"for patterns of lengths: ", [[4, 0]] There all together, 7, different equivalence classes For the equivalence class of patterns, {{[[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 4 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 3, 1], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {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, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [4, 0], [3, 0]]}, has a scheme of depth , 4 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {}], [[2, 4, 1, 3], {}, {1, 2}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 3, 1], {}, {}, {}], [[1, 3, 2], {}, {2}, {}], [[3, 4, 1, 2], {}, {1, 2}, {}], [[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] Out of a total of , 7, cases 2, were successful and , 5, failed Success Rate: , 0.286 Here are the failures {{{[[2, 0], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 0]]}}, {{[[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 0], [3, 0]]}}, {{[[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 0]]}}} {{{[[2, 0], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 0]]}}, {{[[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 0]]}}, { {[[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 0]]}}, { {[[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 0], [3, 0]]}}, {{[[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 0]]}}} "for patterns of lengths: ", [[4, 1]] There all together, 16, different equivalence classes For the equivalence class of patterns, {{[[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 1]]}} the member , {[[4, 1], [1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {1}, {}], [[3, 2, 1], {}, {2}, {}], [[2, 1, 3], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}, {}], [[3, 1, 2], {}, {3}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 15, 54, 235 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 15, 54, 235, 1237, 7790, 57581, 489231, 4690254, 49986715, 585372877, 7463687750, 102854072045, 1522671988215, 24093282856182, 405692082526075, 7242076686885157, 136599856992122366, 2714409550073698925, 56674981258436882463, 1240409916125255533662, 28396256038413772845979, 678620228150165566119421, 16899850691078521962602102, 437837828891602558408686125, 11783055965037826523473187271, 328932078330541852123090999302, 9512432153659253937868832744059] For the equivalence class of patterns, {{[[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 0]]}} the member , {[[4, 0], [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], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 0]]}} the member , {[[3, 0], [2, 0], [4, 1], [1, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {}, {}, {}], [[2, 1, 3], {}, {1}, {}], [[3, 1, 2], {}, {2}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 15, 52, 203 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346, 445958869294805289, 4638590332229999353, 49631246523618756274, 545717047936059989389, 6160539404599934652455, 71339801938860275191172, 846749014511809332450147] For the equivalence class of patterns, {{[[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 0]]}} the member , {[[4, 0], [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, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 1]]}} the member , {[[3, 0], [1, 1], [4, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 15, 52, 203 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346, 445958869294805289, 4638590332229999353, 49631246523618756274, 545717047936059989389, 6160539404599934652455, 71339801938860275191172, 846749014511809332450147] For the equivalence class of patterns, {{[[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 0]]}} the member , {[[4, 0], [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, 0], [2, 1], [1, 0], [4, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 0]]}} the member , {[[4, 0], [1, 0], [2, 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], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 1]]}} the member , {[[3, 0], [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, