 0], [2, 0], [5, 1], [1, 0]]}, {[[4, 1], [2, 0], [1, 1], [3, 0], [5, 0]]}, {[[2, 1], [4, 0], [5, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [5, 1], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 0], [3, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 0], [3, 1], [5, 1], [2, 0]]}, {[[2, 0], [5, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [5, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [3, 1], [1, 0], [4, 1]]}, {[[4, 0], [1, 1], [3, 1], [5, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 1], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [3, 1], [5, 0], [2, 1]]}} the member , {[[2, 0], [5, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [5, 1], [1, 0], [4, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [5, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [4, 0], [2, 1]]}, {[[4, 1], [1, 1], [5, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 0], [1, 1], [4, 1]]}, {[[2, 1], [4, 0], [5, 0], [1, 1], [3, 0]]}, {[[3, 0], [4, 0], [1, 0], [5, 1], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [2, 0], [4, 1]]}} the member , {[[3, 0], [1, 1], [5, 0], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 1], [5, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [5, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [5, 1], [2, 0]]}, {[[4, 1], [3, 0], [1, 0], [5, 0], [2, 1]]}, {[[4, 0], [1, 1], [2, 0], [5, 1], [3, 0]]}, {[[4, 1], [1, 0], [5, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [5, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [5, 1], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [1, 0], [4, 0], [2, 0], [3, 1]]}, {[[4, 0], [2, 0], [1, 1], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 1], [3, 0], [5, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [4, 0], [2, 0], [5, 0], [1, 1]]}, {[[2, 0], [4, 0], [5, 1], [3, 0], [1, 1]]}} the member , {[[4, 0], [2, 0], [1, 1], [3, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [5, 0], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [5, 0], [2, 1]]}, {[[4, 1], [1, 0], [5, 0], [3, 1], [2, 0]]}, {[[4, 0], [1, 0], [2, 1], [5, 1], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [5, 0], [4, 1], [1, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [5, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 0], [5, 1], [2, 0]]}, {[[4, 1], [3, 0], [1, 1], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [5, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [5, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 1], [2, 0], [5, 0], [3, 1]]}} the member , {[[2, 0], [5, 0], [1, 1], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 1], [4, 0], [3, 1], [5, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 0], [5, 0]]}, {[[1, 0], [3, 1], [2, 0], [5, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1], [5, 0], [4, 1]]}, {[[5, 0], [3, 1], [4, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [2, 0], [3, 1], [1, 0]]}, {[[4, 1], [5, 0], [2, 1], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 1], [4, 0], [3, 1], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 0], [3, 1], [5, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 1], [5, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0], [5, 0], [4, 1]]}, {[[5, 0], [3, 0], [4, 1], [1, 1], [2, 0]]}, {[[4, 1], [5, 0], [2, 0], [3, 1], [1, 0]]}, {[[4, 0], [5, 1], [2, 1], [3, 0], [1, 0]]}, {[[5, 0], [3, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 1], [4, 1], [3, 0], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [3, 0], [2, 1], [1, 0], [4, 0]]}, {[[5, 1], [1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [5, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 1], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 0], [5, 1]]}, {[[4, 0], [3, 1], [2, 0], [5, 0], [1, 1]]}, {[[2, 0], [3, 1], [4, 0], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [5, 0], [4, 1], [3, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 0], [2, 1], [1, 0], [4, 1]]}, {[[5, 0], [1, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 1], [5, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [4, 1], [5, 0], [2, 1]]}, {[[4, 0], [3, 1], [2, 0], [5, 1], [1, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1], [5, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 0], [5, 0]]}, {[[1, 0], [5, 1], [2, 0], [3, 1], [4, 0]]}} the member , {[[5, 0], [3, 0], [2, 1], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 0], [2, 0], [1, 1], [4, 1]]}, {[[5, 0], [1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [5, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [4, 0], [5, 1], [2, 1]]}, {[[4, 1], [3, 0], [2, 0], [5, 1], [1, 0]]}, {[[2, 1], [3, 0], [4, 0], [1, 1], [5, 0]]}, {[[4, 1], [1, 1], [2, 0], [3, 0], [5, 0]]}, {[[1, 0], [5, 1], [2, 0], [3, 0], [4, 1]]}} the member , {[[5, 0], [3, 0], [2, 0], [1, 1], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 0], [3, 0], [5, 1]]}, {[[2, 0], [1, 1], [4, 0], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 0], [5, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [2, 0], [3, 0], [1, 1]]}, {[[4, 1], [5, 0], [2, 0], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 0], [1, 1], [2, 0]]}, {[[5, 1], [3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 1], [4, 0], [3, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 1], [4, 0], [3, 0], [5, 0]]}, {[[1, 0], [3, 0], [2, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [2, 0], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 0], [5, 1], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 0], [4, 1], [5, 1], [3, 0]]}, {[[3, 0], [5, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [5, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 1], [5, 0], [4, 0]]}, {[[2, 1], [3, 1], [1, 0], [5, 0], [4, 0]]}, {[[4, 1], [3, 1], [5, 0], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 0], [3, 1], [2, 1]]}, {[[4, 0], [5, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[3, 0], [5, 1], [4, 1], [1, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [5, 0], [1, 0], [4, 0], [3, 1]]}, {[[4, 0], [2, 0], [1, 1], [5, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 1], [4, 0], [2, 0]]}, {[[4, 1], [1, 0], [5, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [1, 0], [4, 1]]}, {[[2, 0], [4, 0], [5, 1], [1, 1], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [5, 0], [2, 1]]}, {[[3, 0], [5, 1], [1, 1], [2, 0], [4, 0]]}} the member , {[[4, 0], [2, 0], [1, 1], [5, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 1], [5, 0], [2, 0]]}, {[[4, 0], [3, 1], [1, 1], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [5, 1], [3, 1], [2, 0]]}, {[[2, 0], [5, 0], [1, 1], [3, 1], [4, 0]]}, {[[4, 0], [1, 0], [2, 1], [5, 0], [3, 1]]}, {[[2, 0], [3, 1], [5, 1], [1, 0], [4, 0]]}} the member , {[[4, 0], [1, 0], [5, 1], [3, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [5, 0], [2, 1]]}, {[[4, 0], [3, 1], [1, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [5, 0], [3, 1], [2, 0]]}, {[[4, 1], [1, 0], [2, 1], [5, 0], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [1, 0], [3, 1], [4, 0]]}} the member , {[[4, 0], [3, 1], [1, 0], [5, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [5, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [4, 1], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 1], [5, 0]]}, {[[4, 0], [3, 1], [2, 1], [5, 0], [1, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [2, 1], [3, 1], [4, 0]]}, {[[5, 0], [3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[5, 0], [1, 0], [4, 1], [3, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [1, 1], [4, 1], [3, 0], [2, 0]]}, {[[5, 0], [3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [4, 0], [5, 0], [2, 1]]}, {[[4, 1], [1, 0], [2, 0], [3, 1], [5, 0]]}, {[[4, 0], [3, 0], [2, 1], [5, 1], [1, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1], [5, 0]]}, {[[1, 0], [5, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[5, 0], [3, 1], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [5, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [4, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [2, 1], [3, 0], [5, 0]]}, {[[4, 1], [3, 1], [2, 0], [5, 0], [1, 0]]}, {[[2, 1], [3, 1], [4, 0], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [2, 0], [3, 1], [4, 1]]}, {[[5, 0], [3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[5, 0], [1, 0], [4, 0], [3, 1], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0], [5, 1], [4, 0]]}, {[[5, 0], [4, 1], [3, 0], [1, 1], [2, 0]]}, {[[5, 0], [4, 1], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 1], [3, 0], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [3, 0], [2, 1], [1, 0]]}, {[[4, 1], [5, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 1], [5, 0]]}, {[[2, 1], [1, 0], [3, 0], [4, 1], [5, 0]]}} the member , {[[1, 0], [2, 1], [3, 0], [5, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [1, 0], [4, 1], [3, 0], [2, 0]]}, {[[5, 1], [3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 1], [3, 1], [4, 0], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [2, 0], [3, 1], [5, 1]]}, {[[4, 0], [3, 0], [2, 1], [5, 0], [1, 1]]}, {[[2, 0], [3, 0], [4, 1], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [5, 0], [4, 0], [3, 1], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [5, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [5, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 0], [5, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 1], [5, 0], [2, 1]]}, {[[4, 1], [1, 0], [5, 1], [3, 0], [2, 0]]}, {[[4, 0], [1, 0], [2, 0], [5, 1], [3, 1]]}, {[[2, 0], [3, 0], [5, 1], [1, 0], [4, 1]]}} the member , {[[2, 0], [5, 0], [4, 0], [1, 1], [3, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [3, 1], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1], [5, 0]]}, {[[5, 0], [3, 1], [2, 1], [4, 0], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 1], [4, 1], [2, 0], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 0], [5, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 1], [5, 0]]}, {[[4, 1], [2, 1], [5, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [5, 0], [2, 1], [4, 1]]}, {[[1, 0], [4, 1], [2, 0], [5, 1], [3, 0]]}, {[[5, 0], [2, 1], [4, 0], [1, 1], [3, 0]]}, {[[5, 0], [3, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[3, 0], [5, 1], [2, 0], [4, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 0], [2, 1], [4, 1], [1, 0]]}, {[[4, 0], [2, 1], [5, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 1], [5, 0]]}, {[[1, 0], [3, 1], [5, 0], [2, 1], [4, 0]]}, {[[5, 0], [3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [4, 1], [2, 1], [5, 0], [3, 0]]}, {[[5, 0], [2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [5, 0], [2, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 0], [3, 1], [1, 1], [2, 0]]}, {[[5, 0], [4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [3, 1], [2, 0], [1, 0]]}, {[[4, 1], [5, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1], [5, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0], [5, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 0], [5, 0]]}} the member , {[[5, 0], [4, 0], [3, 1], [1, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [4, 0], [3, 0], [1, 1], [2, 0]]}, {[[5, 1], [4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0], [5, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [3, 0], [2, 0], [1, 1]]}, {[[4, 1], [5, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0], [4, 0], [5, 1]]}, {[[2, 1], [1, 0], [3, 0], [4, 0], [5, 1]]}} the member , {[[4, 0], [5, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [1, 0], [3, 1], [2, 0], [5, 1]]}, {[[2, 0], [5, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [4, 0], [3, 1], [1, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [4, 0], [3, 1], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [3, 1], [2, 0], [4, 0]]}, {[[4, 0], [2, 0], [3, 1], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 1], [4, 0], [2, 0]]}} the member , {[[4, 0], [1, 0], [3, 1], [2, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 1], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1], [5, 0]]}} the member , {[[5, 0], [4, 1], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [1, 0], [3, 0], [2, 1], [5, 1]]}, {[[2, 0], [5, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [4, 1], [3, 0], [1, 0], [5, 1]]}, {[[1, 1], [4, 1], [3, 0], [5, 0], [2, 0]]}, {[[5, 1], [2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [5, 0], [3, 0], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [3, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 0], [4, 1], [2, 0]]}} the member , {[[4, 0], [1, 0], [3, 0], [2, 1], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 1], [4, 1], [5, 0], [3, 0]]}, {[[3, 0], [5, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [5, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1], [5, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0], [5, 0], [4, 1]]}, {[[4, 0], [3, 1], [5, 0], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [1, 0], [3, 1], [2, 0]]}, {[[4, 0], [5, 1], [2, 1], [1, 0], [3, 0]]}} the member , {[[2, 0], [1, 1], [4, 1], [5, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 0], [5, 1], [3, 0]]}, {[[3, 0], [5, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [5, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0], [5, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0], [5, 1], [4, 0]]}, {[[4, 1], [3, 0], [5, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 0], [3, 0], [2, 1]]}, {[[4, 1], [5, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[2, 0], [1, 1], [5, 0], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [3, 0], [2, 1], [1, 1], [5, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0], [5, 0]]}, {[[2, 0], [3, 0], [4, 1], [5, 1], [1, 0]]}, {[[2, 1], [3, 1], [4, 0], [5, 0], [1, 0]]}, {[[5, 0], [1, 1], [2, 1], [3, 0], [4, 0]]}, {[[5, 0], [1, 0], [2, 0], [3, 1], [4, 1]]}, {[[1, 0], [5, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [5, 0], [4, 0], [3, 1], [2, 1]]}} the member , {[[5, 0], [1, 1], [2, 1], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [3, 1], [2, 0], [1, 1], [5, 0]]}, {[[4, 1], [3, 0], [2, 1], [1, 0], [5, 0]]}, {[[2, 0], [3, 1], [4, 0], [5, 1], [1, 0]]}, {[[2, 1], [3, 0], [4, 1], [5, 0], [1, 0]]}, {[[5, 0], [1, 1], [2, 0], [3, 1], [4, 0]]}, {[[5, 0], [1, 0], [2, 1], [3, 0], [4, 1]]}, {[[1, 0], [5, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [3, 0], [2, 1]]}} the member , {[[5, 0], [1, 1], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 1], [3, 0], [2, 0], [1, 1], [5, 0]]}, {[[2, 1], [3, 0], [4, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [5, 1], [4, 0], [3, 0], [2, 1]]}} the member , {[[5, 0], [1, 1], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [5, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [5, 0], [2, 1]]}, {[[4, 0], [3, 0], [1, 0], [5, 1], [2, 1]]}, {[[4, 1], [1, 0], [2, 0], [5, 1], [3, 0]]}, {[[4, 1], [1, 1], [5, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [5, 0], [1, 1], [4, 1]]}} the member , {[[3, 0], [5, 1], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [3, 1], [2, 1], [1, 0], [5, 0]]}, {[[2, 0], [3, 1], [4, 1], [5, 0], [1, 0]]}, {[[5, 0], [1, 0], [2, 1], [3, 1], [4, 0]]}, {[[1, 0], [5, 0], [4, 1], [3, 1], [2, 0]]}} the member , {[[5, 0], [1, 0], [2, 1], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 0], [2, 0], [3, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0], [5, 0]]}} the member , {[[5, 0], [4, 0], [3, 0], [1, 1], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 1], [5, 0], [3, 0]]}, {[[2, 0], [1, 1], [5, 0], [3, 1], [4, 0]]}, {[[3, 0], [5, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1], [5, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0], [5, 1], [4, 0]]}, {[[4, 0], [3, 1], [5, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 0], [3, 1], [2, 0]]}, {[[4, 1], [5, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[2, 0], [1, 1], [5, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [4, 0], [1, 1], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [5, 1], [2, 0], [3, 1]]}} the member , {[[5, 0], [2, 0], [1, 1], [4, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 0], [5, 0], [2, 1]]}, {[[4, 0], [3, 0], [1, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [5, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [5, 1], [1, 1], [4, 0]]}, {[[4, 1], [1, 0], [2, 0], [5, 0], [3, 1]]}, {[[2, 0], [5, 1], [1, 1], [3, 0], [4, 0]]}} the member , {[[4, 0], [3, 0], [1, 1], [5, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [4, 0], [3, 1], [5, 1], [1, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1], [5, 0]]}, {[[4, 1], [2, 0], [3, 1], [1, 0], [5, 0]]}, {[[2, 1], [4, 0], [3, 1], [5, 0], [1, 0]]}, {[[1, 0], [5, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [5, 0], [3, 1], [4, 0], [2, 1]]}, {[[5, 0], [1, 1], [3, 1], [2, 0], [4, 0]]}, {[[5, 0], [1, 0], [3, 1], [2, 0], [4, 1]]}} the member , {[[1, 0], [5, 1], [3, 1], [4, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 1], [5, 0]]}} the member , {[[5, 0], [4, 1], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [4, 1], [1, 1], [3, 0], [5, 0]]}, {[[4, 0], [2, 1], [5, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1], [5, 0]]}, {[[1, 0], [3, 0], [5, 1], [2, 1], [4, 0]]}, {[[5, 0], [3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 0], [4, 1], [2, 0], [5, 0], [3, 1]]}, {[[5, 0], [2, 1], [4, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [4, 1], [1, 1], [3, 0], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [4, 0], [3, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [3, 0], [4, 1], [5, 0]]}} the member , {[[5, 0], [4, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 0], [4, 1], [5, 0], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [3, 1], [4, 0]]}, {[[3, 1], [5, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 1], [5, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [5, 0], [4, 0]]}, {[[4, 0], [3, 1], [5, 1], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 1], [3, 1], [2, 0]]}, {[[4, 0], [5, 0], [2, 1], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 1], [5, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [3, 0], [2, 0], [1, 1], [5, 1]]}, {[[4, 1], [3, 0], [2, 0], [1, 0], [5, 1]]}, {[[2, 0], [3, 0], [4, 0], [5, 1], [1, 1]]}, {[[2, 1], [3, 0], [4, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 1], [2, 0], [3, 0], [4, 0]]}, {[[5, 1], [1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 1], [5, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [5, 1], [4, 0], [3, 0], [2, 0]]}} the member , {[[4, 0], [3, 0], [2, 0], [1, 1], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [3, 0], [2, 1], [1, 0], [5, 1]]}, {[[4, 0], [3, 1], [2, 0], [1, 0], [5, 1]]}, {[[2, 0], [3, 0], [4, 1], [5, 0], [1, 1]]}, {[[2, 0], [3, 1], [4, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [2, 1], [3, 0], [4, 0]]}, {[[5, 1], [1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 1], [5, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 1], [5, 0], [4, 1], [3, 0], [2, 0]]}} the member , {[[4, 0], [3, 0], [2, 1], [1, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 0], [2, 0], [3, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 1], [3, 0], [4, 0], [5, 0]]}} the member , {[[5, 0], [4, 0], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [2, 1], [4, 0], [1, 0]]}, {[[4, 0], [2, 0], [5, 1], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [3, 1], [5, 1], [2, 0], [4, 0]]}, {[[1, 0], [4, 0], [2, 1], [5, 0], [3, 1]]}, {[[5, 0], [3, 1], [1, 1], [4, 0], [2, 0]]}, {[[5, 0], [2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 0], [4, 0], [1, 1], [3, 1], [5, 0]]}} the member , {[[4, 0], [2, 0], [5, 1], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 1], [5, 0]]}, {[[4, 1], [2, 0], [5, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [3, 1], [5, 0], [2, 0], [4, 1]]}, {[[1, 0], [4, 0], [2, 1], [5, 1], [3, 0]]}, {[[5, 0], [2, 0], [4, 1], [1, 1], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[1, 0], [3, 1], [5, 0], [2, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [2, 1], [3, 0], [1, 1], [5, 0]]}, {[[2, 0], [4, 1], [3, 0], [5, 1], [1, 0]]}, {[[4, 1], [2, 1], [3, 0], [1, 0], [5, 0]]}, {[[2, 1], [4, 1], [3, 0], [5, 0], [1, 0]]}, {[[1, 0], [5, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [5, 0], [3, 0], [4, 1], [2, 1]]}, {[[5, 0], [1, 1], [3, 0], [2, 1], [4, 0]]}, {[[5, 0], [1, 0], [3, 0], [2, 1], [4, 1]]}} the member , {[[1, 0], [5, 1], [3, 0], [4, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [2, 1], [1, 0], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [4, 1], [2, 0], [5, 0], [1, 1]]}, {[[2, 0], [4, 1], [5, 0], [3, 0], [1, 1]]}, {[[5, 1], [1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[4, 0], [2, 1], [1, 0], [3, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 1], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [5, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [4, 0], [5, 1], [3, 1], [1, 0]]}, {[[3, 1], [4, 0], [2, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 1], [5, 0]]}, {[[5, 0], [1, 0], [4, 1], [2, 0], [3, 1]]}} the member , {[[5, 0], [3, 1], [1, 1], [2, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [2, 0], [4, 1], [1, 1], [5, 0]]}, {[[1, 0], [3, 1], [5, 0], [4, 0], [2, 1]]}, {[[5, 0], [3, 1], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [5, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 1], [5, 1], [1, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 1], [5, 0]]}, {[[2, 1], [4, 0], [5, 0], [3, 1], [1, 0]]}, {[[5, 0], [1, 1], [4, 1], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [5, 0], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 0], [3, 0], [1, 1], [4, 1]]}, {[[4, 1], [1, 0], [3, 0], [5, 1], [2, 0]]}, {[[2, 1], [5, 1], [3, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [3, 0], [5, 1], [2, 1]]}, {[[4, 0], [1, 1], [3, 0], [5, 0], [2, 1]]}, {[[4, 1], [1, 1], [3, 0], [5, 0], [2, 0]]}} the member , {[[2, 0], [5, 0], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [4, 1], [3, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [3, 1], [4, 1], [2, 0]]}, {[[5, 0], [1, 0], [3, 1], [2, 1], [4, 0]]}} the member , {[[1, 0], [5, 0], [3, 1], [4, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [4, 0], [3, 1], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [3, 1], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 1], [4, 0], [1, 0]]}} the member , {[[1, 0], [4, 0], [3, 1], [2, 1], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [4, 1], [3, 0], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [3, 0], [4, 1], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 0], [2, 1], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [4, 0], [3, 1], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [3, 1], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [3, 1], [4, 0], [2, 0]]}, {[[5, 1], [1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [4, 0], [3, 1], [5, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 1], [4, 0], [3, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 1], [3, 0], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [3, 0], [2, 1], [5, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 1], [1, 0]]}, {[[5, 0], [2, 0], [3, 0], [4, 1], [1, 1]]}, {[[5, 0], [2, 1], [3, 0], [4, 0], [1, 1]]}, {[[5, 1], [2, 1], [3, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 0], [2, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 1], [4, 0], [3, 1], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [3, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 1], [4, 0], [1, 0]]}, {[[5, 0], [2, 0], [3, 1], [4, 0], [1, 1]]}} the member , {[[1, 0], [4, 0], [3, 1], [2, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 0], [5, 0], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [3, 0], [4, 0]]}, {[[3, 1], [5, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0], [5, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1], [5, 1], [4, 0]]}, {[[4, 0], [3, 0], [5, 1], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [1, 1], [3, 0], [2, 0]]}, {[[4, 1], [5, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [1, 1], [5, 1], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 1], [4, 0], [5, 0], [3, 1]]}, {[[3, 1], [5, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [5, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0], [5, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1], [5, 0], [4, 1]]}, {[[4, 0], [3, 0], [5, 1], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [1, 1], [3, 0], [2, 0]]}, {[[4, 0], [5, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [1, 1], [4, 0], [5, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [2, 1], [3, 0], [1, 0], [5, 1]]}, {[[2, 0], [4, 1], [3, 0], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [3, 0], [4, 1], [2, 0]]}, {[[5, 1], [1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[4, 0], [2, 1], [3, 0], [1, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [5, 1], [3, 1], [1, 0], [2, 0]]}, {[[4, 1], [5, 0], [3, 1], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [3, 1], [1, 1], [2, 0]]}, {[[4, 0], [5, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 1], [5, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 1], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1], [5, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1], [5, 0], [4, 1]]}} the member , {[[4, 0], [5, 1], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [4, 0], [1, 1], [3, 0], [5, 0]]}, {[[3, 1], [5, 1], [2, 0], [4, 0], [1, 0]]}, {[[4, 1], [2, 0], [5, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 0], [5, 0]]}, {[[1, 0], [3, 0], [5, 1], [2, 0], [4, 1]]}, {[[1, 0], [4, 0], [2, 0], [5, 1], [3, 1]]}, {[[5, 0], [2, 0], [4, 0], [1, 1], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [5, 1], [2, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 0], [5, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [4, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1], [5, 0]]}, {[[4, 1], [3, 0], [2, 1], [5, 0], [1, 0]]}, {[[2, 1], [3, 0], [4, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [2, 1], [3, 0], [4, 1]]}, {[[5, 0], [3, 1], [2, 0], [1, 1], [4, 0]]}} the member , {[[5, 0], [1, 0], [4, 1], [3, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 0], [5, 1], [3, 0], [1, 1], [2, 0]]}, {[[4, 1], [5, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0], [5, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0], [5, 0], [4, 1]]}} the member , {[[4, 0], [5, 1], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [5, 1], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 0], [5, 1], [2, 0]]}, {[[4, 1], [3, 0], [2, 0], [5, 0], [1, 1]]}, {[[4, 0], [1, 1], [2, 0], [3, 0], [5, 1]]}, {[[2, 1], [3, 0], [4, 0], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [2, 0], [3, 0], [4, 1]]}, {[[5, 1], [3, 0], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 0], [5, 1], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 1], [5, 0], [3, 0], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0], [5, 0], [4, 1]]}} the member , {[[4, 0], [5, 1], [3, 0], [1, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 1], [3, 0], [5, 0]]}, {[[5, 0], [3, 0], [4, 1], [2, 0], [1, 1]]}, {[[5, 0], [3, 1], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1], [4, 0], [5, 1]]}, {[[1, 0], [3, 1], [2, 0], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [2, 0], [3, 1], [1, 0]]}, {[[5, 1], [4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 1], [5, 0]]}} the member , {[[5, 0], [3, 0], [4, 1], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 0], [3, 1], [5, 1]]}, {[[5, 1], [3, 0], [4, 1], [2, 0], [1, 0]]}, {[[5, 1], [3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 1], [4, 0], [5, 0]]}, {[[1, 1], [3, 1], [2, 0], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [2, 0], [3, 1], [1, 1]]}, {[[5, 0], [4, 0], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [4, 0], [3, 1], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [3, 0], [2, 0], [1, 0], [4, 1]]}, {[[5, 1], [1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [5, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 0], [5, 0], [2, 1]]}, {[[4, 0], [3, 0], [2, 0], [5, 1], [1, 1]]}, {[[2, 0], [3, 0], [4, 0], [1, 1], [5, 1]]}, {[[4, 1], [1, 0], [2, 0], [3, 0], [5, 1]]}, {[[1, 1], [5, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[4, 0], [3, 0], [2, 0], [5, 1], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [4, 1], [5, 0], [3, 1], [1, 0]]}, {[[5, 0], [3, 1], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [4, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 0], [4, 1], [2, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 1], [5, 0]]}, {[[5, 0], [1, 0], [4, 1], [2, 1], [3, 0]]}} the member , {[[5, 0], [3, 1], [1, 0], [2, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [2, 0], [1, 0], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 0], [5, 1]]}, {[[3, 0], [2, 0], [4, 1], [5, 0], [1, 1]]}, {[[1, 1], [4, 0], [5, 0], [3, 1], [2, 0]]}, {[[3, 0], [4, 0], [2, 1], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [4, 1], [2, 0], [3, 0]]}, {[[5, 1], [1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [4, 0], [1, 1]]}} the member , {[[4, 0], [3, 1], [1, 0], [2, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 1], [1, 1], [3, 0], [4, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1], [5, 0]]}, {[[3, 1], [2, 1], [4, 0], [5, 0], [1, 0]]}, {[[1, 0], [4, 1], [5, 1], [3, 0], [2, 0]]}, {[[3, 1], [4, 1], [2, 0], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [4, 0], [2, 1], [3, 1]]}, {[[5, 0], [1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [5, 1], [4, 1], [1, 0]]}} the member , {[[5, 0], [2, 1], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [2, 0], [1, 1], [3, 0], [4, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 0], [5, 1]]}, {[[3, 1], [2, 0], [4, 0], [5, 0], [1, 1]]}, {[[1, 1], [4, 0], [5, 1], [3, 0], [2, 0]]}, {[[3, 1], [4, 0], [2, 0], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [4, 0], [2, 0], [3, 1]]}, {[[5, 1], [1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [5, 1], [4, 0], [1, 1]]}} the member , {[[4, 0], [3, 0], [1, 1], [2, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 0], [4, 0], [2, 1], [1, 1]]}, {[[1, 0], [3, 0], [2, 0], [4, 1], [5, 1]]}, {[[1, 1], [2, 1], [4, 0], [3, 0], [5, 0]]}, {[[5, 1], [4, 1], [2, 0], [3, 0], [1, 0]]}} the member , {[[1, 1], [2, 1], [4, 0], [3, 0], [5, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2], {}, {}, {}], [[], {}, {}, {}], [[1], {}, {}, {}], [[1, 3, 2], {[0, 0, 0, 1]}, {2}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}], [[1, 2, 3], {}, {3}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 43, 146 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 43, 146, 561, 2518, 13563, 88354, 686137, 6191526, 63330147, 720314930, 8985750097, 121722964822, 1777038601387, 27792425428418, 463361639828329, 8200984957695750, 153532638260056115, 3030783297332577234, 62909430552548867009, 1369617842615055417398, 31205406502900428341883, 742544856570425822722146, 18419262048679914109048921, 475489431896489563665405158, 12754122572934844700568361859, 354956979827941488611246511986] For the equivalence class of patterns, { {[[5, 0], [2, 0], [1, 1], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 0], [5, 0]]}, {[[3, 1], [2, 0], [4, 1], [5, 0], [1, 0]]}, {[[1, 0], [4, 0], [5, 1], [3, 1], [2, 0]]}, {[[3, 1], [4, 0], [2, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [4, 1], [2, 0], [3, 1]]}, {[[5, 0], [1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [5, 1], [4, 0], [1, 0]]}} the member , {[[5, 0], [2, 0], [1, 1], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 1], [1, 0], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1], [5, 0]]}, {[[3, 0], [2, 1], [4, 1], [5, 0], [1, 0]]}, {[[1, 0], [4, 1], [5, 0], [3, 1], [2, 0]]}, {[[3, 0], [4, 1], [2, 1], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [4, 1], [2, 1], [3, 0]]}, {[[5, 0], [1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [4, 1], [1, 0]]}} the member , {[[5, 0], [2, 1], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [5, 0], [3, 0], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [4, 1], [3, 0], [5, 0], [2, 1]]}, {[[4, 0], [2, 1], [3, 0], [5, 1], [1, 0]]}, {[[1, 0], [5, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 1], [5, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 1], [5, 0]]}, {[[5, 0], [1, 1], [3, 0], [4, 1], [2, 0]]}} the member , {[[5, 0], [2, 1], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [5, 0], [3, 1], [4, 0], [1, 0]]}, {[[5, 0], [2, 0], [3, 1], [1, 0], [4, 1]]}, {[[4, 0], [2, 0], [3, 1], [5, 1], [1, 0]]}, {[[1, 0], [4, 0], [3, 1], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [3, 1], [4, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 1], [2, 0], [5, 0]]}} the member , {[[5, 0], [2, 0], [3, 1], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [4, 0], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [2, 0], [3, 0], [1, 1]]}} the member , {[[1, 0], [2, 1], [4, 0], [3, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 1], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 1], [5, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [2, 0], [3, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [4, 0], [3, 1], [5, 0]]}, {[[1, 0], [2, 1], [4, 1], [3, 0], [5, 0]]}, {[[5, 0], [3, 0], [4, 1], [2, 1], [1, 0]]}} the member , {[[5, 0], [3, 1], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [2, 1], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 1], [5, 0]]}} the member , {[[5, 0], [3, 1], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 1], [1, 1], [3, 0], [2, 0], [5, 0]]}, {[[2, 1], [5, 1], [3, 0], [4, 0], [1, 0]]}, {[[5, 0], [2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 0], [4, 0], [3, 0], [5, 1], [2, 1]]}, {[[4, 1], [2, 0], [3, 0], [5, 1], [1, 0]]}, {[[1, 0], [5, 1], [3, 0], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [3, 0], [4, 0], [2, 1]]}} the member , {[[5, 0], [2, 0], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 0], [1, 1], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [1, 1], [2, 0], [5, 0]]}, {[[3, 1], [2, 0], [4, 0], [5, 1], [1, 0]]}, {[[1, 0], [4, 0], [5, 1], [3, 0], [2, 1]]}, {[[3, 1], [4, 0], [2, 0], [1, 1], [5, 0]]}, {[[1, 0], [5, 1], [4, 0], [2, 0], [3, 1]]}, {[[5, 0], [1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [5, 1], [4, 0], [1, 0]]}} the member , {[[5, 0], [2, 0], [1, 1], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 0], [1, 0], [3, 1], [4, 1]]}, {[[4, 1], [3, 1], [1, 0], [2, 0], [5, 0]]}, {[[3, 0], [2, 0], [4, 1], [5, 1], [1, 0]]}, {[[1, 0], [4, 0], [5, 0], [3, 1], [2, 1]]}, {[[3, 0], [4, 0], [2, 1], [1, 1], [5, 0]]}, {[[1, 0], [5, 1], [4, 1], [2, 0], [3, 0]]}, {[[5, 0], [1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 1], [5, 0], [4, 0], [1, 0]]}} the member , {[[3, 0], [2, 0], [4, 1], [5, 1], [1, 0]]}, has a scheme of depth , 4 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[3, 1, 2], {}, {2}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[2, 1, 3, 4], {}, {1, 2}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 0]}, {3}, {}], [[3, 1, 4, 2], {}, {1, 2}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1, 3], {}, {}, {}], [[2, 1], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 43, 143 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 43, 143, 511, 1950, 7903, 33848, 152529, 720466, 3555715, 18285538, 97752779, 542107657, 3112916651, 18477588573, 113203102619, 714836382820, 4646688247467, 31057662848411, 213217403924667, 1502038027665181, 10848023762714977, 80253986101845666, 607699244356110457, 4706511987739245606, 37256377296839424605, 301240966383935566872] For the equivalence class of patterns, { {[[5, 0], [2, 1], [1, 0], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [1, 0], [2, 1], [5, 0]]}, {[[3, 0], [2, 1], [4, 0], [5, 1], [1, 0]]}, {[[1, 0], [4, 1], [5, 0], [3, 0], [2, 1]]}, {[[3, 0], [4, 1], [2, 0], [1, 1], [5, 0]]}, {[[1, 0], [5, 1], [4, 0], [2, 1], [3, 0]]}, {[[5, 0], [1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [5, 0], [4, 1], [1, 0]]}} the member , {[[5, 0], [2, 1], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [2, 1], [1, 0], [3, 1]]}, {[[4, 0], [3, 1], [5, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [4, 1], [5, 0], [3, 1]]}, {[[1, 0], [2, 0], [5, 1], [3, 1], [4, 0]]}} the member , {[[5, 0], [4, 0], [1, 1], [3, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 0], [4, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 0], [4, 1], [5, 1]]}, {[[2, 0], [3, 0], [1, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [1, 0], [3, 0], [2, 0]]}, {[[5, 1], [4, 1], [2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 0], [5, 0], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [4, 0], [5, 0], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [3, 0], [4, 0]]}} the member , {[[5, 1], [4, 1], [1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 4 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}], [[2, 1], {}, {}, {}], [[4, 3, 1, 2], {}, {4}, {}], [[2, 1, 3], {[0, 1, 0, 0], [0, 0, 1, 0]}, {3}, {}], [[4, 3, 2, 1], {}, {3}, {}], [[3, 2, 1], {}, {}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}, {}], [[4, 2, 1, 3], {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}, {2}, {}], [ [3, 2, 1, 4], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}, {1}, {}] } Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 43, 147 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 43, 147, 575, 2648, 14617, 96696, 754585, 6794015, 69116493, 781266266, 9688636317, 130551322618, 1897079161639, 29549030800315, 490880073850267, 8660360684895644, 161671375033644161, 3183279386216962364, 65921897499021656917, 1432185084555874648119, 32568286258618860447209, 773610788393026167395774, 19158779222431738193449285, 493839916315590543209759550, 13227980262373620983669281315, 367670743594528620604851233939] For the equivalence class of patterns, { {[[4, 0], [2, 1], [5, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [5, 1], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [5, 0], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [1, 1], [5, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [5, 0], [3, 1]]}, {[[4, 0], [2, 1], [5, 1], [1, 0], [3, 0]]}, {[[3, 0], [5, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [5, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 1], [5, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 1], [2, 1], [5, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [5, 0], [2, 1], [4, 1]]}, {[[2, 0], [4, 1], [1, 0], [5, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [5, 0], [3, 0]]}, {[[4, 0], [2, 1], [5, 0], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [5, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[3, 0], [1, 1], [5, 0], [2, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 1], [1, 1], [4, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [5, 0], [3, 1]]}, {[[4, 0], [1, 1], [5, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [5, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [5, 1], [1, 1], [4, 0]]}, {[[3, 0], [4, 0], [1, 1], [5, 1], [2, 0]]}, {[[2, 1], [4, 0], [5, 0], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [5, 1], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [5, 0], [1, 0], [4, 1], [3, 0]]}, {[[4, 0], [2, 1], [1, 0], [5, 1], [3, 0]]}, {[[4, 1], [1, 0], [5, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [5, 0], [1, 0], [4, 1]]}, {[[2, 0], [4, 1], [5, 0], [1, 1], [3, 0]]}, {[[3, 0], [4, 1], [1, 0], [5, 0], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [2, 1], [4, 0]]}} the member , {[[4, 0], [2, 1], [1, 0], [5, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 1], [4, 0], [5, 0]]}, {[[5, 1], [4, 0], [3, 1], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [3, 1], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1], [4, 0], [5, 1]]}} the member , {[[5, 0], [4, 0], [3, 1], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 1], [5, 0], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [1, 0], [2, 1], [3, 0]]}, {[[4, 1], [5, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [4, 1], [5, 0], [1, 0], [2, 1]]}, {[[3, 0], [4, 1], [5, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 1], [5, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 0], [5, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [5, 0], [4, 1], [3, 1]]}, {[[3, 0], [2, 1], [1, 1], [5, 0], [4, 0]]}, {[[3, 1], [2, 1], [1, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [1, 1], [2, 1], [3, 0]]}, {[[4, 0], [5, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 0], [4, 1], [5, 1], [1, 0], [2, 0]]}, {[[3, 1], [4, 1], [5, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [2, 1], [1, 1], [5, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [2, 1], [4, 1], [5, 0], [3, 0]]}, {[[4, 0], [3, 1], [5, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [5, 0], [3, 1], [4, 0]]}} the member , {[[5, 0], [4, 1], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0], [4, 1], [5, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [1, 0], [3, 0], [2, 1]]}, {[[5, 0], [4, 1], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [2, 1], [4, 0], [5, 1], [3, 0]]}, {[[4, 1], [3, 0], [5, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [5, 0], [3, 0], [4, 1]]}} the member , {[[5, 0], [4, 1], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [5, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 1], [5, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [1, 1], [3, 0], [2, 0]]}, {[[5, 0], [4, 1], [2, 0], [1, 0], [3, 1]]}, {[[4, 0], [3, 0], [5, 1], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [4, 0], [5, 0], [3, 1]]}, {[[1, 0], [2, 1], [5, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1], [4, 1], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 1], [5, 1], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1], [5, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [1, 1], [2, 0], [3, 0]]}, {[[4, 1], [5, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [4, 0], [5, 1], [1, 1], [2, 0]]}, {[[3, 1], [4, 0], [5, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 1], [5, 1], [4, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 0], [5, 1], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [1, 0], [3, 1], [2, 1]]}, {[[1, 0], [2, 0], [4, 1], [5, 1], [3, 0]]}, {[[5, 0], [4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 1], [3, 1], [1, 0], [4, 0], [5, 0]]}, {[[4, 1], [3, 1], [5, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [5, 0], [3, 1], [4, 1]]}} the member , {[[3, 0], [5, 1], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 1], [1, 0], [5, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [5, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1], [5, 0], [4, 1]]}, {[[4, 1], [5, 0], [1, 1], [2, 0], [3, 0]]}, {[[4, 0], [5, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [4, 0], [5, 1], [1, 0], [2, 1]]}, {[[3, 1], [4, 0], [5, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 1], [5, 0], [4, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 1], [4, 0], [3, 0], [1, 1]]}, {[[5, 1], [2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 1], [5, 0]]}, {[[1, 0], [3, 0], [4, 0], [2, 1], [5, 1]]}, {[[1, 0], [4, 1], [2, 0], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 1], [4, 1], [2, 0], [3, 0], [5, 0]]}, {[[5, 0], [3, 0], [2, 0], [4, 1], [1, 1]]}} the member , {[[5, 0], [2, 1], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 0], [1, 1], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 1], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1], [5, 0]]}, {[[3, 0], [4, 1], [1, 1], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [5, 1], [2, 1], [3, 0]]}, {[[1, 0], [4, 1], [5, 0], [2, 0], [3, 1]]}} the member , {[[5, 0], [2, 0], [1, 1], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [2, 1], [1, 0], [3, 0], [4, 0]]}, {[[4, 0], [3, 0], [1, 0], [2, 1], [5, 1]]}, {[[3, 0], [2, 1], [4, 0], [5, 0], [1, 1]]}, {[[1, 1], [4, 1], [5, 0], [3, 0], [2, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [4, 0], [2, 1], [3, 0]]}, {[[5, 1], [1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [5, 0], [4, 1], [1, 1]]}} the member , {[[4, 0], [3, 0], [1, 0], [2, 1], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 0], [1, 0], [4, 1], [3, 1]]}, {[[4, 0], [2, 1], [1, 1], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 1], [4, 1], [2, 0]]}, {[[4, 0], [1, 0], [5, 0], [2, 1], [3, 1]]}, {[[3, 1], [2, 1], [5, 0], [1, 0], [4, 0]]}, {[[2, 0], [4, 1], [5, 1], [1, 0], [3, 0]]}, {[[3, 1], [4, 1], [1, 0], [5, 0], [2, 0]]}, {[[3, 0], [5, 0], [1, 1], [2, 1], [4, 0]]}} the member , {[[3, 0], [1, 0], [5, 1], [4, 1], [2, 0]]}, has a scheme of depth , 4 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[2, 1, 3], {}, {}, {}], [[2, 1], {}, {}, {}], [[3, 2, 1], {}, {2}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[3, 2, 4, 1], {}, {1, 2}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 1, 3, 4], {}, {3}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 43, 144 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 43, 144, 522, 2030, 8398, 36714, 168793, 813112, 4091735, 21451972, 116891160, 660554822, 3863775322, 23353384298, 145634065581, 935743895590, 6187151514364, 42050180222692, 293448121230999, 2100678197412864, 15412129725384549, 115792230146080556, 890171843268057735, 6997332749495145226, 56203343917413053980, 460985881186029443024] For the equivalence class of patterns, { {[[2, 0], [5, 0], [1, 1], [4, 0], [3, 1]]}, {[[4, 0], [2, 0], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [4, 0], [2, 0]]}, {[[4, 0], [1, 0], [5, 1], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 1], [1, 0], [4, 0]]}, {[[3, 1], [4, 0], [1, 1], [5, 0], [2, 0]]}, {[[2, 0], [4, 0], [5, 1], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [5, 0], [1, 1], [4, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 1], [4, 1], [3, 0], [1, 0], [5, 0]]}, {[[5, 0], [2, 1], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [4, 1], [3, 0], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [3, 0], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [3, 0], [5, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 1], [5, 0]]}, {[[5, 0], [1, 0], [3, 0], [4, 1], [2, 1]]}} the member , {[[5, 0], [2, 1], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 0], [1, 1], [4, 1], [3, 0]]}, {[[4, 0], [2, 1], [1, 0], [5, 0], [3, 1]]}, {[[4, 0], [1, 0], [5, 1], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [5, 1], [1, 0], [4, 0]]}, {[[3, 0], [4, 1], [1, 1], [5, 0], [2, 0]]}, {[[2, 0], [4, 1], [5, 0], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [5, 0], [1, 1], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [5, 1], [1, 0], [4, 1], [3, 0]]}, {[[4, 1], [2, 1], [1, 0], [5, 0], [3, 0]]}, {[[4, 0], [1, 1], [5, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [5, 0], [4, 1], [2, 1]]}, {[[3, 0], [2, 1], [5, 0], [1, 1], [4, 0]]}, {[[3, 0], [4, 1], [1, 0], [5, 1], [2, 0]]}, {[[2, 1], [4, 1], [5, 0], [1, 0], [3, 0]]}, {[[3, 0], [5, 0], [1, 0], [2, 1], [4, 1]]}} the member , {[[3, 0], [2, 1], [5, 0], [1, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [2, 0], [5, 1], [4, 1], [3, 0]]}, {[[5, 0], [4, 0], [1, 1], [2, 1], [3, 0]]}, {[[5, 0], [4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 0], [2, 0], [5, 0], [4, 1], [3, 1]]}, {[[3, 0], [2, 1], [1, 1], [4, 0], [5, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 0], [5, 0]]}, {[[3, 0], [4, 1], [5, 1], [2, 0], [1, 0]]}, {[[3, 1], [4, 1], [5, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [5, 1], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [2, 1], [5, 0], [4, 1], [3, 0]]}, {[[5, 0], [4, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [4, 1], [5, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [5, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[4, 1], [2, 1], [1, 0], [3, 0], [5, 0]]}, {[[5, 0], [3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [2, 1], [4, 0], [1, 1], [5, 0]]}, {[[1, 0], [3, 0], [5, 0], [4, 1], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [4, 1], [2, 0], [5, 1], [1, 0]]}, {[[2, 1], [4, 1], [5, 0], [3, 0], [1, 0]]}, {[[5, 0], [1, 1], [4, 0], [2, 1], [3, 0]]}} the member , {[[5, 0], [3, 0], [1, 0], [2, 1], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 1], [1, 1], [2, 0], [3, 0]]}, {[[5, 0], [4, 1], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [2, 1], [5, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [5, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1], [4, 1], [5, 0]]}, {[[3, 1], [2, 0], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [4, 0], [5, 1], [2, 1], [1, 0]]}, {[[3, 1], [4, 0], [5, 0], [2, 1], [1, 0]]}} the member , {[[5, 0], [4, 1], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [1, 0], [2, 0], [4, 0], [5, 1]]}, {[[3, 1], [5, 0], [4, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [2, 0], [1, 0], [3, 1]]}, {[[4, 0], [3, 0], [5, 1], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [4, 0], [5, 0], [3, 1]]}, {[[1, 1], [2, 0], [5, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1], [4, 0], [5, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[3, 1], [1, 1], [2, 0], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 0], [2, 0], [1, 0]]}, {[[4, 1], [3, 0], [5, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [4, 0], [5, 1], [3, 1]]}, {[[1, 0], [2, 0], [5, 1], [3, 0], [4, 1]]}} the member , {[[5, 0], [4, 0], [1, 1], [3, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 0], [2, 0], [5, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [4, 0], [5, 0]]}, {[[3, 1], [4, 0], [5, 1], [2, 0], [1, 0]]}} the member , {[[5, 0], [4, 0], [1, 1], [2, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 0], [3, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 0], [5, 0]]}} the member , {[[1, 0], [2, 0], [3, 1], [4, 1], [5, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [3, 0], [1, 1], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [5, 1], [4, 1], [2, 0]]}, {[[3, 1], [2, 1], [4, 0], [1, 0], [5, 0]]}, {[[1, 0], [5, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 1], [4, 1], [2, 0], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 0], [5, 0]]}, {[[2, 0], [4, 1], [5, 1], [3, 0], [1, 0]]}, {[[5, 0], [1, 0], [4, 0], [2, 1], [3, 1]]}} the member , {[[5, 0], [3, 0], [1, 1], [2, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [5, 0], [2, 1], [3, 0]]}} the member , {[[5, 0], [2, 1], [1, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 1], [2, 0], [1, 0], [4, 1], [3, 0]]}, {[[5, 1], [2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 1], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [4, 0], [1, 0], [2, 1], [5, 1]]}, {[[1, 1], [4, 0], [5, 0], [2, 1], [3, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 1], [5, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [5, 0], [4, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[1, 0], [3, 1], [2, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [2, 1], [3, 1], [1, 0]]}, {[[5, 0], [3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [2, 1], [5, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[5, 0], [2, 1], [1, 1], [4, 0], [3, 0]]}, {[[5, 0], [2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [2, 0], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 1], [5, 0], [4, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [5, 1], [2, 0], [3, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [5, 0], [2, 1], [3, 1]]}} the member , {[[5, 0], [2, 1], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] For the equivalence class of patterns, { {[[2, 0], [1, 1], [4, 0], [5, 1], [3, 0]]}, {[[3, 0], [5, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [5, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0], [5, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0], [5, 0], [4, 1]]}, {[[4, 1], [3, 0], [5, 0], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [1, 0], [3, 0], [2, 1]]}, {[[4, 0], [5, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[2, 0], [1, 1], [4, 0], [5, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 14, 42, 132 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304] Out of a total of , 172, cases 136, were successful and , 36, failed Success Rate: , 0.791 Here are the failures {{{[[3, 0], [5, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [5, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [5, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [5, 1], [2, 0]]}, {[[4, 1], [3, 1], [1, 0], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [5, 0], [3, 1], [2, 1]]}, {[[4, 0], [1, 1], [2, 1], [5, 0], [3, 0]]}, {[[2, 1], [3, 1], [5, 0], [1, 0], [4, 0]]}}, { {[[5, 1], [1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0], [5, 1]]}, {[[1, 1], [3, 1], [5, 0], [4, 0], [2, 0]]}, {[[5, 1], [3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [5, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 1], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [1, 0], [3, 1], [5, 1]]}, {[[2, 0], [4, 0], [5, 0], [3, 1], [1, 1]]}}, { {[[2, 0], [4, 0], [3, 0], [1, 1], [5, 1]]}, {[[4, 1], [1, 0], [3, 0], [2, 0], [5, 1]]}, {[[2, 1], [5, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [4, 0], [3, 0], [5, 0], [2, 1]]}, {[[5, 1], [2, 0], [3, 0], [1, 0], [4, 1]]}, {[[4, 0], [2, 0], [3, 0], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [3, 0], [2, 0], [4, 0]]}, {[[5, 1], [1, 1], [3, 0], [4, 0], [2, 0]]}}, { {[[5, 1], [1, 1], [4, 0], [2, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [2, 0], [4, 0], [1, 1], [5, 1]]}, {[[5, 1], [3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 1], [3, 0], [5, 0], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 0], [5, 1], [1, 1]]}, {[[2, 1], [4, 0], [5, 0], [3, 0], [1, 1]]}}, { {[[2, 0], [1, 0], [4, 1], [3, 0], [5, 1]]}, {[[2, 0], [1, 0], [4, 0], [3, 1], [5, 1]]}, {[[1, 1], [3, 0], [2, 1], [5, 0], [4, 0]]}, {[[1, 1], [3, 1], [2, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [2, 0], [3, 1], [1, 1]]}, {[[4, 0], [5, 0], [2, 1], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 1], [1, 0], [2, 0]]}, {[[5, 1], [3, 1], [4, 0], [1, 0], [2, 0]]}}, { {[[2, 0], [5, 1], [1, 0], [4, 0], [3, 1]]}, {[[4, 1], [2, 0], [1, 1], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 1], [4, 0], [2, 1]]}, {[[4, 0], [1, 1], [5, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [1, 1], [4, 0]]}, {[[2, 1], [4, 0], [5, 1], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [5, 1], [2, 0]]}, {[[3, 0], [5, 0], [1, 1], [2, 0], [4, 1]]}}, { {[[3, 0], [5, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 0], [5, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [5, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [5, 1], [2, 1]]}, {[[4, 1], [3, 0], [1, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [5, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [5, 0], [1, 1], [4, 0]]}, {[[4, 1], [1, 1], [2, 0], [5, 0], [3, 0]]}}, { {[[3, 0], [1, 1], [5, 0], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [1, 0], [5, 1], [3, 0]]}, {[[4, 1], [2, 0], [5, 0], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [1, 0], [4, 0], [2, 1]]}}, { {[[4, 0], [1, 1], [3, 0], [2, 0], [5, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [3, 0], [4, 0], [1, 1]]}, {[[5, 1], [2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [4, 0], [3, 0], [5, 1], [2, 0]]}, {[[4, 1], [2, 0], [3, 0], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [3, 0], [2, 0], [4, 1]]}, {[[5, 1], [1, 0], [3, 0], [4, 0], [2, 1]]}}, { {[[5, 1], [4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1], [4, 0], [5, 1]]}}, { {[[5, 1], [4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 1], [3, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 0], [4, 1], [5, 1]]}}, { {[[2, 0], [1, 0], [4, 0], [5, 1], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [3, 0], [4, 1]]}, {[[3, 1], [5, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 1], [2, 0], [5, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 1], [5, 0], [4, 0]]}, {[[4, 1], [3, 0], [5, 1], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 1], [3, 0], [2, 1]]}, {[[4, 0], [5, 0], [2, 0], [1, 1], [3, 1]]}}, { {[[4, 1], [2, 0], [3, 0], [1, 1], [5, 0]]}, {[[2, 1], [4, 0], [3, 0], [5, 1], [1, 0]]}, {[[1, 0], [5, 1], [3, 0], [4, 0], [2, 1]]}, {[[5, 0], [1, 1], [3, 0], [2, 0], [4, 1]]}}, { {[[5, 1], [4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0], [4, 0], [5, 1]]}}, { {[[2, 1], [5, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [5, 1], [3, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [3, 0], [5, 1], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [5, 0], [2, 1]]}}, { {[[3, 0], [5, 0], [2, 1], [4, 0], [1, 1]]}, {[[4, 0], [2, 0], [5, 0], [3, 1], [1, 1]]}, {[[2, 0], [4, 0], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [1, 0], [4, 1], [2, 0], [5, 1]]}, {[[1, 1], [3, 1], [5, 0], [2, 0], [4, 0]]}, {[[1, 1], [4, 0], [2, 1], [5, 0], [3, 0]]}, {[[5, 1], [2, 0], [4, 1], [1, 0], [3, 0]]}, {[[5, 1], [3, 1], [1, 0], [4, 0], [2, 0]]}}, { {[[2, 0], [4, 0], [3, 0], [5, 1], [1, 1]]}, {[[4, 0], [2, 0], [3, 0], [1, 1], [5, 1]]}, {[[4, 1], [2, 0], [3, 0], [1, 0], [5, 1]]}, {[[2, 1], [4, 0], [3, 0], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [3, 0], [4, 0], [2, 0]]}, {[[5, 1], [1, 0], [3, 0], [2, 0], [4, 1]]}, {[[5, 1], [1, 1], [3, 0], [2, 0], [4, 0]]}}, { {[[3, 0], [5, 0], [2, 0], [4, 1], [1, 1]]}, {[[4, 0], [2, 1], [5, 0], [3, 0], [1, 1]]}, {[[2, 0], [4, 1], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [1, 0], [4, 0], [2, 1], [5, 1]]}, {[[1, 1], [3, 0], [5, 0], [2, 1], [4, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [4, 1], [2, 0], [5, 0], [3, 0]]}, {[[5, 1], [2, 1], [4, 0], [1, 0], [3, 0]]}}, { {[[1, 1], [4, 0], [3, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 0], [1, 1]]}}, { {[[2, 1], [1, 1], [4, 0], [5, 0], [3, 0]]}, {[[3, 0], [5, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 1], [5, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0], [5, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 0], [5, 1], [4, 1]]}, {[[4, 0], [3, 0], [5, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [1, 0], [3, 0], [2, 0]]}, {[[4, 1], [5, 1], [2, 0], [1, 0], [3, 0]]}}, { {[[4, 0], [5, 0], [3, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 0], [5, 0], [4, 0]]}}, { {[[3, 0], [5, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [4, 0], [1, 0], [3, 0], [5, 1]]}, {[[4, 1], [2, 0], [5, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [3, 0], [5, 0], [2, 0], [4, 1]]}, {[[1, 1], [4, 0], [2, 0], [5, 1], [3, 0]]}, {[[5, 1], [2, 0], [4, 0], [1, 1], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 0], [2, 1]]}}, { {[[3, 1], [5, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [4, 0], [1, 1], [3, 0], [5, 1]]}, {[[4, 0], [2, 0], [5, 1], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [3, 0], [5, 1], [2, 0], [4, 0]]}, {[[5, 1], [3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 0], [5, 0], [3, 1]]}, {[[5, 1], [2, 0], [4, 0], [1, 0], [3, 1]]}}, { {[[4, 0], [2, 0], [5, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [4, 0], [2, 0]]}}, { {[[5, 1], [3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [4, 0], [3, 0], [5, 1]]}, {[[5, 1], [4, 0], [2, 0], [3, 0], [1, 1]]}}, { {[[5, 1], [2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [2, 0], [4, 0], [1, 1]]}}, { {[[5, 1], [2, 0], [1, 0], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [1, 0], [2, 0], [5, 1]]}, {[[3, 0], [2, 0], [4, 0], [5, 1], [1, 1]]}, {[[1, 1], [4, 0], [5, 0], [3, 0], [2, 1]]}, {[[3, 0], [4, 0], [2, 0], [1, 1], [5, 1]]}, {[[1, 1], [5, 1], [4, 0], [2, 0], [3, 0]]}, {[[5, 1], [1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [5, 0], [4, 0], [1, 1]]}}, { {[[2, 1], [5, 0], [1, 1], [4, 0], [3, 0]]}, {[[4, 0], [2, 0], [1, 0], [5, 1], [3, 1]]}, {[[4, 1], [1, 0], [5, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 1], [5, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [5, 1], [1, 0], [4, 1]]}, {[[3, 0], [4, 0], [1, 1], [5, 0], [2, 1]]}, {[[2, 0], [4, 0], [5, 0], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [1, 0], [2, 0], [4, 0]]}}, { {[[2, 0], [1, 0], [5, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [5, 1], [1, 0], [2, 0]]}}, { {[[1, 1], [2, 0], [5, 0], [4, 1], [3, 0]]}, {[[5, 1], [4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [4, 1], [5, 0], [2, 0], [1, 1]]}}, { {[[3, 0], [1, 0], [2, 1], [4, 0], [5, 1]]}, {[[3, 0], [5, 0], [4, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 1], [2, 0]]}, {[[5, 1], [4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 0], [5, 1]]}, {[[4, 0], [3, 1], [5, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [4, 1], [5, 0], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [3, 1], [4, 0]]}}, { {[[5, 1], [4, 0], [1, 1], [2, 0], [3, 0]]}, {[[5, 1], [4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [5, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1], [4, 0], [5, 1]]}, {[[3, 1], [2, 0], [1, 0], [4, 0], [5, 1]]}, {[[3, 1], [4, 0], [5, 0], [2, 0], [1, 1]]}, {[[3, 0], [4, 0], [5, 1], [2, 0], [1, 1]]}}, { {[[3, 0], [1, 1], [2, 0], [4, 0], [5, 1]]}, {[[3, 0], [5, 1], [4, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 0], [2, 1]]}, {[[5, 1], [4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [4, 0], [5, 1], [3, 0]]}, {[[4, 1], [3, 0], [5, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [5, 0], [3, 0], [4, 1]]}}, { {[[5, 1], [4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1], [5, 1]]}, {[[3, 0], [4, 0], [5, 0], [2, 1], [1, 1]]}}, { {[[2, 1], [1, 1], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [4, 0], [5, 0], [1, 1], [2, 1]]}}, { {[[5, 1], [2, 0], [1, 1], [4, 0], [3, 0]]}, {[[5, 1], [2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [5, 1], [4, 0], [1, 1]]}, {[[3, 0], [4, 0], [1, 1], [2, 0], [5, 1]]}, {[[3, 1], [4, 0], [1, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [5, 1], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [5, 0], [2, 0], [3, 1]]}}} {{{[[3, 0], [5, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [5, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [5, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [5, 1], [2, 0]]}, {[[4, 1], [3, 1], [1, 0], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [5, 0], [3, 1], [2, 1]]}, {[[4, 0], [1, 1], [2, 1], [5, 0], [3, 0]]}, {[[2, 1], [3, 1], [5, 0], [1, 0], [4, 0]]}}, { {[[5, 1], [1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0], [5, 1]]}, {[[1, 1], [3, 1], [5, 0], [4, 0], [2, 0]]}, {[[5, 1], [3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [5, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 1], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [1, 0], [3, 1], [5, 1]]}, {[[2, 0], [4, 0], [5, 0], [3, 1], [1, 1]]}}, { {[[2, 0], [4, 0], [3, 0], [1, 1], [5, 1]]}, {[[4, 1], [1, 0], [3, 0], [2, 0], [5, 1]]}, {[[2, 1], [5, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [4, 0], [3, 0], [5, 0], [2, 1]]}, {[[5, 1], [2, 0], [3, 0], [1, 0], [4, 1]]}, {[[4, 0], [2, 0], [3, 0], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [3, 0], [2, 0], [4, 0]]}, {[[5, 1], [1, 1], [3, 0], [4, 0], [2, 0]]}}, { {[[5, 1], [1, 1], [4, 0], [2, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [2, 0], [4, 0], [1, 1], [5, 1]]}, {[[5, 1], [3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 1], [3, 0], [5, 0], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 0], [5, 1], [1, 1]]}, {[[2, 1], [4, 0], [5, 0], [3, 0], [1, 1]]}}, { {[[2, 0], [1, 0], [4, 1], [3, 0], [5, 1]]}, {[[2, 0], [1, 0], [4, 0], [3, 1], [5, 1]]}, {[[1, 1], [3, 0], [2, 1], [5, 0], [4, 0]]}, {[[1, 1], [3, 1], [2, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [2, 0], [3, 1], [1, 1]]}, {[[4, 0], [5, 0], [2, 1], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 1], [1, 0], [2, 0]]}, {[[5, 1], [3, 1], [4, 0], [1, 0], [2, 0]]}}, { {[[2, 0], [5, 1], [1, 0], [4, 0], [3, 1]]}, {[[4, 1], [2, 0], [1, 1], [5, 0], [3, 0]]}, {[[3, 0], [1, 0], [5, 1], [4, 0], [2, 1]]}, {[[4, 0], [1, 1], [5, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [1, 1], [4, 0]]}, {[[2, 1], [4, 0], [5, 1], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [5, 1], [2, 0]]}, {[[3, 0], [5, 0], [1, 1], [2, 0], [4, 1]]}}, { {[[3, 0], [5, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 0], [5, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [5, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [5, 1], [2, 1]]}, {[[4, 1], [3, 0], [1, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [5, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [5, 0], [1, 1], [4, 0]]}, {[[4, 1], [1, 1], [2, 0], [5, 0], [3, 0]]}}, { {[[3, 0], [1, 1], [5, 0], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [1, 0], [5, 1], [3, 0]]}, {[[4, 1], [2, 0], [5, 0], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [1, 0], [4, 0], [2, 1]]}}, { {[[4, 0], [1, 1], [3, 0], [2, 0], [5, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [3, 0], [4, 0], [1, 1]]}, {[[5, 1], [2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [4, 0], [3, 0], [5, 1], [2, 0]]}, {[[4, 1], [2, 0], [3, 0], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [3, 0], [2, 0], [4, 1]]}, {[[5, 1], [1, 0], [3, 0], [4, 0], [2, 1]]}}, { {[[5, 1], [4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1], [4, 0], [5, 1]]}}, { {[[5, 1], [4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 1], [3, 0], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 0], [4, 1], [5, 1]]}}, { {[[2, 0], [1, 0], [4, 0], [5, 1], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [3, 0], [4, 1]]}, {[[3, 1], [5, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 1], [2, 0], [5, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 1], [5, 0], [4, 0]]}, {[[4, 1], [3, 0], [5, 1], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 1], [3, 0], [2, 1]]}, {[[4, 0], [5, 0], [2, 0], [1, 1], [3, 1]]}}, { {[[4, 1], [2, 0], [3, 0], [1, 1], [5, 0]]}, {[[2, 1], [4, 0], [3, 0], [5, 1], [1, 0]]}, {[[1, 0], [5, 1], [3, 0], [4, 0], [2, 1]]}, {[[5, 0], [1, 1], [3, 0], [2, 0], [4, 1]]}}, { {[[5, 1], [4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0], [4, 0], [5, 1]]}}, { {[[2, 1], [5, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [5, 1], [3, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [3, 0], [5, 1], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [5, 0], [2, 1]]}}, { {[[3, 0], [5, 0], [2, 1], [4, 0], [1, 1]]}, {[[4, 0], [2, 0], [5, 0], [3, 1], [1, 1]]}, {[[2, 0], [4, 0], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [1, 0], [4, 1], [2, 0], [5, 1]]}, {[[1, 1], [3, 1], [5, 0], [2, 0], [4, 0]]}, {[[1, 1], [4, 0], [2, 1], [5, 0], [3, 0]]}, {[[5, 1], [2, 0], [4, 1], [1, 0], [3, 0]]}, {[[5, 1], [3, 1], [1, 0], [4, 0], [2, 0]]}}, { {[[2, 0], [4, 0], [3, 0], [5, 1], [1, 1]]}, {[[4, 0], [2, 0], [3, 0], [1, 1], [5, 1]]}, {[[4, 1], [2, 0], [3, 0], [1, 0], [5, 1]]}, {[[2, 1], [4, 0], [3, 0], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [3, 0], [4, 0], [2, 0]]}, {[[5, 1], [1, 0], [3, 0], [2, 0], [4, 1]]}, {[[5, 1], [1, 1], [3, 0], [2, 0], [4, 0]]}}, { {[[3, 0], [5, 0], [2, 0], [4, 1], [1, 1]]}, {[[4, 0], [2, 1], [5, 0], [3, 0], [1, 1]]}, {[[2, 0], [4, 1], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [1, 0], [4, 0], [2, 1], [5, 1]]}, {[[1, 1], [3, 0], [5, 0], [2, 1], [4, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [4, 1], [2, 0], [5, 0], [3, 0]]}, {[[5, 1], [2, 1], [4, 0], [1, 0], [3, 0]]}}, { {[[1, 1], [4, 0], [3, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 0], [1, 1]]}}, { {[[2, 1], [1, 1], [4, 0], [5, 0], [3, 0]]}, {[[3, 0], [5, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 1], [5, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0], [5, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 0], [5, 1], [4, 1]]}, {[[4, 0], [3, 0], [5, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [1, 0], [3, 0], [2, 0]]}, {[[4, 1], [5, 1], [2, 0], [1, 0], [3, 0]]}}, { {[[4, 0], [5, 0], [3, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 0], [5, 0], [4, 0]]}}, { {[[3, 0], [5, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [4, 0], [1, 0], [3, 0], [5, 1]]}, {[[4, 1], [2, 0], [5, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [3, 0], [5, 0], [2, 0], [4, 1]]}, {[[1, 1], [4, 0], [2, 0], [5, 1], [3, 0]]}, {[[5, 1], [2, 0], [4, 0], [1, 1], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 0], [2, 1]]}}, { {[[3, 1], [5, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [4, 0], [1, 1], [3, 0], [5, 1]]}, {[[4, 0], [2, 0], [5, 1], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [3, 0], [5, 1], [2, 0], [4, 0]]}, {[[5, 1], [3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 0], [5, 0], [3, 1]]}, {[[5, 1], [2, 0], [4, 0], [1, 0], [3, 1]]}}, { {[[4, 0], [2, 0], [5, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [4, 0], [2, 0]]}}, { {[[5, 1], [3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [4, 0], [3, 0], [5, 1]]}, {[[5, 1], [4, 0], [2, 0], [3, 0], [1, 1]]}}, { {[[5, 1], [2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [2, 0], [4, 0], [1, 1]]}}, { {[[5, 1], [2, 0], [1, 0], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [1, 0], [2, 0], [5, 1]]}, {[[3, 0], [2, 0], [4, 0], [5, 1], [1, 1]]}, {[[1, 1], [4, 0], [5, 0], [3, 0], [2, 1]]}, {[[3, 0], [4, 0], [2, 0], [1, 1], [5, 1]]}, {[[1, 1], [5, 1], [4, 0], [2, 0], [3, 0]]}, {[[5, 1], [1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [5, 0], [4, 0], [1, 1]]}}, { {[[2, 1], [5, 0], [1, 1], [4, 0], [3, 0]]}, {[[4, 0], [2, 0], [1, 0], [5, 1], [3, 1]]}, {[[4, 1], [1, 0], [5, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 1], [5, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [5, 1], [1, 0], [4, 1]]}, {[[3, 0], [4, 0], [1, 1], [5, 0], [2, 1]]}, {[[2, 0], [4, 0], [5, 0], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [1, 0], [2, 0], [4, 0]]}}, { {[[2, 0], [1, 0], [5, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [5, 1], [1, 0], [2, 0]]}}, { {[[1, 1], [2, 0], [5, 0], [4, 1], [3, 0]]}, {[[5, 1], [4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [4, 1], [5, 0], [2, 0], [1, 1]]}}, { {[[3, 0], [1, 0], [2, 1], [4, 0], [5, 1]]}, {[[3, 0], [5, 0], [4, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 1], [2, 0]]}, {[[5, 1], [4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 0], [5, 1]]}, {[[4, 0], [3, 1], [5, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [4, 1], [5, 0], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [3, 1], [4, 0]]}}, { {[[5, 1], [4, 0], [1, 1], [2, 0], [3, 0]]}, {[[5, 1], [4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [5, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1], [4, 0], [5, 1]]}, {[[3, 1], [2, 0], [1, 0], [4, 0], [5, 1]]}, {[[3, 1], [4, 0], [5, 0], [2, 0], [1, 1]]}, {[[3, 0], [4, 0], [5, 1], [2, 0], [1, 1]]}}, { {[[3, 0], [1, 1], [2, 0], [4, 0], [5, 1]]}, {[[3, 0], [5, 1], [4, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 0], [2, 1]]}, {[[5, 1], [4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [4, 0], [5, 1], [3, 0]]}, {[[4, 1], [3, 0], [5, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [5, 0], [3, 0], [4, 1]]}}, { {[[5, 1], [4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1], [5, 1]]}, {[[3, 0], [4, 0], [5, 0], [2, 1], [1, 1]]}}, { {[[2, 1], [1, 1], [5, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [4, 0], [5, 0], [1, 1], [2, 1]]}}, { {[[5, 1], [2, 0], [1, 1], [4, 0], [3, 0]]}, {[[5, 1], [2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [5, 1], [4, 0], [1, 1]]}, {[[3, 0], [4, 0], [1, 1], [2, 0], [5, 1]]}, {[[3, 1], [4, 0], [1, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [5, 1], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [5, 0], [2, 0], [3, 1]]}}} "for patterns of lengths: ", [[5, 3]] There all together, 172, different equivalence classes For the equivalence class of patterns, { {[[2, 1], [4, 0], [5, 1], [1, 1], [3, 0]]}, {[[2, 1], [5, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [5, 1], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [5, 0], [1, 1], [4, 1]]}, {[[4, 1], [2, 0], [1, 1], [5, 1], [3, 0]]}, {[[4, 1], [1, 1], [5, 0], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [1, 0], [5, 1], [2, 1]]}, {[[3, 0], [5, 1], [1, 1], [2, 0], [4, 1]]}} the member , {[[2, 1], [4, 0], [5, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 1], [5, 1], [1, 0], [3, 1]]}, {[[2, 0], [5, 0], [1, 1], [4, 1], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [4, 1], [2, 0]]}, {[[3, 1], [2, 1], [5, 1], [1, 0], [4, 0]]}, {[[3, 1], [4, 1], [1, 1], [5, 0], [2, 0]]}, {[[4, 0], [1, 0], [5, 1], [2, 1], [3, 1]]}, {[[4, 0], [2, 1], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [2, 1], [4, 0]]}} the member , {[[2, 0], [4, 1], [5, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [5, 1], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [5, 0], [3, 1], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [5, 0], [3, 1], [1, 1], [4, 0]]}, {[[4, 1], [1, 0], [3, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [3, 1], [5, 0], [2, 1]]}, {[[4, 0], [1, 0], [3, 1], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [3, 1], [5, 0], [2, 0]]}} the member , {[[2, 0], [5, 1], [3, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [5, 1], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [5, 0], [3, 1], [1, 0], [4, 1]]}, {[[4, 0], [1, 1], [3, 1], [5, 1], [2, 0]]}, {[[4, 1], [1, 0], [3, 1], [5, 0], [2, 1]]}} the member , {[[2, 0], [5, 1], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [5, 1], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [5, 0], [3, 0], [1, 1], [4, 1]]}, {[[4, 0], [1, 1], [3, 0], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [3, 0], [5, 0], [2, 1]]}, {[[4, 1], [1, 1], [3, 0], [5, 1], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [5, 1], [2, 1]]}} the member , {[[2, 0], [5, 1], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1], [4, 1], [5, 1]]}, {[[1, 1], [2, 1], [3, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [3, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 0], [4, 1], [5, 1]]}, {[[1, 1], [2, 1], [3, 0], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [3, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [3, 0], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [3, 0], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 1], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [3, 1], [4, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 1], [4, 1], [5, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [3, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [3, 1], [4, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 1], [5, 0], [1, 1], [3, 1]]}, {[[2, 1], [5, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 1], [1, 1], [5, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [5, 1], [1, 0], [4, 1]]}, {[[3, 0], [4, 1], [1, 1], [5, 0], [2, 1]]}, {[[4, 0], [2, 1], [1, 0], [5, 1], [3, 1]]}, {[[3, 1], [5, 1], [1, 0], [2, 1], [4, 0]]}, {[[4, 1], [1, 0], [5, 1], [2, 1], [3, 0]]}} the member , {[[2, 0], [4, 1], [5, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 1], [5, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 1], [5, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0], [5, 1]]}, {[[2, 0], [1, 1], [3, 1], [4, 0], [5, 1]]}, {[[4, 1], [5, 0], [3, 1], [2, 0], [1, 1]]}, {[[4, 0], [5, 1], [3, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [3, 1], [1, 0], [2, 1]]}, {[[5, 1], [4, 0], [3, 1], [1, 1], [2, 0]]}} the member , {[[1, 1], [2, 0], [3, 1], [5, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 1], [5, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 1], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 1], [5, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 1], [5, 0]]}, {[[4, 1], [5, 0], [3, 1], [2, 1], [1, 0]]}, {[[4, 0], [5, 1], [3, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 1], [1, 0], [2, 1]]}, {[[5, 0], [4, 1], [3, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 1], [5, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 0], [4, 1], [5, 0]]}, {[[4, 1], [5, 1], [3, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [2, 1], [3, 0], [5, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [3, 0], [5, 0], [4, 1]]}, {[[1, 1], [2, 1], [3, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 1], [5, 1]]}, {[[2, 1], [1, 0], [3, 0], [4, 1], [5, 1]]}, {[[4, 1], [5, 0], [3, 0], [2, 1], [1, 1]]}, {[[4, 0], [5, 1], [3, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [3, 0], [1, 0], [2, 1]]}, {[[5, 1], [4, 1], [3, 0], [1, 1], [2, 0]]}} the member , {[[1, 1], [2, 1], [3, 0], [5, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [3, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 1], [4, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0], [4, 1], [5, 1]]}, {[[1, 1], [2, 1], [3, 0], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [3, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [3, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 1], [4, 0], [5, 0]]}, {[[4, 1], [5, 1], [3, 1], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [3, 1], [1, 1], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1], [5, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [3, 1], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1], [5, 1]]}, {[[4, 0], [5, 0], [3, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 1], [2, 1], [3, 1], [5, 0], [4, 0]]}, has a scheme of depth , 4 here it is: {[[], {}, {}, {}], [ [1, 2, 3, 4], {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {4}, {}] , [[2, 1], {[0, 0, 0]}, {1}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 1, 0], [1, 0, 0]}, {}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0]}, {}, {}], [[1], {[1, 0]}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 2, 6 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 0], [4, 0], [5, 1]]}, {[[4, 1], [5, 1], [3, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 1], [2, 0], [3, 0], [5, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 1], [3, 0], [5, 0]]}, {[[1, 1], [2, 1], [4, 0], [3, 1], [5, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 1], [5, 1]]}, {[[1, 0], [3, 1], [2, 0], [4, 1], [5, 1]]}, {[[5, 0], [3, 1], [4, 0], [2, 1], [1, 1]]}, {[[5, 0], [3, 0], [4, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 0], [3, 1], [1, 0]]}, {[[5, 1], [4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[1, 1], [2, 1], [4, 1], [3, 0], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 1], [3, 1], [5, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0], [5, 1]]}, {[[5, 0], [3, 1], [4, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 1], [3, 1], [1, 0]]}} the member , {[[1, 1], [2, 0], [4, 1], [3, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 0], [3, 1], [5, 1]]}, {[[1, 1], [2, 0], [4, 1], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 1], [4, 0], [5, 1]]}, {[[1, 1], [3, 1], [2, 0], [4, 0], [5, 1]]}, {[[5, 1], [3, 0], [4, 1], [2, 0], [1, 1]]}, {[[5, 1], [3, 1], [4, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 0], [3, 1], [1, 1]]}, {[[5, 1], [4, 0], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [4, 0], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 1], [3, 0], [5, 1]]}, {[[1, 0], [2, 1], [4, 0], [3, 1], [5, 1]]}, {[[1, 1], [3, 0], [2, 1], [4, 1], [5, 0]]}, {[[1, 1], [3, 1], [2, 0], [4, 1], [5, 0]]}, {[[5, 1], [3, 0], [4, 1], [2, 1], [1, 0]]}, {[[5, 1], [3, 1], [4, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 1], [3, 0], [1, 1]]}, {[[5, 0], [4, 1], [2, 0], [3, 1], [1, 1]]}} the member , {[[1, 0], [2, 1], [4, 1], [3, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 1], [3, 1], [5, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 1], [5, 0]]}, {[[5, 0], [3, 1], [4, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [4, 1], [3, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 1], [3, 1], [5, 1]]}, {[[1, 1], [3, 1], [2, 1], [4, 0], [5, 0]]}, {[[5, 1], [3, 1], [4, 1], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [2, 1], [3, 1], [1, 1]]}} the member , {[[1, 0], [2, 0], [4, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [4, 1], [5, 1], [3, 1]]}, {[[1, 0], [2, 0], [5, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 1], [4, 0], [5, 0]]}, {[[3, 1], [1, 1], [2, 1], [4, 0], [5, 0]]}, {[[4, 1], [3, 1], [5, 1], [2, 0], [1, 0]]}, {[[5, 0], [4, 0], [1, 1], [3, 1], [2, 1]]}, {[[5, 0], [4, 0], [2, 1], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [4, 1], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 1], [5, 0], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1], [5, 1]]}, {[[3, 0], [1, 0], [2, 1], [4, 1], [5, 1]]}, {[[4, 0], [3, 1], [5, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [1, 0], [3, 1], [2, 0]]}, {[[5, 1], [4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [5, 0], [4, 1], [2, 1], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 0], [5, 1], [3, 1]]}, {[[1, 1], [2, 0], [5, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 1], [4, 0], [5, 1]]}, {[[3, 1], [1, 1], [2, 0], [4, 0], [5, 1]]}, {[[4, 1], [3, 0], [5, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 1], [3, 0], [2, 1]]}, {[[5, 1], [4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 0], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [4, 0], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 1], [5, 1], [3, 0]]}, {[[1, 1], [2, 0], [5, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 0], [4, 0], [5, 1]]}, {[[3, 0], [1, 1], [2, 1], [4, 0], [5, 1]]}, {[[4, 1], [3, 1], [5, 0], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [5, 1], [4, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[1, 1], [2, 0], [4, 1], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 1], [5, 0], [3, 1]]}, {[[1, 0], [2, 1], [5, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 1], [5, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 1], [5, 0]]}, {[[4, 0], [3, 1], [5, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [5, 0], [4, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 1], [1, 0], [3, 1]]}} the member , {[[1, 0], [2, 1], [4, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 1], [5, 1], [3, 0]]}, {[[1, 0], [2, 1], [5, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 0], [4, 1], [5, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 1], [5, 0]]}, {[[4, 1], [3, 1], [5, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [5, 1], [4, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 1], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 1], [4, 1], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 0], [5, 1], [3, 1]]}, {[[1, 0], [2, 1], [5, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 1], [4, 1], [5, 0]]}, {[[3, 1], [1, 1], [2, 0], [4, 1], [5, 0]]}, {[[4, 1], [3, 0], [5, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [1, 1], [3, 0], [2, 1]]}, {[[3, 1], [5, 1], [4, 0], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 0], [1, 1], [3, 1]]}} the member , {[[1, 0], [2, 1], [4, 0], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 0], [5, 0], [3, 1]]}, {[[1, 1], [2, 1], [5, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 1], [5, 1]]}, {[[3, 1], [1, 0], [2, 0], [4, 1], [5, 1]]}, {[[4, 0], [3, 0], [5, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [1, 1], [3, 0], [2, 0]]}, {[[3, 1], [5, 0], [4, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[1, 1], [2, 1], [4, 0], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 0], [5, 1], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0], [4, 1], [5, 1]]}, {[[3, 0], [1, 1], [2, 0], [4, 1], [5, 1]]}, {[[4, 1], [3, 0], [5, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [5, 1], [4, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[2, 1], [3, 0], [1, 0], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 0], [5, 1], [4, 1], [3, 1]]}, {[[3, 1], [2, 1], [1, 1], [4, 0], [5, 0]]}, {[[5, 0], [4, 0], [1, 1], [2, 1], [3, 1]]}, {[[3, 1], [4, 1], [5, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [5, 1], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 1], [5, 0], [3, 1]]}, {[[1, 1], [2, 0], [5, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0], [5, 1]]}, {[[3, 1], [1, 0], [2, 1], [4, 0], [5, 1]]}, {[[4, 0], [3, 1], [5, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [1, 1], [3, 1], [2, 0]]}, {[[5, 1], [4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [4, 1], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [4, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [5, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1], [4, 1], [5, 1]]}, {[[3, 1], [2, 0], [1, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [1, 1], [2, 0], [3, 0]]}, {[[5, 1], [4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [5, 0], [2, 1], [1, 1]]}, {[[3, 0], [4, 0], [5, 1], [2, 1], [1, 1]]}} the member , {[[3, 0], [2, 0], [1, 1], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [5, 0], [4, 1], [3, 1]]}, {[[1, 1], [2, 0], [5, 1], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 0], [5, 1]]}, {[[3, 1], [2, 1], [1, 0], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [1, 0], [2, 1], [3, 1]]}, {[[5, 1], [4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 1], [4, 1], [5, 0], [2, 0], [1, 1]]}, {[[3, 0], [4, 1], [5, 1], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [5, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 0], [5, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [5, 1], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [5, 1], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [5, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [5, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [5, 1], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [2, 1], [5, 1], [4, 1], [3, 0]]}, {[[1, 0], [2, 1], [5, 0], [4, 1], [3, 1]]}, {[[3, 0], [2, 1], [1, 1], [4, 1], [5, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [1, 1], [2, 1], [3, 0]]}, {[[5, 0], [4, 1], [1, 0], [2, 1], [3, 1]]}, {[[3, 1], [4, 1], [5, 0], [2, 1], [1, 0]]}, {[[3, 0], [4, 1], [5, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [5, 1], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [2, 1], [5, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [4, 1], [5, 0], [2, 1], [1, 1]]}} the member , {[[3, 0], [2, 1], [1, 0], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1], [5, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [4, 0], [3, 1], [5, 0]]}, {[[2, 1], [1, 1], [4, 1], [3, 0], [5, 0]]}, {[[4, 1], [5, 1], [2, 0], [3, 1], [1, 0]]}, {[[4, 1], [5, 1], [2, 1], [3, 0], [1, 0]]}, {[[5, 0], [3, 0], [4, 1], [1, 1], [2, 1]]}, {[[5, 0], [3, 1], [4, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1], [5, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [2, 1], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1], [5, 1]]}, {[[4, 0], [5, 0], [2, 1], [3, 1], [1, 1]]}, {[[5, 1], [3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [4, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [4, 0], [3, 0], [5, 1]]}, {[[4, 1], [5, 1], [2, 0], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[2, 1], [1, 1], [4, 0], [3, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 1], [5, 0], [4, 1]]}, {[[1, 1], [3, 1], [2, 0], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 1], [5, 1]]}, {[[2, 1], [1, 0], [4, 1], [3, 0], [5, 1]]}, {[[4, 0], [5, 1], [2, 0], [3, 1], [1, 1]]}, {[[4, 1], [5, 0], [2, 1], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [4, 1], [1, 0], [2, 1]]}, {[[5, 1], [3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 1], [5, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 1], [5, 1], [4, 0]]}, {[[1, 1], [3, 1], [2, 0], [5, 0], [4, 1]]}, {[[2, 1], [1, 0], [4, 0], [3, 1], [5, 1]]}, {[[2, 0], [1, 1], [4, 1], [3, 0], [5, 1]]}, {[[4, 0], [5, 1], [2, 1], [3, 0], [1, 1]]}, {[[4, 1], [5, 0], [2, 0], [3, 1], [1, 1]]}, {[[5, 1], [3, 0], [4, 1], [1, 1], [2, 0]]}, {[[5, 1], [3, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[1, 1], [3, 0], [2, 1], [5, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [2, 1], [5, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 1], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 1], [5, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 1], [5, 0]]}, {[[4, 1], [5, 0], [2, 1], [3, 1], [1, 0]]}, {[[4, 0], [5, 1], [2, 1], [3, 1], [1, 0]]}, {[[5, 0], [3, 1], [4, 1], [1, 0], [2, 1]]}, {[[5, 0], [3, 1], [4, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 1], [2, 1], [5, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [4, 1], [2, 1], [5, 1]]}, {[[1, 1], [3, 1], [4, 0], [2, 1], [5, 0]]}, {[[1, 1], [4, 1], [2, 1], [3, 0], [5, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 1], [5, 1]]}, {[[5, 0], [2, 1], [4, 0], [3, 1], [1, 1]]}, {[[5, 1], [2, 1], [4, 1], [3, 0], [1, 0]]}, {[[5, 1], [3, 1], [2, 0], [4, 1], [1, 0]]}, {[[5, 0], [3, 0], [2, 1], [4, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [4, 1], [2, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [4, 1], [2, 0], [5, 1]]}, {[[1, 1], [3, 1], [4, 1], [2, 0], [5, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1], [5, 1]]}, {[[1, 1], [4, 0], [2, 1], [3, 1], [5, 0]]}, {[[5, 1], [2, 0], [4, 1], [3, 1], [1, 0]]}, {[[5, 0], [2, 0], [4, 1], [3, 1], [1, 1]]}, {[[5, 1], [3, 1], [2, 1], [4, 0], [1, 0]]}, {[[5, 0], [3, 1], [2, 1], [4, 0], [1, 1]]}} the member , {[[1, 0], [3, 1], [4, 1], [2, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 0], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [2, 0], [3, 0], [5, 1]]}, {[[5, 1], [2, 1], [4, 0], [3, 0], [1, 1]]}, {[[5, 1], [3, 0], [2, 0], [4, 1], [1, 1]]}} the member , {[[1, 1], [3, 0], [4, 0], [2, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [4, 1], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 1], [5, 0]]}, {[[5, 0], [2, 1], [4, 1], [3, 1], [1, 0]]}, {[[5, 0], [3, 1], [2, 1], [4, 1], [1, 0]]}} the member , {[[1, 0], [3, 1], [4, 1], [2, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 1], [2, 1], [5, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 1], [5, 1]]}, {[[1, 0], [4, 1], [2, 1], [3, 0], [5, 1]]}, {[[1, 1], [4, 1], [2, 0], [3, 1], [5, 0]]}, {[[5, 0], [2, 1], [4, 1], [3, 0], [1, 1]]}, {[[5, 1], [2, 1], [4, 0], [3, 1], [1, 0]]}, {[[5, 0], [3, 1], [2, 0], [4, 1], [1, 1]]}, {[[5, 1], [3, 0], [2, 1], [4, 1], [1, 0]]}} the member , {[[1, 1], [3, 0], [4, 1], [2, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 0], [1, 1], [5, 1], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 1], [5, 1], [2, 0], [4, 0]]}, {[[4, 1], [2, 0], [5, 1], [1, 0], [3, 1]]}, {[[3, 1], [5, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [5, 0], [1, 1], [4, 0], [2, 1]]}, {[[4, 0], [2, 0], [5, 1], [1, 1], [3, 1]]}} the member , {[[2, 0], [4, 0], [1, 1], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [4, 1], [5, 1], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [4, 0], [1, 1], [5, 0]]}, {[[2, 1], [5, 1], [4, 1], [3, 0], [1, 0]]}, {[[5, 0], [1, 1], [4, 0], [3, 1], [2, 1]]}, {[[4, 1], [1, 1], [2, 1], [3, 0], [5, 0]]}, {[[4, 1], [3, 1], [2, 0], [5, 1], [1, 0]]}, {[[5, 0], [3, 0], [2, 1], [1, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [4, 1], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [4, 1], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [2, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 0], [5, 1]]}, {[[2, 0], [5, 0], [4, 1], [3, 1], [1, 1]]}, {[[5, 1], [1, 0], [4, 1], [3, 1], [2, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 1], [5, 1]]}, {[[4, 0], [3, 1], [2, 1], [5, 0], [1, 1]]}, {[[5, 1], [3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [4, 1], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 0], [5, 1], [2, 1]]}, {[[1, 1], [5, 1], [2, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [4, 0], [1, 1], [5, 1]]}, {[[2, 1], [5, 1], [4, 0], [3, 0], [1, 1]]}, {[[5, 1], [1, 1], [4, 0], [3, 0], [2, 1]]}, {[[5, 1], [3, 0], [2, 0], [1, 1], [4, 1]]}, {[[4, 1], [3, 0], [2, 0], [5, 1], [1, 1]]}, {[[4, 1], [1, 1], [2, 0], [3, 0], [5, 1]]}} the member , {[[1, 1], [3, 0], [4, 0], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 1], [5, 0], [2, 1]]}, {[[1, 1], [5, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1], [5, 1]]}, {[[2, 1], [5, 0], [4, 1], [3, 0], [1, 1]]}, {[[5, 1], [1, 1], [4, 0], [3, 1], [2, 0]]}, {[[5, 1], [3, 0], [2, 1], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 1], [3, 0], [5, 1]]}, {[[4, 0], [3, 1], [2, 0], [5, 1], [1, 1]]}} the member , {[[1, 1], [3, 0], [4, 1], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 1], [5, 1], [2, 0]]}, {[[1, 1], [5, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [4, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [4, 1], [3, 0], [1, 1]]}, {[[5, 1], [1, 0], [4, 0], [3, 1], [2, 1]]}, {[[5, 1], [3, 0], [2, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 1], [3, 0], [5, 1]]}, {[[4, 1], [3, 1], [2, 0], [5, 0], [1, 1]]}} the member , {[[2, 1], [3, 1], [4, 0], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [4, 1], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [2, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 1], [5, 0]]}, {[[2, 1], [5, 0], [4, 1], [3, 1], [1, 0]]}, {[[5, 0], [1, 1], [4, 1], [3, 1], [2, 0]]}, {[[5, 0], [3, 1], [2, 1], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 1], [3, 1], [5, 0]]}, {[[4, 0], [3, 1], [2, 1], [5, 1], [1, 0]]}} the member , {[[1, 0], [3, 1], [4, 1], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [4, 1], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [2, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [4, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [4, 1], [3, 1], [1, 0]]}, {[[5, 0], [1, 0], [4, 1], [3, 1], [2, 1]]}, {[[5, 0], [3, 1], [2, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 1], [3, 1], [5, 0]]}, {[[4, 1], [3, 1], [2, 1], [5, 0], [1, 0]]}} the member , {[[1, 0], [3, 1], [4, 1], [5, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [4, 0], [5, 1], [2, 1]]}, {[[1, 0], [5, 1], [2, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [4, 1], [1, 1], [5, 0]]}, {[[2, 1], [5, 1], [4, 0], [3, 1], [1, 0]]}, {[[5, 0], [1, 1], [4, 1], [3, 0], [2, 1]]}, {[[5, 0], [3, 1], [2, 0], [1, 1], [4, 1]]}, {[[4, 1], [3, 0], [2, 1], [5, 1], [1, 0]]}, {[[4, 1], [1, 1], [2, 0], [3, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [4, 0], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [4, 0], [5, 0], [2, 1]]}, {[[1, 1], [5, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1], [5, 1]]}, {[[2, 1], [5, 0], [4, 0], [3, 1], [1, 1]]}, {[[5, 1], [1, 1], [4, 1], [3, 0], [2, 0]]}, {[[5, 1], [3, 1], [2, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 0], [3, 1], [5, 1]]}, {[[4, 0], [3, 0], [2, 1], [5, 1], [1, 1]]}} the member , {[[1, 1], [3, 1], [4, 0], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [4, 0], [5, 1], [2, 0]]}, {[[1, 1], [5, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [4, 1], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [4, 0], [3, 1], [1, 1]]}, {[[5, 1], [1, 0], [4, 1], [3, 0], [2, 1]]}, {[[5, 1], [3, 1], [2, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1], [5, 1]]}, {[[4, 1], [3, 0], [2, 1], [5, 0], [1, 1]]}} the member , {[[2, 1], [3, 0], [4, 1], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 1], [2, 0], [4, 0]]}, {[[1, 1], [4, 0], [2, 1], [5, 0], [3, 1]]}, {[[2, 0], [4, 0], [1, 1], [3, 1], [5, 1]]}, {[[3, 1], [1, 0], [4, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [4, 1], [1, 0], [3, 1]]}, {[[5, 1], [3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [5, 0], [2, 1], [4, 0], [1, 1]]}, {[[4, 0], [2, 0], [5, 1], [3, 1], [1, 1]]}} the member , {[[1, 1], [3, 1], [5, 1], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 0], [2, 1], [4, 1]]}, {[[1, 1], [4, 1], [2, 0], [5, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 0], [5, 1]]}, {[[3, 0], [1, 1], [4, 0], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [4, 0], [1, 1], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [5, 1], [2, 0], [4, 1], [1, 1]]}, {[[4, 1], [2, 1], [5, 0], [3, 0], [1, 1]]}} the member , {[[1, 1], [3, 0], [5, 0], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 1], [2, 0], [4, 1]]}, {[[1, 1], [4, 0], [2, 0], [5, 1], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [3, 0], [5, 1]]}, {[[3, 1], [1, 1], [4, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [4, 0], [1, 1], [3, 1]]}, {[[5, 1], [3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [5, 1], [2, 0], [4, 0], [1, 1]]}, {[[4, 1], [2, 0], [5, 1], [3, 0], [1, 1]]}} the member , {[[2, 1], [4, 0], [1, 1], [3, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 1], [2, 1], [4, 0]]}, {[[1, 1], [4, 1], [2, 0], [5, 0], [3, 1]]}, {[[2, 0], [4, 1], [1, 1], [3, 0], [5, 1]]}, {[[3, 1], [1, 0], [4, 0], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [4, 0], [1, 0], [3, 1]]}, {[[5, 1], [3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [5, 0], [2, 0], [4, 1], [1, 1]]}, {[[4, 0], [2, 1], [5, 1], [3, 0], [1, 1]]}} the member , {[[1, 1], [3, 0], [5, 1], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 1], [2, 0], [4, 1]]}, {[[1, 0], [4, 0], [2, 1], [5, 1], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [3, 1], [5, 0]]}, {[[3, 1], [1, 1], [4, 1], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [4, 1], [1, 1], [3, 1]]}, {[[5, 0], [3, 1], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [5, 1], [2, 1], [4, 0], [1, 0]]}, {[[4, 1], [2, 0], [5, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 1], [5, 1], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 1], [2, 1], [4, 0]]}, {[[1, 0], [4, 1], [2, 1], [5, 0], [3, 1]]}, {[[2, 0], [4, 1], [1, 1], [3, 1], [5, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [4, 1], [1, 0], [3, 1]]}, {[[5, 0], [3, 1], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [5, 0], [2, 1], [4, 1], [1, 0]]}, {[[4, 0], [2, 1], [5, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 1], [5, 1], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 0], [2, 1], [4, 1]]}, {[[1, 0], [4, 1], [2, 1], [5, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 1], [5, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [4, 1], [1, 1], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [5, 1], [2, 1], [4, 1], [1, 0]]}, {[[4, 1], [2, 1], [5, 0], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 1], [5, 0], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [5, 1], [4, 1], [2, 1]]}, {[[1, 0], [5, 1], [2, 0], [4, 1], [3, 1]]}, {[[2, 1], [4, 1], [5, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 1], [4, 0], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [4, 0], [2, 1], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [2, 1], [4, 1]]}, {[[3, 1], [4, 1], [2, 0], [5, 1], [1, 0]]}, {[[4, 1], [2, 1], [1, 1], [3, 0], [5, 0]]}} the member , {[[1, 0], [3, 0], [5, 1], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 1], [4, 0], [2, 0]]}, {[[1, 1], [5, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [4, 0], [5, 1], [3, 1], [1, 1]]}, {[[3, 1], [2, 0], [4, 1], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [4, 1], [2, 0], [3, 1]]}, {[[5, 1], [3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [4, 0], [2, 1], [5, 0], [1, 1]]}, {[[4, 0], [2, 0], [1, 1], [3, 1], [5, 1]]}} the member , {[[2, 0], [4, 0], [5, 1], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 0], [4, 1], [2, 1]]}, {[[1, 1], [5, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [4, 1], [5, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 1], [4, 0], [1, 1], [5, 1]]}, {[[5, 1], [1, 1], [4, 0], [2, 1], [3, 0]]}, {[[5, 1], [3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [4, 1], [2, 0], [5, 1], [1, 1]]}, {[[4, 1], [2, 1], [1, 0], [3, 0], [5, 1]]}} the member , {[[1, 1], [3, 0], [5, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 1], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [4, 0], [5, 1], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [4, 0], [1, 1], [5, 1]]}, {[[5, 1], [1, 1], [4, 0], [2, 0], [3, 1]]}, {[[5, 1], [3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [4, 0], [2, 0], [5, 1], [1, 1]]}, {[[4, 1], [2, 0], [1, 1], [3, 0], [5, 1]]}} the member , {[[1, 1], [3, 0], [5, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 1], [4, 1], [2, 0]]}, {[[1, 1], [5, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [4, 1], [5, 1], [3, 0], [1, 1]]}, {[[3, 1], [2, 1], [4, 0], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [4, 0], [2, 1], [3, 1]]}, {[[5, 1], [3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 1], [4, 1], [2, 0], [5, 0], [1, 1]]}, {[[4, 0], [2, 1], [1, 1], [3, 0], [5, 1]]}} the member , {[[2, 0], [4, 1], [5, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 1], [4, 0], [2, 1]]}, {[[1, 0], [5, 1], [2, 1], [4, 0], [3, 1]]}, {[[2, 1], [4, 0], [5, 1], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [4, 1], [2, 0], [3, 1]]}, {[[5, 0], [3, 1], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [4, 0], [2, 1], [5, 1], [1, 0]]}, {[[4, 1], [2, 0], [1, 1], [3, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [5, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 0], [2, 0], [4, 1]]}, {[[1, 1], [4, 0], [2, 1], [5, 1], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [1, 1], [4, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [2, 1], [4, 0], [1, 1]]}, {[[4, 1], [2, 0], [5, 0], [3, 1], [1, 1]]}, {[[5, 1], [3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 1], [4, 0], [1, 0], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 0], [2, 1], [4, 0]]}, {[[1, 1], [4, 1], [2, 1], [5, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [1, 0], [4, 1], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [5, 0], [2, 1], [4, 1], [1, 1]]}, {[[4, 0], [2, 1], [5, 0], [3, 1], [1, 1]]}, {[[5, 1], [3, 1], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 0], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 1], [4, 1], [2, 0]]}, {[[1, 0], [5, 0], [2, 1], [4, 1], [3, 1]]}, {[[2, 0], [4, 1], [5, 1], [3, 1], [1, 0]]}, {[[3, 1], [2, 1], [4, 1], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [4, 1], [2, 1], [3, 1]]}, {[[5, 0], [3, 1], [1, 1], [2, 1], [4, 0]]}, {[[3, 1], [4, 1], [2, 1], [5, 0], [1, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [5, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 0], [4, 1], [2, 1]]}, {[[1, 0], [5, 1], [2, 1], [4, 1], [3, 0]]}, {[[2, 1], [4, 1], [5, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 1], [4, 1], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [4, 1], [2, 1], [3, 0]]}, {[[5, 0], [3, 1], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [4, 1], [2, 1], [5, 1], [1, 0]]}, {[[4, 1], [2, 1], [1, 0], [3, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [5, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 0], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [4, 0], [5, 0], [3, 1], [1, 1]]}, {[[3, 0], [2, 0], [4, 1], [1, 1], [5, 1]]}, {[[5, 1], [1, 1], [4, 1], [2, 0], [3, 0]]}, {[[5, 1], [3, 1], [1, 0], [2, 0], [4, 1]]}, {[[4, 1], [2, 0], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [4, 0], [2, 1], [5, 1], [1, 1]]}} the member , {[[2, 1], [4, 0], [5, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 0], [4, 1], [2, 0]]}, {[[1, 1], [5, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [4, 1], [5, 0], [3, 1], [1, 1]]}, {[[3, 0], [2, 1], [4, 1], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [4, 1], [2, 1], [3, 0]]}, {[[5, 1], [3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [4, 1], [2, 1], [5, 0], [1, 1]]}, {[[4, 0], [2, 1], [1, 0], [3, 1], [5, 1]]}} the member , {[[2, 0], [4, 1], [5, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 1], [4, 1], [5, 0], [3, 0]]}, {[[2, 1], [1, 1], [5, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0], [5, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1], [5, 1], [4, 1]]}, {[[4, 0], [3, 1], [5, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [1, 0], [3, 1], [2, 0]]}, {[[4, 1], [5, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [5, 0], [4, 1], [1, 1], [2, 1]]}} the member , {[[2, 1], [1, 1], [4, 1], [5, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 0], [5, 1], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 1], [5, 1], [4, 0]]}, {[[3, 1], [1, 1], [2, 0], [5, 0], [4, 1]]}, {[[4, 1], [3, 0], [5, 1], [1, 1], [2, 0]]}, {[[4, 1], [5, 0], [2, 0], [1, 1], [3, 1]]}, {[[4, 0], [5, 1], [1, 1], [3, 0], [2, 1]]}, {[[3, 1], [5, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [4, 0], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 1], [5, 0], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [5, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 1], [5, 0], [4, 1]]}, {[[4, 0], [3, 1], [5, 1], [1, 1], [2, 0]]}, {[[4, 1], [5, 0], [2, 1], [1, 0], [3, 1]]}, {[[4, 0], [5, 1], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [5, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [4, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 1], [5, 1], [3, 0]]}, {[[2, 0], [1, 1], [5, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 0], [5, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 1], [5, 0], [4, 1]]}, {[[4, 1], [3, 1], [5, 0], [1, 1], [2, 0]]}, {[[4, 1], [5, 0], [2, 1], [1, 1], [3, 0]]}, {[[4, 0], [5, 1], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [5, 1], [4, 1], [1, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [4, 1], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 1], [4, 1], [5, 0], [3, 1]]}, {[[2, 1], [1, 0], [5, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [5, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 1], [5, 1], [4, 0]]}, {[[4, 0], [3, 1], [5, 1], [1, 0], [2, 1]]}, {[[4, 0], [5, 1], [2, 1], [1, 0], [3, 1]]}, {[[4, 1], [5, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [5, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 1], [4, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 1], [4, 1], [5, 1], [3, 0]]}, {[[2, 1], [1, 0], [5, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 0], [5, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 1], [5, 1], [4, 0]]}, {[[4, 1], [3, 1], [5, 0], [1, 0], [2, 1]]}, {[[4, 0], [5, 1], [2, 1], [1, 1], [3, 0]]}, {[[4, 1], [5, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [5, 1], [4, 1], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 1], [4, 1], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [4, 1], [5, 1], [3, 1]]}, {[[2, 0], [1, 0], [5, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 1], [5, 0], [4, 0]]}, {[[3, 1], [1, 1], [2, 1], [5, 0], [4, 0]]}, {[[4, 1], [3, 1], [5, 1], [1, 0], [2, 0]]}, {[[4, 0], [5, 0], [1, 1], [3, 1], [2, 1]]}, {[[4, 0], [5, 0], [2, 1], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [4, 1], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 0], [3, 1], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [3, 1], [2, 0], [5, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 0], [5, 1]]}, {[[5, 0], [2, 0], [3, 1], [4, 1], [1, 1]]}, {[[5, 1], [2, 1], [3, 1], [4, 0], [1, 0]]}, {[[5, 1], [2, 0], [3, 1], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 1], [4, 0], [1, 1]]}} the member , {[[1, 0], [4, 0], [3, 1], [2, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [3, 1], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [3, 1], [4, 1], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 1], [2, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [3, 0], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [3, 0], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [3, 0], [4, 1], [1, 1]]}, {[[5, 1], [2, 1], [3, 0], [4, 1], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 0], [2, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 1], [3, 1], [5, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 1], [5, 1], [4, 0]]}, {[[4, 1], [5, 0], [3, 1], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [3, 1], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 1], [3, 1], [5, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 1], [3, 1], [5, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 1], [5, 0], [4, 1]]}, {[[4, 1], [5, 0], [3, 1], [1, 0], [2, 1]]}, {[[4, 0], [5, 1], [3, 1], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 1], [3, 1], [5, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 1], [3, 0], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 0], [5, 0], [4, 1]]}, {[[2, 1], [1, 1], [3, 0], [5, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 0], [3, 0], [1, 1], [2, 1]]}, {[[4, 0], [5, 1], [3, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [3, 0], [1, 0], [2, 1]]}, {[[4, 1], [5, 1], [3, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 1], [3, 0], [5, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 0], [3, 1], [5, 1], [2, 1]]}, {[[1, 0], [5, 1], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 1], [1, 1], [5, 0]]}, {[[2, 1], [5, 1], [3, 1], [4, 0], [1, 0]]}, {[[5, 0], [1, 1], [3, 1], [4, 0], [2, 1]]}, {[[5, 0], [2, 0], [3, 1], [1, 1], [4, 1]]}, {[[4, 1], [1, 1], [3, 1], [2, 0], [5, 0]]}, {[[4, 1], [2, 0], [3, 1], [5, 1], [1, 0]]}} the member , {[[1, 0], [4, 0], [3, 1], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [3, 1], [5, 0], [2, 0]]}, {[[1, 1], [5, 0], [3, 1], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 1], [1, 0], [5, 1]]}, {[[2, 0], [5, 0], [3, 1], [4, 1], [1, 1]]}, {[[5, 1], [1, 0], [3, 1], [4, 1], [2, 0]]}, {[[5, 1], [2, 1], [3, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 1], [5, 1]]}, {[[4, 0], [2, 1], [3, 1], [5, 0], [1, 1]]}} the member , {[[2, 0], [4, 1], [3, 1], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [3, 0], [5, 1], [2, 1]]}, {[[1, 1], [5, 1], [3, 0], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 1], [5, 1]]}, {[[2, 1], [5, 1], [3, 0], [4, 0], [1, 1]]}, {[[5, 1], [1, 1], [3, 0], [4, 0], [2, 1]]}, {[[5, 1], [2, 0], [3, 0], [1, 1], [4, 1]]}, {[[4, 1], [2, 0], [3, 0], [5, 1], [1, 1]]}, {[[4, 1], [1, 1], [3, 0], [2, 0], [5, 1]]}} the member , {[[2, 1], [4, 0], [3, 0], [1, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 1], [3, 1], [5, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1], [5, 1], [4, 1]]}, {[[4, 0], [5, 0], [3, 1], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [3, 1], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 1], [3, 1], [5, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [3, 1], [5, 0], [2, 1]]}, {[[1, 1], [5, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 1], [5, 1]]}, {[[2, 1], [5, 0], [3, 1], [4, 0], [1, 1]]}, {[[5, 1], [1, 1], [3, 1], [4, 0], [2, 0]]}, {[[5, 1], [2, 0], [3, 1], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [3, 1], [2, 0], [5, 1]]}, {[[4, 0], [2, 0], [3, 1], [5, 1], [1, 1]]}} the member , {[[1, 1], [4, 0], [3, 1], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [3, 1], [5, 1], [2, 0]]}, {[[1, 1], [5, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 1], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [3, 1], [4, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 1], [4, 0], [2, 1]]}, {[[5, 1], [2, 0], [3, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [3, 1], [2, 0], [5, 1]]}, {[[4, 1], [2, 0], [3, 1], [5, 0], [1, 1]]}} the member , {[[2, 1], [4, 0], [3, 1], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [3, 1], [5, 0], [2, 1]]}, {[[1, 0], [5, 1], [3, 1], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 1], [1, 1], [5, 0]]}, {[[2, 1], [5, 0], [3, 1], [4, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 1], [4, 1], [2, 0]]}, {[[5, 0], [2, 1], [3, 1], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [3, 1], [2, 1], [5, 0]]}, {[[4, 0], [2, 1], [3, 1], [5, 1], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 1], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [3, 1], [5, 1], [2, 0]]}, {[[1, 0], [5, 0], [3, 1], [2, 1], [4, 1]]}, {[[2, 1], [4, 1], [3, 1], [1, 0], [5, 0]]}, {[[2, 0], [5, 1], [3, 1], [4, 1], [1, 0]]}, {[[5, 0], [1, 0], [3, 1], [4, 1], [2, 1]]}, {[[5, 0], [2, 1], [3, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [3, 1], [2, 1], [5, 0]]}, {[[4, 1], [2, 1], [3, 1], [5, 0], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 1], [5, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [3, 0], [5, 1], [2, 1]]}, {[[1, 0], [5, 1], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [4, 1], [3, 0], [1, 1], [5, 0]]}, {[[2, 1], [5, 1], [3, 0], [4, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 0], [4, 1], [2, 1]]}, {[[5, 0], [2, 1], [3, 0], [1, 1], [4, 1]]}, {[[4, 1], [1, 1], [3, 0], [2, 1], [5, 0]]}, {[[4, 1], [2, 1], [3, 0], [5, 1], [1, 0]]}} the member , {[[1, 0], [4, 1], [3, 0], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [3, 0], [5, 0], [2, 1]]}, {[[1, 1], [5, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 1], [5, 1]]}, {[[2, 1], [5, 0], [3, 0], [4, 1], [1, 1]]}, {[[5, 1], [1, 1], [3, 0], [4, 1], [2, 0]]}, {[[5, 1], [2, 1], [3, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [3, 0], [2, 1], [5, 1]]}, {[[4, 0], [2, 1], [3, 0], [5, 1], [1, 1]]}} the member , {[[1, 1], [4, 1], [3, 0], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [3, 0], [5, 1], [2, 0]]}, {[[1, 1], [5, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [4, 1], [3, 0], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [3, 0], [4, 1], [1, 1]]}, {[[5, 1], [1, 0], [3, 0], [4, 1], [2, 1]]}, {[[5, 1], [2, 1], [3, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 1], [5, 1]]}, {[[4, 1], [2, 1], [3, 0], [5, 0], [1, 1]]}} the member , {[[2, 1], [4, 1], [3, 0], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 0], [5, 1], [2, 1], [3, 1]]}, {[[1, 0], [4, 1], [5, 1], [2, 0], [3, 1]]}, {[[3, 1], [2, 1], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [4, 1], [1, 1], [2, 0], [5, 0]]}, {[[3, 1], [4, 0], [1, 1], [2, 1], [5, 0]]}, {[[5, 0], [2, 0], [1, 1], [4, 1], [3, 1]]}, {[[5, 0], [2, 1], [1, 1], [4, 0], [3, 1]]}} the member , {[[1, 0], [4, 0], [5, 1], [2, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [5, 1], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [5, 0], [2, 1], [3, 1]]}, {[[3, 0], [2, 0], [5, 1], [4, 1], [1, 1]]}, {[[3, 1], [2, 1], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [4, 0], [1, 1], [2, 1], [5, 1]]}, {[[3, 1], [4, 1], [1, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 1], [1, 1], [4, 0], [3, 0]]}, {[[5, 1], [2, 0], [1, 0], [4, 1], [3, 1]]}} the member , {[[1, 1], [4, 1], [5, 1], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [5, 1], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 1], [4, 0], [1, 1]]}, {[[3, 1], [4, 0], [1, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 1], [4, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [5, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [5, 1], [2, 1], [3, 0]]}, {[[1, 1], [4, 1], [5, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 1], [5, 1], [4, 0], [1, 1]]}, {[[3, 1], [4, 0], [1, 0], [2, 1], [5, 1]]}, {[[3, 0], [4, 1], [1, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 1], [4, 1], [3, 0]]}, {[[5, 1], [2, 1], [1, 0], [4, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [5, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [5, 0], [2, 1], [3, 1]]}, {[[1, 0], [4, 1], [5, 1], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 1], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [4, 1], [1, 1], [2, 1], [5, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [1, 1], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [4, 1], [5, 0], [2, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [5, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [4, 1], [1, 0], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [1, 0], [4, 1], [3, 0]]}} the member , {[[3, 0], [2, 1], [5, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [4, 1], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [2, 1], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 0], [5, 1]]}} the member , {[[2, 0], [3, 1], [4, 1], [5, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [5, 1], [4, 1], [3, 0], [2, 1]]}, {[[1, 0], [5, 1], [4, 0], [3, 1], [2, 1]]}, {[[2, 1], [3, 0], [4, 1], [5, 1], [1, 0]]}, {[[2, 1], [3, 1], [4, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [2, 1], [3, 0], [4, 1]]}, {[[5, 0], [1, 1], [2, 0], [3, 1], [4, 1]]}, {[[4, 1], [3, 1], [2, 0], [1, 1], [5, 0]]}, {[[4, 1], [3, 0], [2, 1], [1, 1], [5, 0]]}} the member , {[[1, 0], [5, 1], [4, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [5, 1], [4, 1], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [3, 1], [2, 1]]}, {[[2, 1], [3, 1], [4, 1], [5, 0], [1, 0]]}, {[[2, 0], [3, 1], [4, 1], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [2, 1], [3, 1], [4, 0]]}, {[[5, 0], [1, 0], [2, 1], [3, 1], [4, 1]]}, {[[4, 1], [3, 1], [2, 1], [1, 0], [5, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 1], [5, 0]]}} the member , {[[1, 0], [5, 1], [4, 1], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 1], [5, 0], [1, 0], [3, 1]]}, {[[2, 0], [5, 1], [1, 1], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [5, 0], [4, 1], [2, 1]]}, {[[3, 0], [2, 1], [5, 1], [1, 1], [4, 0]]}, {[[3, 0], [4, 1], [1, 1], [5, 1], [2, 0]]}, {[[4, 1], [2, 1], [1, 0], [5, 0], [3, 1]]}, {[[4, 0], [1, 1], [5, 1], [2, 1], [3, 0]]}, {[[3, 1], [5, 0], [1, 0], [2, 1], [4, 1]]}} the member , {[[2, 1], [4, 1], [5, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [5, 1], [3, 1], [2, 0]]}, {[[1, 1], [5, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [5, 1], [4, 0], [1, 1]]}, {[[3, 1], [2, 0], [4, 1], [5, 0], [1, 1]]}, {[[3, 1], [4, 0], [2, 1], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [2, 1], [4, 0], [3, 1]]}, {[[4, 0], [3, 1], [1, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 1], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [5, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [5, 1], [3, 0], [2, 1]]}, {[[1, 0], [5, 1], [4, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 1], [4, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [2, 0], [4, 1], [3, 1]]}, {[[4, 1], [3, 0], [1, 1], [2, 1], [5, 0]]}, {[[3, 1], [4, 1], [2, 0], [1, 1], [5, 0]]}, {[[5, 0], [2, 1], [1, 1], [3, 0], [4, 1]]}} the member , {[[1, 0], [4, 1], [5, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [5, 1], [3, 1], [2, 0]]}, {[[1, 0], [5, 0], [4, 1], [2, 1], [3, 1]]}, {[[2, 0], [3, 1], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 1], [4, 1], [5, 0], [1, 0]]}, {[[3, 1], [4, 1], [2, 1], [1, 0], [5, 0]]}, {[[5, 0], [1, 0], [2, 1], [4, 1], [3, 1]]}, {[[4, 0], [3, 1], [1, 1], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [1, 1], [3, 1], [4, 0]]}} the member , {[[1, 0], [4, 1], [5, 1], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 1], [5, 0], [3, 1], [2, 1]]}, {[[1, 0], [5, 1], [4, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 1], [5, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 1], [4, 1], [5, 1], [1, 0]]}, {[[3, 0], [4, 1], [2, 1], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [2, 1], [4, 1], [3, 0]]}, {[[5, 0], [2, 1], [1, 0], [3, 1], [4, 1]]}, {[[4, 1], [3, 1], [1, 0], [2, 1], [5, 0]]}} the member , {[[1, 0], [4, 1], [5, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [4, 0], [5, 1], [3, 1], [2, 1]]}, {[[1, 0], [5, 1], [4, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 1], [5, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 1], [5, 1], [1, 0]]}, {[[3, 1], [4, 0], [2, 1], [1, 1], [5, 0]]}, {[[5, 0], [1, 1], [2, 1], [4, 0], [3, 1]]}, {[[4, 1], [3, 1], [1, 1], [2, 0], [5, 0]]}, {[[5, 0], [2, 0], [1, 1], [3, 1], [4, 1]]}} the member , {[[1, 0], [4, 0], [5, 1], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [5, 1], [3, 0], [2, 0]]}, {[[1, 1], [5, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 0], [5, 1], [4, 1], [1, 1]]}, {[[3, 1], [2, 1], [4, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 1], [4, 1], [2, 0], [1, 0], [5, 1]]}, {[[4, 0], [3, 0], [1, 1], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [5, 1], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [5, 0], [3, 1], [2, 1]]}, {[[1, 1], [5, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 1], [5, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [4, 1], [5, 1], [1, 1]]}, {[[3, 0], [4, 0], [2, 1], [1, 1], [5, 1]]}, {[[5, 1], [1, 1], [2, 1], [4, 0], [3, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 0], [3, 1], [4, 1]]}} the member , {[[1, 1], [4, 0], [5, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 0], [5, 1], [3, 0], [2, 1]]}, {[[1, 1], [5, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [5, 1], [4, 0], [1, 1]]}, {[[3, 1], [2, 0], [4, 0], [5, 1], [1, 1]]}, {[[3, 1], [4, 0], [2, 0], [1, 1], [5, 1]]}, {[[5, 1], [1, 1], [2, 0], [4, 0], [3, 1]]}, {[[4, 1], [3, 0], [1, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [1, 1], [3, 0], [4, 1]]}} the member , {[[2, 1], [3, 0], [5, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [5, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 0], [4, 1], [5, 1], [1, 1]]}, {[[2, 1], [3, 1], [4, 0], [5, 0], [1, 1]]}, {[[5, 1], [1, 1], [2, 1], [3, 0], [4, 0]]}, {[[5, 1], [1, 0], [2, 0], [3, 1], [4, 1]]}, {[[4, 0], [3, 0], [2, 1], [1, 1], [5, 1]]}, {[[4, 1], [3, 1], [2, 0], [1, 0], [5, 1]]}} the member , {[[2, 0], [3, 0], [4, 1], [5, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [5, 0], [3, 0], [2, 1]]}, {[[1, 1], [5, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 1], [4, 0], [5, 1], [1, 1]]}, {[[3, 0], [4, 1], [2, 0], [1, 1], [5, 1]]}, {[[5, 1], [1, 1], [2, 0], [4, 1], [3, 0]]}, {[[5, 1], [2, 1], [1, 0], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [1, 0], [2, 1], [5, 1]]}} the member , {[[2, 1], [3, 0], [5, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [4, 1], [5, 0], [3, 1], [2, 0]]}, {[[1, 1], [5, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 1], [4, 1], [5, 0], [1, 1]]}, {[[3, 0], [4, 1], [2, 1], [1, 0], [5, 1]]}, {[[5, 1], [1, 0], [2, 1], [4, 1], [3, 0]]}, {[[5, 1], [2, 1], [1, 0], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1], [5, 1]]}} the member , {[[2, 0], [3, 1], [5, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [5, 1], [3, 1], [4, 0], [2, 1]]}, {[[2, 1], [4, 0], [3, 1], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 1], [2, 0], [4, 1]]}, {[[4, 1], [2, 0], [3, 1], [1, 1], [5, 0]]}} the member , {[[1, 0], [5, 1], [3, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [5, 1], [3, 1], [4, 1], [2, 0]]}, {[[1, 0], [5, 0], [3, 1], [4, 1], [2, 1]]}, {[[2, 1], [4, 1], [3, 1], [5, 0], [1, 0]]}, {[[2, 0], [4, 1], [3, 1], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 1], [2, 1], [4, 0]]}, {[[5, 0], [1, 0], [3, 1], [2, 1], [4, 1]]}, {[[4, 0], [2, 1], [3, 1], [1, 1], [5, 0]]}, {[[4, 1], [2, 1], [3, 1], [1, 0], [5, 0]]}} the member , {[[1, 0], [5, 1], [3, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [5, 1], [3, 0], [4, 1], [2, 1]]}, {[[2, 1], [4, 1], [3, 0], [5, 1], [1, 0]]}, {[[5, 0], [1, 1], [3, 0], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [3, 0], [1, 1], [5, 0]]}} the member , {[[1, 0], [5, 1], [3, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [4, 1], [3, 1], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 1], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 0], [5, 1]]}} the member , {[[2, 0], [4, 1], [3, 1], [5, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [5, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 1], [5, 1], [1, 1]]}, {[[2, 1], [4, 0], [3, 1], [5, 0], [1, 1]]}, {[[5, 1], [1, 0], [3, 1], [2, 0], [4, 1]]}, {[[5, 1], [1, 1], [3, 1], [2, 0], [4, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1], [5, 1]]}, {[[4, 1], [2, 0], [3, 1], [1, 0], [5, 1]]}} the member , {[[2, 0], [4, 0], [3, 1], [5, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 1], [5, 0], [1, 1], [3, 0]]}, {[[2, 1], [5, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [4, 1], [2, 1]]}, {[[3, 0], [2, 1], [5, 0], [1, 1], [4, 1]]}, {[[4, 1], [1, 1], [5, 0], [2, 1], [3, 0]]}, {[[3, 0], [4, 1], [1, 0], [5, 1], [2, 1]]}, {[[3, 0], [5, 1], [1, 0], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [1, 0], [5, 1], [3, 0]]}} the member , {[[2, 1], [4, 1], [5, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [5, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [4, 1], [3, 0], [5, 0], [1, 1]]}, {[[2, 0], [4, 1], [3, 0], [5, 1], [1, 1]]}, {[[5, 1], [1, 1], [3, 0], [2, 1], [4, 0]]}, {[[5, 1], [1, 0], [3, 0], [2, 1], [4, 1]]}, {[[4, 0], [2, 1], [3, 0], [1, 1], [5, 1]]}, {[[4, 1], [2, 1], [3, 0], [1, 0], [5, 1]]}} the member , {[[2, 1], [4, 1], [3, 0], [5, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [4, 0], [3, 0], [5, 1], [1, 1]]}, {[[5, 1], [1, 1], [3, 0], [2, 0], [4, 1]]}, {[[4, 1], [2, 0], [3, 0], [1, 1], [5, 1]]}} the member , {[[1, 1], [5, 1], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 1], [5, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [4, 1], [5, 0], [1, 1]]}, {[[2, 0], [3, 1], [4, 0], [5, 1], [1, 1]]}, {[[5, 1], [1, 1], [2, 0], [3, 1], [4, 0]]}, {[[5, 1], [1, 0], [2, 1], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [2, 1], [1, 0], [5, 1]]}, {[[4, 0], [3, 1], [2, 0], [1, 1], [5, 1]]}} the member , {[[2, 1], [3, 0], [4, 1], [5, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 1], [5, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [4, 0], [5, 1], [1, 1]]}, {[[5, 1], [1, 1], [2, 0], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [2, 0], [1, 1], [5, 1]]}} the member , {[[2, 1], [3, 0], [4, 0], [5, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 1], [4, 0], [5, 0], [3, 1]]}, {[[2, 1], [1, 1], [5, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1], [5, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0], [5, 1], [4, 1]]}, {[[4, 0], [3, 0], [5, 1], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [1, 1], [3, 0], [2, 0]]}, {[[4, 1], [5, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[2, 1], [1, 1], [4, 0], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 1], [4, 0], [5, 1], [3, 0]]}, {[[2, 1], [1, 1], [5, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0], [5, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0], [5, 1], [4, 1]]}, {[[4, 1], [3, 0], [5, 0], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [1, 0], [3, 0], [2, 1]]}, {[[4, 1], [5, 1], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [4, 0], [1, 1], [2, 1]]}} the member , {[[2, 1], [1, 1], [4, 0], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 0], [1, 0], [5, 1], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [5, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 1], [5, 0], [2, 0], [4, 1]]}, {[[3, 1], [5, 1], [1, 0], [4, 0], [2, 1]]}, {[[4, 1], [2, 0], [5, 0], [1, 1], [3, 1]]}, {[[4, 1], [2, 0], [5, 1], [1, 1], [3, 0]]}, {[[3, 0], [5, 1], [1, 1], [4, 0], [2, 1]]}} the member , {[[2, 1], [4, 0], [1, 0], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [5, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [4, 0], [5, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 1], [5, 0], [4, 1]]}, {[[3, 1], [1, 1], [2, 0], [5, 1], [4, 0]]}, {[[4, 1], [3, 0], [5, 1], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [1, 1], [3, 0], [2, 1]]}, {[[4, 0], [5, 1], [2, 0], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [5, 1], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [1, 0], [5, 1], [4, 1], [3, 1]]}, {[[3, 1], [2, 1], [1, 1], [5, 0], [4, 0]]}, {[[4, 0], [5, 0], [1, 1], [2, 1], [3, 1]]}, {[[3, 1], [4, 1], [5, 1], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [5, 1], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 0], [5, 1], [1, 1], [3, 1]]}, {[[2, 1], [5, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 1], [1, 1], [5, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [5, 1], [1, 0], [4, 1]]}, {[[3, 1], [5, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [4, 0], [1, 1], [5, 0], [2, 1]]}, {[[4, 1], [1, 0], [5, 1], [2, 0], [3, 1]]}, {[[4, 0], [2, 0], [1, 1], [5, 1], [3, 1]]}} the member , {[[2, 0], [4, 0], [5, 1], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 1], [5, 1], [4, 0], [3, 0]]}, {[[2, 1], [1, 1], [5, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1], [5, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 0], [2, 0], [3, 1]]}, {[[4, 1], [5, 1], [1, 1], [2, 0], [3, 0]]}, {[[3, 1], [4, 0], [5, 0], [1, 1], [2, 1]]}, {[[3, 0], [4, 0], [5, 1], [1, 1], [2, 1]]}} the member , {[[2, 1], [1, 1], [5, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [5, 0], [4, 1], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 1], [5, 1], [4, 0]]}, {[[3, 1], [2, 1], [1, 0], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [1, 1], [2, 1], [3, 0]]}, {[[4, 1], [5, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 0], [4, 1], [5, 1], [1, 1], [2, 0]]}, {[[3, 1], [4, 1], [5, 0], [1, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [5, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [5, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [5, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 1], [5, 1], [4, 0]]}, {[[4, 1], [5, 0], [1, 1], [2, 0], [3, 1]]}, {[[4, 0], [5, 1], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [4, 0], [5, 1], [1, 0], [2, 1]]}, {[[3, 1], [4, 0], [5, 1], [1, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [5, 1], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 1], [5, 1], [1, 0], [3, 0]]}, {[[2, 0], [5, 1], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [5, 1], [4, 1], [2, 1]]}, {[[3, 1], [2, 1], [5, 0], [1, 1], [4, 0]]}, {[[3, 0], [5, 0], [1, 1], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [1, 1], [5, 0], [3, 0]]}, {[[4, 0], [1, 1], [5, 0], [2, 1], [3, 1]]}, {[[3, 1], [4, 1], [1, 0], [5, 1], [2, 0]]}} the member , {[[2, 1], [4, 1], [5, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 0], [5, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [5, 0], [4, 1], [3, 1]]}, {[[3, 0], [2, 1], [1, 1], [5, 0], [4, 1]]}, {[[3, 1], [2, 1], [1, 0], [5, 1], [4, 0]]}, {[[4, 1], [5, 0], [1, 1], [2, 1], [3, 0]]}, {[[4, 0], [5, 1], [1, 0], [2, 1], [3, 1]]}, {[[3, 0], [4, 1], [5, 1], [1, 0], [2, 1]]}, {[[3, 1], [4, 1], [5, 0], [1, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [5, 1], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [1, 1], [5, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [4, 1], [5, 0], [1, 1], [2, 1]]}} the member , {[[2, 1], [1, 1], [5, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 0], [5, 1], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [5, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 0], [5, 0], [2, 1]]}, {[[4, 1], [1, 1], [5, 1], [3, 0], [2, 0]]}, {[[3, 1], [5, 1], [2, 0], [1, 0], [4, 1]]}, {[[4, 0], [3, 0], [1, 1], [5, 1], [2, 1]]}, {[[4, 1], [1, 0], [2, 0], [5, 1], [3, 1]]}} the member , {[[2, 0], [3, 0], [5, 1], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [3, 1], [5, 1], [1, 0], [4, 0]]}, {[[2, 0], [5, 0], [1, 1], [3, 1], [4, 1]]}, {[[2, 0], [5, 1], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [2, 1], [5, 0], [3, 1]]}, {[[4, 0], [1, 0], [5, 1], [3, 1], [2, 1]]}, {[[3, 1], [5, 0], [2, 1], [1, 1], [4, 0]]}, {[[4, 1], [3, 1], [1, 1], [5, 0], [2, 0]]}} the member , {[[2, 1], [3, 1], [5, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [3, 0], [5, 0], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [5, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [2, 0], [5, 1], [3, 0]]}, {[[3, 0], [5, 1], [2, 0], [1, 1], [4, 1]]}, {[[4, 1], [3, 0], [1, 0], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [5, 0], [3, 0], [2, 1]]}} the member , {[[2, 1], [3, 0], [5, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [3, 0], [5, 1], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [5, 1], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 0], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [2, 0], [5, 1], [3, 1]]}, {[[4, 1], [1, 0], [5, 1], [3, 0], [2, 1]]}, {[[3, 1], [5, 1], [2, 0], [1, 1], [4, 0]]}, {[[4, 1], [3, 0], [1, 1], [5, 0], [2, 1]]}} the member , {[[2, 1], [3, 0], [5, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [3, 0], [5, 1], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [1, 1], [3, 0], [4, 1]]}, {[[2, 1], [5, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 0], [5, 1], [2, 1]]}, {[[4, 1], [3, 0], [1, 1], [5, 1], [2, 0]]}, {[[4, 1], [1, 1], [2, 0], [5, 0], [3, 1]]}, {[[4, 0], [1, 1], [5, 1], [3, 0], [2, 1]]}, {[[3, 1], [5, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[2, 1], [3, 0], [5, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [5, 1], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [5, 0], [4, 1], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 1], [5, 0], [2, 0]]}, {[[4, 1], [1, 0], [5, 1], [3, 1], [2, 0]]}, {[[3, 1], [5, 1], [2, 1], [1, 0], [4, 0]]}, {[[4, 0], [3, 1], [1, 1], [5, 0], [2, 1]]}, {[[4, 0], [1, 0], [2, 1], [5, 1], [3, 1]]}} the member , {[[2, 0], [3, 1], [5, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 0], [5, 0], [1, 1], [3, 1]]}, {[[2, 1], [5, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 1], [5, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [5, 1], [1, 1], [4, 1]]}, {[[3, 0], [4, 0], [1, 1], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [5, 1], [2, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [5, 1], [3, 1]]}, {[[3, 1], [5, 1], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 1], [4, 0], [5, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [5, 1], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [1, 1], [3, 1], [4, 0]]}, {[[2, 1], [5, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 1], [5, 0], [2, 1]]}, {[[4, 0], [1, 1], [5, 1], [3, 1], [2, 0]]}, {[[3, 1], [5, 0], [2, 1], [1, 0], [4, 1]]}, {[[4, 0], [3, 1], [1, 1], [5, 1], [2, 0]]}, {[[4, 1], [1, 0], [2, 1], [5, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [5, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [3, 1], [5, 0], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 1], [5, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [5, 0], [2, 1]]}, {[[4, 1], [1, 0], [2, 1], [5, 1], [3, 0]]}, {[[3, 0], [5, 1], [2, 1], [1, 0], [4, 1]]}, {[[4, 1], [1, 1], [5, 0], [3, 1], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [5, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [5, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [3, 1], [5, 0], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [5, 1], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [2, 1], [5, 1], [3, 0]]}, {[[4, 1], [1, 0], [5, 0], [3, 1], [2, 1]]}, {[[3, 0], [5, 1], [2, 1], [1, 1], [4, 0]]}, {[[4, 1], [3, 1], [1, 0], [5, 0], [2, 1]]}} the member , {[[2, 1], [3, 1], [5, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 1], [5, 1], [1, 1], [3, 0]]}, {[[2, 1], [5, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 1], [5, 1], [4, 1], [2, 0]]}, {[[3, 1], [2, 1], [5, 0], [1, 0], [4, 1]]}, {[[3, 1], [4, 1], [1, 0], [5, 0], [2, 1]]}, {[[4, 0], [2, 1], [1, 1], [5, 1], [3, 0]]}, {[[3, 0], [5, 1], [1, 1], [2, 1], [4, 0]]}, {[[4, 1], [1, 0], [5, 0], [2, 1], [3, 1]]}} the member , {[[2, 0], [4, 1], [5, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [3, 1], [5, 0], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [1, 0], [3, 1], [4, 1]]}, {[[2, 1], [5, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [5, 1], [2, 1]]}, {[[3, 0], [5, 0], [2, 1], [1, 1], [4, 1]]}, {[[4, 0], [1, 1], [5, 0], [3, 1], [2, 1]]}, {[[4, 1], [3, 1], [1, 0], [5, 1], [2, 0]]}, {[[4, 1], [1, 1], [2, 1], [5, 0], [3, 0]]}} the member , {[[2, 1], [3, 1], [5, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 1], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [5, 1], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 1], [1, 1], [5, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [5, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [5, 1], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [5, 1], [1, 1], [3, 0]]}, {[[4, 1], [2, 1], [5, 0], [1, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [5, 1], [1, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 1], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 0], [5, 1], [1, 0], [3, 1]]}, {[[2, 0], [5, 1], [1, 1], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [5, 1], [1, 1], [4, 0]]}, {[[4, 1], [2, 0], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [4, 0], [1, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [5, 1], [2, 0], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [2, 0], [4, 1]]}} the member , {[[2, 1], [4, 0], [5, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 0], [4, 1], [1, 0], [5, 1], [3, 1]]}, {[[2, 1], [4, 1], [1, 1], [5, 0], [3, 0]]}, {[[3, 1], [1, 1], [5, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [5, 1], [2, 1], [4, 1]]}, {[[3, 1], [5, 1], [1, 0], [4, 1], [2, 0]]}, {[[4, 1], [2, 1], [5, 1], [1, 0], [3, 0]]}, {[[4, 0], [2, 1], [5, 0], [1, 1], [3, 1]]}, {[[3, 0], [5, 0], [1, 1], [4, 1], [2, 1]]}} the member , {[[2, 0], [4, 1], [1, 0], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[2, 1], [4, 1], [1, 0], [5, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 0], [2, 1], [4, 1]]}, {[[3, 0], [5, 1], [1, 0], [4, 1], [2, 1]]}, {[[4, 1], [2, 1], [5, 0], [1, 1], [3, 0]]}} the member , {[[2, 1], [4, 1], [1, 0], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] For the equivalence class of patterns, { {[[1, 0], [3, 0], [5, 1], [2, 1], [4, 1]]}, {[[1, 0], [4, 1], [2, 0], [5, 1], [3, 1]]}, {[[2, 1], [4, 1], [1, 1], [3, 0], [5, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 1], [5, 0]]}, {[[5, 0], [2, 1], [4, 0], [1, 1], [3, 1]]}, {[[5, 0], [3, 0], [1, 1], [4, 1], [2, 1]]}, {[[3, 1], [5, 1], [2, 0], [4, 1], [1, 0]]}, {[[4, 1], [2, 1], [5, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [5, 1], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 1, 1, 1 Using the scheme, the first, , 31, terms are [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] Out of a total of , 172, cases 168, were successful and , 4, failed Success Rate: , 0.977 Here are the failures {{{[[1, 1], [2, 1], [4, 0], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 1], [5, 1]]}, {[[5, 1], [3, 0], [4, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 0], [3, 0], [1, 1]]}}, { {[[1, 1], [3, 0], [4, 1], [2, 0], [5, 1]]}, {[[1, 1], [3, 1], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 1], [5, 1]]}, {[[1, 1], [4, 0], [2, 1], [3, 0], [5, 1]]}, {[[5, 1], [2, 0], [4, 0], [3, 1], [1, 1]]}, {[[5, 1], [2, 0], [4, 1], [3, 0], [1, 1]]}, {[[5, 1], [3, 1], [2, 0], [4, 0], [1, 1]]}, {[[5, 1], [3, 0], [2, 1], [4, 0], [1, 1]]}}, { {[[1, 1], [4, 0], [3, 0], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [3, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 1], [1, 1]]}, {[[5, 1], [2, 1], [3, 0], [4, 0], [1, 1]]}}, { {[[1, 1], [4, 0], [3, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 1], [4, 0], [1, 1]]}}} {{{[[1, 1], [2, 1], [4, 0], [3, 0], [5, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 1], [5, 1]]}, {[[5, 1], [3, 0], [4, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 0], [3, 0], [1, 1]]}}, { {[[1, 1], [3, 0], [4, 1], [2, 0], [5, 1]]}, {[[1, 1], [3, 1], [4, 0], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [2, 0], [3, 1], [5, 1]]}, {[[1, 1], [4, 0], [2, 1], [3, 0], [5, 1]]}, {[[5, 1], [2, 0], [4, 0], [3, 1], [1, 1]]}, {[[5, 1], [2, 0], [4, 1], [3, 0], [1, 1]]}, {[[5, 1], [3, 1], [2, 0], [4, 0], [1, 1]]}, {[[5, 1], [3, 0], [2, 1], [4, 0], [1, 1]]}}, { {[[1, 1], [4, 0], [3, 0], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [3, 0], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 0], [4, 1], [1, 1]]}, {[[5, 1], [2, 1], [3, 0], [4, 0], [1, 1]]}}, { {[[1, 1], [4, 0], [3, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 0], [3, 1], [4, 0], [1, 1]]}}} "for patterns of lengths: ", [[5, 4]] There all together, 89, different equivalence classes For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 1], [5, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 1], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [5, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 1], [4, 1], [5, 0]]}, {[[4, 1], [3, 1], [5, 1], [2, 1], [1, 0]]}, {[[5, 0], [4, 1], [2, 1], [1, 1], [3, 1]]}, {[[5, 0], [4, 1], [1, 1], [3, 1], [2, 1]]}, {[[3, 1], [1, 1], [2, 1], [4, 1], [5, 0]]}} the member , {[[1, 0], [2, 1], [4, 1], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [5, 1], [4, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 1], [4, 0], [5, 1], [3, 1]]}, {[[2, 1], [1, 1], [5, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 1], [5, 1], [4, 1]]}, {[[4, 1], [3, 0], [5, 1], [1, 1], [2, 1]]}, {[[3, 1], [1, 1], [2, 0], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 1], [3, 0], [2, 1]]}, {[[4, 1], [5, 1], [2, 0], [1, 1], [3, 1]]}} the member , {[[3, 1], [5, 1], [4, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [5, 0], [4, 1], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [2, 1], [1, 0], [3, 1]]}, {[[2, 1], [1, 1], [4, 1], [5, 0], [3, 1]]}, {[[2, 1], [1, 1], [5, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [5, 1], [4, 1]]}, {[[4, 0], [3, 1], [5, 1], [1, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 1], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 1], [3, 1], [2, 0]]}} the member , {[[3, 1], [5, 0], [4, 1], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [5, 1], [4, 1], [1, 0], [2, 1]]}, {[[4, 1], [5, 0], [2, 1], [1, 1], [3, 1]]}, {[[2, 1], [1, 0], [4, 1], [5, 1], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 1], [5, 1], [4, 0]]}, {[[4, 1], [3, 1], [5, 1], [1, 1], [2, 0]]}, {[[3, 1], [1, 1], [2, 1], [5, 0], [4, 1]]}, {[[4, 0], [5, 1], [1, 1], [3, 1], [2, 1]]}} the member , {[[3, 1], [5, 1], [4, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [5, 1], [4, 1], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [2, 1], [1, 1], [3, 1]]}, {[[2, 0], [1, 1], [4, 1], [5, 1], [3, 1]]}, {[[2, 1], [1, 0], [5, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 1], [5, 0], [4, 1]]}, {[[4, 1], [3, 1], [5, 1], [1, 0], [2, 1]]}, {[[3, 1], [1, 1], [2, 1], [5, 1], [4, 0]]}, {[[4, 1], [5, 0], [1, 1], [3, 1], [2, 1]]}} the member , {[[3, 1], [5, 1], [4, 1], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [5, 1], [4, 1], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [2, 1], [1, 1], [3, 0]]}, {[[2, 1], [1, 1], [4, 1], [5, 1], [3, 0]]}, {[[2, 1], [1, 1], [5, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 0], [5, 1], [4, 1]]}, {[[4, 1], [3, 1], [5, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 1], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [1, 0], [3, 1], [2, 1]]}} the member , {[[3, 0], [5, 1], [4, 1], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [2, 1], [1, 1], [5, 0]]}, {[[1, 0], [4, 1], [5, 1], [3, 1], [2, 1]]}, {[[4, 1], [3, 1], [1, 1], [2, 1], [5, 0]]}, {[[1, 0], [5, 1], [4, 1], [2, 1], [3, 1]]}, {[[5, 0], [1, 1], [2, 1], [4, 1], [3, 1]]}, {[[5, 0], [2, 1], [1, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 1], [4, 1], [5, 1], [1, 0]]}} the member , {[[3, 1], [4, 1], [2, 1], [1, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [4, 1], [2, 1], [1, 1], [5, 1]]}, {[[4, 1], [3, 1], [1, 0], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [5, 0], [3, 1], [2, 1]]}, {[[1, 1], [5, 1], [4, 1], [2, 1], [3, 0]]}, {[[5, 1], [1, 1], [2, 1], [4, 1], [3, 0]]}, {[[5, 1], [2, 1], [1, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 1], [4, 1], [5, 1], [1, 1]]}} the member , {[[3, 0], [4, 1], [2, 1], [1, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [5, 1], [2, 0], [3, 1], [1, 1]]}, {[[4, 1], [5, 1], [2, 1], [3, 0], [1, 1]]}, {[[2, 1], [1, 1], [4, 0], [3, 1], [5, 1]]}, {[[2, 1], [1, 1], [4, 1], [3, 0], [5, 1]]}, {[[1, 1], [3, 1], [2, 0], [5, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 1], [5, 1], [4, 1]]}, {[[5, 1], [3, 1], [4, 0], [1, 1], [2, 1]]}, {[[5, 1], [3, 0], [4, 1], [1, 1], [2, 1]]}} the member , {[[4, 1], [5, 1], [2, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [5, 0], [3, 1], [1, 1]]}, {[[1, 1], [4, 1], [2, 1], [5, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [5, 1], [2, 1], [4, 1], [1, 1]]}, {[[5, 1], [3, 1], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 1], [4, 1], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [4, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 1], [5, 0], [2, 1], [4, 1]]}} the member , {[[4, 1], [2, 1], [5, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [5, 0], [1, 1], [2, 1]]}, {[[3, 0], [4, 1], [5, 1], [1, 1], [2, 1]]}, {[[2, 1], [1, 1], [5, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 1], [5, 1], [4, 1], [3, 0]]}, {[[4, 1], [5, 1], [1, 0], [2, 1], [3, 1]]}, {[[4, 1], [5, 1], [1, 1], [2, 1], [3, 0]]}, {[[3, 1], [2, 1], [1, 0], [5, 1], [4, 1]]}, {[[3, 0], [2, 1], [1, 1], [5, 1], [4, 1]]}} the member , {[[3, 1], [4, 1], [5, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 0], [5, 1], [1, 1], [2, 1]]}, {[[2, 1], [1, 1], [5, 1], [4, 0], [3, 1]]}, {[[4, 1], [5, 1], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [5, 1], [4, 1]]}} the member , {[[3, 1], [4, 0], [5, 1], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [5, 1], [1, 0], [2, 1]]}, {[[3, 1], [4, 1], [5, 1], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [5, 1], [4, 1], [3, 1]]}, {[[2, 0], [1, 1], [5, 1], [4, 1], [3, 1]]}, {[[4, 1], [5, 0], [1, 1], [2, 1], [3, 1]]}, {[[4, 0], [5, 1], [1, 1], [2, 1], [3, 1]]}, {[[3, 1], [2, 1], [1, 1], [5, 0], [4, 1]]}, {[[3, 1], [2, 1], [1, 1], [5, 1], [4, 0]]}} the member , {[[3, 1], [4, 1], [5, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [4, 0], [2, 1], [3, 1], [5, 1]]}, {[[5, 1], [2, 0], [4, 1], [3, 1], [1, 1]]}, {[[5, 1], [3, 1], [2, 1], [4, 0], [1, 1]]}, {[[1, 1], [3, 1], [4, 1], [2, 0], [5, 1]]}} the member , {[[1, 1], [4, 0], [2, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [5, 1], [2, 1], [3, 1], [1, 0]]}, {[[2, 1], [1, 1], [4, 1], [3, 1], [5, 0]]}, {[[5, 0], [3, 1], [4, 1], [1, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 1], [5, 1], [4, 1]]}} the member , {[[4, 1], [5, 1], [2, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 0], [5, 1], [2, 1], [3, 1], [1, 1]]}, {[[4, 1], [5, 0], [2, 1], [3, 1], [1, 1]]}, {[[2, 1], [1, 0], [4, 1], [3, 1], [5, 1]]}, {[[2, 0], [1, 1], [4, 1], [3, 1], [5, 1]]}, {[[1, 1], [3, 1], [2, 1], [5, 0], [4, 1]]}, {[[1, 1], [3, 1], [2, 1], [5, 1], [4, 0]]}, {[[5, 1], [3, 1], [4, 1], [1, 1], [2, 0]]}, {[[5, 1], [3, 1], [4, 1], [1, 0], [2, 1]]}} the member , {[[4, 0], [5, 1], [2, 1], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [5, 1], [3, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 1], [3, 0], [5, 1], [4, 1]]}} the member , {[[4, 1], [5, 1], [3, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [5, 0], [2, 1], [1, 1]]}, {[[3, 0], [4, 1], [5, 1], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [5, 1], [4, 1], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [4, 1], [3, 1]]}, {[[5, 1], [4, 1], [1, 0], [2, 1], [3, 1]]}, {[[5, 1], [4, 1], [1, 1], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 1], [5, 1]]}, {[[3, 1], [2, 1], [1, 0], [4, 1], [5, 1]]}} the member , {[[3, 1], [4, 1], [5, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 0], [5, 1], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [5, 1], [4, 0], [3, 1]]}, {[[5, 1], [4, 1], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 1], [4, 1], [5, 1]]}} the member , {[[3, 1], [4, 0], [5, 1], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 0], [3, 1], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [3, 1], [5, 0], [2, 1]]}, {[[4, 1], [1, 1], [3, 1], [5, 1], [2, 0]]}, {[[4, 0], [1, 1], [3, 1], [5, 1], [2, 1]]}, {[[2, 1], [5, 0], [3, 1], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [3, 1], [1, 0], [4, 1]]}, {[[2, 1], [5, 1], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [3, 1], [1, 1], [4, 1]]}} the member , {[[4, 1], [1, 0], [3, 1], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [4, 0], [3, 1], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [3, 1], [2, 0], [5, 1]]}, {[[5, 1], [2, 1], [3, 1], [4, 0], [1, 1]]}, {[[5, 1], [2, 0], [3, 1], [4, 1], [1, 1]]}} the member , {[[1, 1], [4, 0], [3, 1], [2, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [5, 1], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [5, 1], [4, 1], [3, 1]]}, {[[5, 1], [4, 0], [1, 1], [2, 1], [3, 1]]}, {[[3, 1], [2, 1], [1, 1], [4, 0], [5, 1]]}} the member , {[[3, 1], [4, 1], [5, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 0], [3, 1], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [3, 1], [2, 0], [4, 1]]}, {[[4, 1], [1, 1], [3, 1], [2, 0], [5, 1]]}, {[[5, 1], [1, 1], [3, 1], [4, 0], [2, 1]]}, {[[5, 1], [2, 0], [3, 1], [1, 1], [4, 1]]}, {[[2, 1], [4, 0], [3, 1], [1, 1], [5, 1]]}, {[[2, 1], [5, 1], [3, 1], [4, 0], [1, 1]]}, {[[1, 1], [4, 0], [3, 1], [5, 1], [2, 1]]}} the member , {[[4, 1], [2, 0], [3, 1], [5, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [5, 1], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [5, 1], [4, 1], [3, 1]]}, {[[5, 0], [4, 1], [1, 1], [2, 1], [3, 1]]}, {[[3, 1], [2, 1], [1, 1], [4, 1], [5, 0]]}} the member , {[[3, 1], [4, 1], [5, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [5, 1], [3, 0], [1, 1]]}, {[[1, 1], [4, 1], [2, 0], [5, 1], [3, 1]]}, {[[5, 1], [2, 1], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [2, 0], [4, 1], [1, 1]]}, {[[2, 1], [4, 1], [1, 1], [3, 0], [5, 1]]}, {[[5, 1], [3, 0], [1, 1], [4, 1], [2, 1]]}, {[[3, 1], [1, 1], [4, 0], [2, 1], [5, 1]]}, {[[1, 1], [3, 0], [5, 1], [2, 1], [4, 1]]}} the member , {[[4, 1], [2, 1], [5, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 1], [2, 0], [3, 1], [5, 1]]}, {[[1, 1], [5, 1], [2, 1], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [2, 1], [5, 1], [1, 1]]}, {[[5, 1], [1, 1], [4, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [4, 1], [1, 1], [5, 1]]}, {[[5, 1], [3, 1], [2, 0], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [4, 0], [3, 1], [1, 1]]}, {[[1, 1], [3, 1], [4, 0], [5, 1], [2, 1]]}} the member , {[[4, 1], [1, 1], [2, 0], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[5, 1], [2, 1], [3, 1], [4, 1], [1, 0]]}, {[[5, 0], [2, 1], [3, 1], [4, 1], [1, 1]]}, {[[1, 1], [4, 1], [3, 1], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 1], [5, 1]]}} the member , {[[5, 1], [2, 1], [3, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 0], [2, 1], [3, 1], [5, 1]]}, {[[1, 1], [5, 1], [2, 1], [3, 1], [4, 0]]}, {[[5, 1], [1, 1], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 1], [5, 1]]}, {[[4, 0], [3, 1], [2, 1], [5, 1], [1, 1]]}, {[[5, 1], [3, 1], [2, 1], [1, 0], [4, 1]]}, {[[2, 1], [5, 0], [4, 1], [3, 1], [1, 1]]}, {[[1, 1], [3, 1], [4, 1], [5, 0], [2, 1]]}} the member , {[[4, 1], [1, 0], [2, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 1], [2, 1], [3, 0], [5, 1]]}, {[[1, 1], [5, 1], [2, 0], [3, 1], [4, 1]]}, {[[5, 1], [1, 1], [4, 0], [3, 1], [2, 1]]}, {[[4, 1], [3, 1], [2, 0], [5, 1], [1, 1]]}, {[[2, 1], [3, 1], [4, 0], [1, 1], [5, 1]]}, {[[5, 1], [3, 0], [2, 1], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [4, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [4, 1], [5, 1], [2, 1]]}} the member , {[[4, 1], [1, 1], [2, 1], [3, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 1], [2, 1], [3, 1], [5, 0]]}, {[[1, 0], [5, 1], [2, 1], [3, 1], [4, 1]]}, {[[5, 0], [1, 1], [4, 1], [3, 1], [2, 1]]}, {[[2, 1], [3, 1], [4, 1], [1, 1], [5, 0]]}, {[[4, 1], [3, 1], [2, 1], [5, 1], [1, 0]]}, {[[5, 0], [3, 1], [2, 1], [1, 1], [4, 1]]}, {[[2, 1], [5, 1], [4, 1], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [4, 1], [5, 1], [2, 1]]}} the member , {[[4, 1], [1, 1], [2, 1], [3, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 0], [1, 1], [2, 1], [3, 1], [5, 1]]}, {[[1, 1], [5, 0], [2, 1], [3, 1], [4, 1]]}, {[[5, 1], [1, 0], [4, 1], [3, 1], [2, 1]]}, {[[2, 1], [3, 1], [4, 1], [1, 0], [5, 1]]}, {[[4, 1], [3, 1], [2, 1], [5, 0], [1, 1]]}, {[[5, 1], [3, 1], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [5, 1], [4, 1], [3, 1], [1, 1]]}, {[[1, 1], [3, 1], [4, 1], [5, 1], [2, 0]]}} the member , {[[4, 0], [1, 1], [2, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [3, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [3, 0], [2, 1], [1, 1]]}} the member , {[[1, 1], [2, 1], [3, 0], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [3, 1], [1, 0], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [2, 1], [5, 1], [3, 0]]}, {[[2, 1], [3, 1], [5, 0], [1, 1], [4, 1]]}, {[[3, 0], [5, 1], [2, 1], [1, 1], [4, 1]]}, {[[4, 1], [1, 1], [5, 0], [3, 1], [2, 1]]}, {[[2, 1], [5, 1], [1, 0], [3, 1], [4, 1]]}, {[[2, 1], [5, 1], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [5, 1], [2, 1]]}} the member , {[[4, 1], [3, 1], [1, 0], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [3, 0], [1, 1], [5, 1], [2, 1]]}, {[[4, 1], [1, 1], [2, 0], [5, 1], [3, 1]]}, {[[3, 1], [5, 1], [2, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [5, 1], [1, 1], [4, 1]]}, {[[4, 1], [1, 1], [5, 1], [3, 0], [2, 1]]}, {[[2, 1], [5, 1], [1, 1], [3, 0], [4, 1]]}, {[[2, 1], [5, 1], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 0], [5, 1], [2, 1]]}} the member , {[[4, 1], [3, 0], [1, 1], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [3, 1], [1, 1], [5, 0], [2, 1]]}, {[[4, 0], [1, 1], [2, 1], [5, 1], [3, 1]]}, {[[2, 1], [3, 1], [5, 1], [1, 0], [4, 1]]}, {[[3, 1], [5, 1], [2, 1], [1, 1], [4, 0]]}, {[[4, 1], [1, 0], [5, 1], [3, 1], [2, 1]]}, {[[2, 1], [5, 0], [1, 1], [3, 1], [4, 1]]}, {[[2, 0], [5, 1], [4, 1], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 1], [5, 1], [2, 0]]}} the member , {[[4, 1], [3, 1], [1, 1], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 1], [5, 1], [4, 1]]}, {[[4, 1], [5, 1], [3, 1], [2, 1], [1, 0]]}, {[[2, 1], [1, 1], [3, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [3, 1], [1, 1], [2, 1]]}} the member , {[[1, 0], [2, 1], [3, 1], [5, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 0], [5, 1], [1, 1], [3, 1]]}, {[[3, 1], [5, 1], [1, 1], [4, 0], [2, 1]]}, {[[2, 1], [4, 0], [1, 1], [5, 1], [3, 1]]}, {[[3, 1], [1, 1], [5, 1], [2, 0], [4, 1]]}} the member , {[[4, 1], [2, 0], [5, 1], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [5, 0], [3, 1], [1, 1], [2, 1]]}, {[[4, 1], [5, 1], [3, 1], [1, 0], [2, 1]]}, {[[4, 1], [5, 1], [3, 1], [1, 1], [2, 0]]}, {[[4, 0], [5, 1], [3, 1], [1, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 1], [5, 1], [4, 1]]}, {[[2, 1], [1, 1], [3, 1], [5, 0], [4, 1]]}, {[[2, 1], [1, 1], [3, 1], [5, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 1], [5, 1], [4, 1]]}} the member , {[[4, 1], [5, 0], [3, 1], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 0], [3, 1], [5, 1]]}, {[[1, 1], [2, 1], [4, 1], [3, 0], [5, 1]]}, {[[1, 1], [3, 1], [2, 0], [4, 1], [5, 1]]}, {[[1, 1], [3, 0], [2, 1], [4, 1], [5, 1]]}, {[[5, 1], [3, 1], [4, 0], [2, 1], [1, 1]]}, {[[5, 1], [3, 0], [4, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 0], [3, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 1], [2, 1], [4, 0], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [5, 1], [3, 0], [2, 1], [1, 1]]}, {[[2, 1], [1, 1], [3, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [3, 0], [1, 1], [2, 1]]}, {[[1, 1], [2, 1], [3, 0], [5, 1], [4, 1]]}} the member , {[[4, 1], [5, 1], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [5, 1], [3, 1], [2, 0], [1, 1]]}, {[[2, 1], [1, 1], [3, 1], [4, 0], [5, 1]]}, {[[1, 1], [2, 0], [3, 1], [5, 1], [4, 1]]}, {[[5, 1], [4, 0], [3, 1], [1, 1], [2, 1]]}} the member , {[[4, 1], [5, 1], [3, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 0], [3, 1], [4, 1], [5, 1]]}, {[[1, 1], [2, 1], [3, 1], [4, 0], [5, 1]]}, {[[5, 1], [4, 0], [3, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [3, 1], [4, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[5, 0], [4, 1], [3, 1], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [3, 1], [4, 1], [5, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [3, 1], [2, 1], [1, 0]]}} the member , {[[5, 0], [4, 1], [3, 1], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 1], [4, 0], [2, 1]]}, {[[3, 1], [4, 0], [2, 1], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [2, 1], [4, 0], [3, 1]]}, {[[5, 1], [1, 1], [4, 1], [2, 0], [3, 1]]}, {[[5, 1], [3, 1], [1, 1], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [5, 1], [3, 1], [1, 1]]}, {[[4, 1], [2, 0], [1, 1], [3, 1], [5, 1]]}, {[[3, 1], [2, 0], [4, 1], [1, 1], [5, 1]]}} the member , {[[1, 1], [3, 1], [5, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[5, 1], [1, 1], [2, 0], [3, 1], [4, 1]]}, {[[5, 1], [1, 1], [2, 1], [3, 0], [4, 1]]}, {[[4, 1], [3, 1], [2, 0], [1, 1], [5, 1]]}, {[[4, 1], [3, 0], [2, 1], [1, 1], [5, 1]]}, {[[1, 1], [5, 1], [4, 0], [3, 1], [2, 1]]}, {[[1, 1], [5, 1], [4, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 1], [4, 0], [5, 1], [1, 1]]}, {[[2, 1], [3, 0], [4, 1], [5, 1], [1, 1]]}} the member , {[[5, 1], [1, 1], [2, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [4, 1], [3, 0], [2, 1], [5, 1]]}, {[[5, 1], [2, 1], [3, 0], [4, 1], [1, 1]]}} the member , {[[1, 1], [4, 1], [3, 0], [2, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 0], [2, 1], [5, 1], [3, 1]]}, {[[4, 0], [3, 1], [1, 1], [5, 1], [2, 1]]}, {[[3, 1], [5, 1], [2, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 1], [5, 1], [1, 1], [4, 1]]}, {[[4, 1], [1, 1], [5, 1], [3, 1], [2, 0]]}, {[[2, 1], [5, 1], [1, 1], [3, 1], [4, 0]]}, {[[2, 1], [5, 0], [4, 1], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [4, 1], [5, 0], [2, 1]]}} the member , {[[4, 1], [1, 0], [2, 1], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [3, 0], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [3, 0], [2, 1], [4, 1]]}, {[[5, 1], [1, 1], [3, 0], [4, 1], [2, 1]]}, {[[4, 1], [1, 1], [3, 0], [2, 1], [5, 1]]}, {[[2, 1], [4, 1], [3, 0], [1, 1], [5, 1]]}, {[[2, 1], [5, 1], [3, 0], [4, 1], [1, 1]]}, {[[1, 1], [4, 1], [3, 0], [5, 1], [2, 1]]}, {[[5, 1], [2, 1], [3, 0], [1, 1], [4, 1]]}} the member , {[[4, 1], [2, 1], [3, 0], [5, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 1], [2, 0], [4, 1]]}, {[[4, 1], [2, 0], [5, 1], [3, 1], [1, 1]]}, {[[1, 1], [4, 0], [2, 1], [5, 1], [3, 1]]}, {[[5, 1], [2, 0], [4, 1], [1, 1], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [3, 1], [5, 1]]}, {[[5, 1], [3, 1], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [5, 1], [2, 1], [4, 0], [1, 1]]}, {[[3, 1], [1, 1], [4, 1], [2, 0], [5, 1]]}} the member , {[[1, 1], [3, 1], [5, 1], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 1], [2, 1], [5, 0], [3, 1]]}, {[[4, 1], [3, 1], [1, 1], [5, 1], [2, 0]]}, {[[3, 1], [5, 0], [2, 1], [1, 1], [4, 1]]}, {[[2, 1], [3, 1], [5, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [5, 1], [3, 1], [2, 1]]}, {[[2, 0], [5, 1], [1, 1], [3, 1], [4, 1]]}, {[[2, 1], [5, 1], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 1], [5, 1], [2, 1]]}} the member , {[[4, 1], [1, 1], [2, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 0], [5, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 0], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [5, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 1], [4, 1], [5, 1]]}, {[[4, 1], [3, 0], [5, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [1, 1], [3, 0], [2, 1]]}, {[[3, 1], [1, 1], [2, 0], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [2, 0], [1, 1], [3, 1]]}} the member , {[[1, 1], [2, 1], [4, 0], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 1], [4, 1], [2, 1]]}, {[[3, 1], [4, 1], [2, 1], [5, 1], [1, 0]]}, {[[1, 0], [5, 1], [2, 1], [4, 1], [3, 1]]}, {[[5, 0], [1, 1], [4, 1], [2, 1], [3, 1]]}, {[[5, 0], [3, 1], [1, 1], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [1, 1], [3, 1], [5, 0]]}, {[[2, 1], [4, 1], [5, 1], [3, 1], [1, 0]]}, {[[3, 1], [2, 1], [4, 1], [1, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [5, 1], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [5, 1], [3, 0], [4, 1], [2, 1]]}, {[[5, 1], [1, 1], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [4, 1], [3, 0], [5, 1], [1, 1]]}, {[[4, 1], [2, 1], [3, 0], [1, 1], [5, 1]]}} the member , {[[1, 1], [5, 1], [3, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 0], [2, 1], [1, 1], [5, 1]]}, {[[4, 1], [3, 1], [1, 1], [2, 0], [5, 1]]}, {[[1, 1], [4, 0], [5, 1], [3, 1], [2, 1]]}, {[[1, 1], [5, 1], [4, 1], [2, 0], [3, 1]]}, {[[5, 1], [1, 1], [2, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 1], [5, 1], [4, 0], [1, 1]]}, {[[5, 1], [2, 0], [1, 1], [3, 1], [4, 1]]}, {[[3, 1], [2, 0], [4, 1], [5, 1], [1, 1]]}} the member , {[[3, 1], [4, 0], [2, 1], [1, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 1], [5, 0], [3, 1]]}, {[[3, 1], [5, 0], [4, 1], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [5, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 1], [5, 1]]}, {[[4, 0], [3, 1], [5, 1], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 1], [1, 0], [3, 1]]}, {[[5, 1], [4, 1], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 1], [5, 1]]}} the member , {[[1, 1], [2, 1], [4, 1], [5, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 1], [3, 1], [5, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 1], [5, 1]]}, {[[5, 1], [4, 1], [2, 1], [3, 1], [1, 0]]}, {[[5, 0], [3, 1], [4, 1], [2, 1], [1, 1]]}} the member , {[[1, 1], [2, 1], [4, 1], [3, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [5, 1], [3, 1], [4, 0], [2, 1]]}, {[[5, 1], [1, 1], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [4, 0], [3, 1], [5, 1], [1, 1]]}, {[[4, 1], [2, 0], [3, 1], [1, 1], [5, 1]]}} the member , {[[1, 1], [5, 1], [3, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [1, 0], [5, 1], [2, 1]]}, {[[3, 0], [5, 1], [1, 1], [2, 1], [4, 1]]}, {[[4, 1], [1, 1], [5, 0], [2, 1], [3, 1]]}, {[[2, 1], [4, 1], [5, 1], [1, 1], [3, 0]]}, {[[2, 1], [5, 1], [1, 0], [4, 1], [3, 1]]}, {[[4, 1], [2, 1], [1, 1], [5, 1], [3, 0]]}, {[[3, 0], [1, 1], [5, 1], [4, 1], [2, 1]]}, {[[3, 1], [2, 1], [5, 0], [1, 1], [4, 1]]}} the member , {[[3, 1], [4, 1], [1, 0], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 1], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [5, 1], [3, 1], [1, 1]]}, {[[1, 1], [4, 1], [2, 1], [5, 0], [3, 1]]}, {[[2, 0], [4, 1], [1, 1], [3, 1], [5, 1]]}, {[[5, 1], [3, 1], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [5, 0], [2, 1], [4, 1], [1, 1]]}, {[[5, 1], [2, 1], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [4, 1], [2, 1], [5, 1]]}} the member , {[[1, 1], [3, 1], [5, 1], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [5, 1], [3, 1], [4, 1], [2, 1]]}, {[[5, 0], [1, 1], [3, 1], [2, 1], [4, 1]]}, {[[2, 1], [4, 1], [3, 1], [5, 1], [1, 0]]}, {[[4, 1], [2, 1], [3, 1], [1, 1], [5, 0]]}} the member , {[[1, 0], [5, 1], [3, 1], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [4, 1], [2, 0], [3, 1], [5, 1]]}, {[[1, 1], [4, 1], [2, 1], [3, 0], [5, 1]]}, {[[5, 1], [2, 1], [4, 0], [3, 1], [1, 1]]}, {[[5, 1], [2, 1], [4, 1], [3, 0], [1, 1]]}, {[[5, 1], [3, 1], [2, 0], [4, 1], [1, 1]]}, {[[1, 1], [3, 1], [4, 0], [2, 1], [5, 1]]}, {[[1, 1], [3, 0], [4, 1], [2, 1], [5, 1]]}, {[[5, 1], [3, 0], [2, 1], [4, 1], [1, 1]]}} the member , {[[1, 1], [4, 1], [2, 0], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [3, 1], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [3, 1], [2, 1], [4, 1]]}, {[[4, 0], [1, 1], [3, 1], [2, 1], [5, 1]]}, {[[5, 1], [1, 0], [3, 1], [4, 1], [2, 1]]}, {[[5, 1], [2, 1], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [4, 1], [3, 1], [1, 0], [5, 1]]}, {[[2, 0], [5, 1], [3, 1], [4, 1], [1, 1]]}, {[[1, 1], [4, 1], [3, 1], [5, 1], [2, 0]]}} the member , {[[4, 1], [2, 1], [3, 1], [5, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 0], [1, 1], [5, 1], [2, 1]]}, {[[3, 1], [5, 1], [1, 1], [2, 0], [4, 1]]}, {[[4, 1], [1, 1], [5, 1], [2, 0], [3, 1]]}, {[[2, 1], [4, 0], [5, 1], [1, 1], [3, 1]]}, {[[2, 1], [5, 1], [1, 1], [4, 0], [3, 1]]}, {[[4, 1], [2, 0], [1, 1], [5, 1], [3, 1]]}, {[[3, 1], [1, 1], [5, 1], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [5, 1], [1, 1], [4, 1]]}} the member , {[[3, 1], [4, 0], [1, 1], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 1], [3, 1], [5, 1]]}, {[[1, 1], [3, 1], [2, 1], [4, 0], [5, 1]]}, {[[5, 1], [3, 1], [4, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 1], [3, 1], [1, 1]]}} the member , {[[1, 1], [2, 0], [4, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [3, 1], [5, 1], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [5, 1], [3, 1], [1, 0]]}, {[[1, 0], [4, 1], [2, 1], [5, 1], [3, 1]]}, {[[5, 0], [2, 1], [4, 1], [1, 1], [3, 1]]}, {[[2, 1], [4, 1], [1, 1], [3, 1], [5, 0]]}, {[[5, 0], [3, 1], [1, 1], [4, 1], [2, 1]]}, {[[3, 1], [5, 1], [2, 1], [4, 1], [1, 0]]}, {[[3, 1], [1, 1], [4, 1], [2, 1], [5, 0]]}} the member , {[[1, 0], [3, 1], [5, 1], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [3, 1], [5, 1], [1, 0]]}, {[[1, 0], [5, 1], [3, 1], [2, 1], [4, 1]]}, {[[4, 1], [1, 1], [3, 1], [2, 1], [5, 0]]}, {[[5, 0], [1, 1], [3, 1], [4, 1], [2, 1]]}, {[[5, 0], [2, 1], [3, 1], [1, 1], [4, 1]]}, {[[2, 1], [4, 1], [3, 1], [1, 1], [5, 0]]}, {[[2, 1], [5, 1], [3, 1], [4, 1], [1, 0]]}, {[[1, 0], [4, 1], [3, 1], [5, 1], [2, 1]]}} the member , {[[4, 1], [2, 1], [3, 1], [5, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 0], [2, 1], [4, 1], [3, 1], [5, 1]]}, {[[1, 1], [3, 1], [2, 1], [4, 1], [5, 0]]}, {[[5, 0], [4, 1], [2, 1], [3, 1], [1, 1]]}, {[[5, 1], [3, 1], [4, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [4, 1], [3, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [1, 1], [5, 0], [2, 1]]}, {[[3, 1], [5, 1], [1, 1], [2, 1], [4, 0]]}, {[[4, 1], [1, 0], [5, 1], [2, 1], [3, 1]]}, {[[2, 0], [4, 1], [5, 1], [1, 1], [3, 1]]}, {[[2, 1], [5, 0], [1, 1], [4, 1], [3, 1]]}, {[[3, 1], [1, 1], [5, 1], [4, 1], [2, 0]]}, {[[4, 0], [2, 1], [1, 1], [5, 1], [3, 1]]}, {[[3, 1], [2, 1], [5, 1], [1, 0], [4, 1]]}} the member , {[[3, 1], [4, 1], [1, 1], [5, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 0], [2, 1], [3, 1], [1, 1], [5, 1]]}, {[[1, 1], [5, 0], [3, 1], [4, 1], [2, 1]]}, {[[1, 1], [5, 1], [3, 1], [4, 1], [2, 0]]}, {[[5, 1], [1, 0], [3, 1], [2, 1], [4, 1]]}, {[[5, 1], [1, 1], [3, 1], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 1], [5, 1], [1, 1]]}, {[[2, 1], [4, 1], [3, 1], [5, 0], [1, 1]]}, {[[4, 1], [2, 1], [3, 1], [1, 0], [5, 1]]}} the member , {[[4, 0], [2, 1], [3, 1], [1, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 0], [4, 1], [2, 1]]}, {[[3, 0], [4, 1], [2, 1], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [2, 1], [4, 1], [3, 0]]}, {[[5, 1], [1, 1], [4, 1], [2, 1], [3, 0]]}, {[[5, 1], [3, 1], [1, 0], [2, 1], [4, 1]]}, {[[2, 1], [4, 1], [5, 0], [3, 1], [1, 1]]}, {[[4, 1], [2, 1], [1, 0], [3, 1], [5, 1]]}, {[[3, 0], [2, 1], [4, 1], [1, 1], [5, 1]]}} the member , {[[1, 1], [3, 1], [5, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [1, 1], [3, 0], [5, 1], [2, 1]]}, {[[2, 1], [5, 1], [3, 0], [1, 1], [4, 1]]}} the member , {[[4, 1], [1, 1], [3, 0], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [1, 1], [5, 1], [2, 0]]}, {[[3, 1], [5, 0], [1, 1], [2, 1], [4, 1]]}, {[[4, 0], [1, 1], [5, 1], [2, 1], [3, 1]]}, {[[2, 1], [4, 1], [5, 1], [1, 0], [3, 1]]}, {[[2, 0], [5, 1], [1, 1], [4, 1], [3, 1]]}, {[[4, 1], [2, 1], [1, 1], [5, 0], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [4, 1], [2, 1]]}, {[[3, 1], [2, 1], [5, 1], [1, 1], [4, 0]]}} the member , {[[3, 1], [4, 1], [1, 1], [5, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 0], [2, 1], [3, 1], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [3, 1], [2, 1], [4, 0]]}, {[[4, 1], [1, 0], [3, 1], [2, 1], [5, 1]]}, {[[5, 1], [1, 1], [3, 1], [4, 1], [2, 0]]}, {[[5, 1], [2, 1], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [4, 1], [3, 1], [1, 1], [5, 1]]}, {[[2, 1], [5, 0], [3, 1], [4, 1], [1, 1]]}, {[[1, 1], [4, 1], [3, 1], [5, 0], [2, 1]]}} the member , {[[4, 0], [2, 1], [3, 1], [5, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 0], [5, 1], [4, 1], [2, 1]]}, {[[3, 1], [4, 1], [2, 0], [5, 1], [1, 1]]}, {[[1, 1], [5, 1], [2, 0], [4, 1], [3, 1]]}, {[[5, 1], [1, 1], [4, 0], [2, 1], [3, 1]]}, {[[5, 1], [3, 0], [1, 1], [2, 1], [4, 1]]}, {[[4, 1], [2, 1], [1, 1], [3, 0], [5, 1]]}, {[[2, 1], [4, 1], [5, 1], [3, 0], [1, 1]]}, {[[3, 1], [2, 1], [4, 0], [1, 1], [5, 1]]}} the member , {[[1, 1], [3, 0], [5, 1], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 0], [4, 1], [5, 1], [3, 1]]}, {[[3, 1], [5, 1], [4, 1], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [5, 1], [3, 1], [4, 1]]}, {[[2, 1], [3, 1], [1, 1], [4, 0], [5, 1]]}, {[[4, 1], [3, 1], [5, 1], [2, 0], [1, 1]]}, {[[5, 1], [4, 0], [2, 1], [1, 1], [3, 1]]}, {[[5, 1], [4, 0], [1, 1], [3, 1], [2, 1]]}, {[[3, 1], [1, 1], [2, 1], [4, 0], [5, 1]]}} the member , {[[1, 1], [2, 0], [4, 1], [5, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [3, 1], [5, 1], [4, 1], [2, 0]]}, {[[3, 1], [4, 1], [2, 1], [5, 0], [1, 1]]}, {[[1, 1], [5, 0], [2, 1], [4, 1], [3, 1]]}, {[[5, 1], [1, 0], [4, 1], [2, 1], [3, 1]]}, {[[5, 1], [3, 1], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [5, 1], [3, 1], [1, 1]]}, {[[4, 0], [2, 1], [1, 1], [3, 1], [5, 1]]}, {[[3, 1], [2, 1], [4, 1], [1, 0], [5, 1]]}} the member , {[[1, 1], [3, 1], [5, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [5, 1], [1, 0], [3, 1]]}, {[[4, 0], [2, 1], [5, 1], [1, 1], [3, 1]]}, {[[3, 1], [5, 0], [1, 1], [4, 1], [2, 1]]}, {[[3, 1], [5, 1], [1, 1], [4, 1], [2, 0]]}, {[[2, 1], [4, 1], [1, 1], [5, 0], [3, 1]]}, {[[2, 0], [4, 1], [1, 1], [5, 1], [3, 1]]}, {[[3, 1], [1, 0], [5, 1], [2, 1], [4, 1]]}, {[[3, 1], [1, 1], [5, 1], [2, 1], [4, 0]]}} the member , {[[4, 1], [2, 1], [5, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [2, 1], [1, 0], [5, 1]]}, {[[1, 1], [4, 1], [5, 1], [3, 1], [2, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 1], [5, 1]]}, {[[1, 1], [5, 0], [4, 1], [2, 1], [3, 1]]}, {[[5, 1], [1, 0], [2, 1], [4, 1], [3, 1]]}, {[[5, 1], [2, 1], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [5, 1], [4, 1], [1, 1]]}, {[[3, 1], [2, 1], [4, 1], [5, 0], [1, 1]]}} the member , {[[3, 1], [4, 1], [2, 1], [1, 0], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [2, 1], [5, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 1], [5, 1], [4, 1], [1, 1]]}, {[[3, 1], [4, 1], [1, 0], [2, 1], [5, 1]]}, {[[3, 0], [4, 1], [1, 1], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [5, 1], [2, 1], [3, 0]]}, {[[5, 1], [2, 1], [1, 0], [4, 1], [3, 1]]}, {[[5, 1], [2, 1], [1, 1], [4, 1], [3, 0]]}, {[[1, 1], [4, 1], [5, 0], [2, 1], [3, 1]]}} the member , {[[3, 1], [2, 1], [5, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[5, 1], [1, 0], [2, 1], [3, 1], [4, 1]]}, {[[5, 1], [1, 1], [2, 1], [3, 1], [4, 0]]}, {[[4, 1], [3, 1], [2, 1], [1, 0], [5, 1]]}, {[[1, 1], [5, 0], [4, 1], [3, 1], [2, 1]]}, {[[1, 1], [5, 1], [4, 1], [3, 1], [2, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 1], [5, 1]]}, {[[2, 1], [3, 1], [4, 1], [5, 0], [1, 1]]}, {[[2, 0], [3, 1], [4, 1], [5, 1], [1, 1]]}} the member , {[[5, 1], [1, 0], [2, 1], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [4, 1], [2, 1], [3, 1], [5, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 1], [5, 1]]}, {[[5, 1], [2, 1], [4, 1], [3, 1], [1, 0]]}, {[[5, 1], [3, 1], [2, 1], [4, 1], [1, 0]]}, {[[5, 0], [3, 1], [2, 1], [4, 1], [1, 1]]}, {[[1, 1], [3, 1], [4, 1], [2, 1], [5, 0]]}, {[[1, 0], [3, 1], [4, 1], [2, 1], [5, 1]]}, {[[5, 0], [2, 1], [4, 1], [3, 1], [1, 1]]}} the member , {[[1, 1], [4, 1], [2, 1], [3, 1], [5, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 0], [4, 1], [1, 1], [5, 1], [2, 1]]}, {[[3, 1], [5, 1], [1, 0], [2, 1], [4, 1]]}, {[[4, 1], [1, 1], [5, 1], [2, 1], [3, 0]]}, {[[2, 1], [4, 1], [5, 0], [1, 1], [3, 1]]}, {[[2, 1], [5, 1], [1, 1], [4, 1], [3, 0]]}, {[[4, 1], [2, 1], [1, 0], [5, 1], [3, 1]]}, {[[3, 1], [1, 1], [5, 0], [4, 1], [2, 1]]}, {[[3, 0], [2, 1], [5, 1], [1, 1], [4, 1]]}} the member , {[[3, 0], [4, 1], [1, 1], [5, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[5, 0], [1, 1], [2, 1], [3, 1], [4, 1]]}, {[[1, 0], [5, 1], [4, 1], [3, 1], [2, 1]]}, {[[4, 1], [3, 1], [2, 1], [1, 1], [5, 0]]}, {[[2, 1], [3, 1], [4, 1], [5, 1], [1, 0]]}} the member , {[[5, 0], [1, 1], [2, 1], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [4, 1], [5, 1], [3, 0]]}, {[[1, 1], [2, 1], [5, 0], [3, 1], [4, 1]]}, {[[3, 0], [5, 1], [4, 1], [2, 1], [1, 1]]}, {[[2, 1], [3, 1], [1, 0], [4, 1], [5, 1]]}, {[[4, 1], [3, 1], [5, 0], [2, 1], [1, 1]]}, {[[5, 1], [4, 1], [2, 1], [1, 1], [3, 0]]}, {[[5, 1], [4, 1], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 1], [4, 1], [5, 1]]}} the member , {[[1, 1], [2, 1], [4, 1], [5, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [2, 0], [5, 1], [4, 1], [1, 1]]}, {[[3, 1], [2, 1], [5, 1], [4, 0], [1, 1]]}, {[[3, 1], [4, 0], [1, 1], [2, 1], [5, 1]]}, {[[3, 1], [4, 1], [1, 1], [2, 0], [5, 1]]}, {[[1, 1], [4, 1], [5, 1], [2, 0], [3, 1]]}, {[[5, 1], [2, 0], [1, 1], [4, 1], [3, 1]]}, {[[5, 1], [2, 1], [1, 1], [4, 0], [3, 1]]}, {[[1, 1], [4, 0], [5, 1], [2, 1], [3, 1]]}} the member , {[[3, 1], [2, 0], [5, 1], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[4, 1], [2, 1], [5, 0], [1, 1], [3, 1]]}, {[[4, 1], [2, 1], [5, 1], [1, 1], [3, 0]]}, {[[3, 1], [5, 1], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [5, 1], [1, 1], [4, 1], [2, 1]]}, {[[2, 1], [4, 1], [1, 0], [5, 1], [3, 1]]}, {[[2, 1], [4, 1], [1, 1], [5, 1], [3, 0]]}, {[[3, 1], [1, 1], [5, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [5, 1], [2, 1], [4, 1]]}} the member , {[[4, 1], [2, 1], [5, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [4, 1], [2, 0], [1, 1], [5, 1]]}, {[[4, 1], [3, 0], [1, 1], [2, 1], [5, 1]]}, {[[1, 1], [4, 1], [5, 1], [3, 0], [2, 1]]}, {[[5, 1], [1, 1], [2, 0], [4, 1], [3, 1]]}, {[[1, 1], [5, 1], [4, 0], [2, 1], [3, 1]]}, {[[5, 1], [2, 1], [1, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [5, 1], [4, 1], [1, 1]]}, {[[3, 1], [2, 1], [4, 0], [5, 1], [1, 1]]}} the member , {[[3, 1], [4, 1], [2, 0], [1, 1], [5, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[1, 1], [2, 1], [3, 1], [5, 1], [4, 0]]}, {[[4, 1], [5, 0], [3, 1], [2, 1], [1, 1]]}, {[[4, 0], [5, 1], [3, 1], [2, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 1], [4, 1], [5, 1]]}, {[[2, 0], [1, 1], [3, 1], [4, 1], [5, 1]]}, {[[1, 1], [2, 1], [3, 1], [5, 0], [4, 1]]}, {[[5, 1], [4, 1], [3, 1], [1, 0], [2, 1]]}, {[[5, 1], [4, 1], [3, 1], [1, 1], [2, 0]]}} the member , {[[1, 1], [2, 1], [3, 1], [5, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] For the equivalence class of patterns, { {[[3, 1], [2, 1], [5, 1], [4, 1], [1, 0]]}, {[[3, 1], [4, 1], [1, 1], [2, 1], [5, 0]]}, {[[1, 0], [4, 1], [5, 1], [2, 1], [3, 1]]}, {[[5, 0], [2, 1], [1, 1], [4, 1], [3, 1]]}} the member , {[[3, 1], [2, 1], [5, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 0, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] Out of a total of , 89, cases 89, were successful and , 0, failed Success Rate: , 1. Here are the failures {} {}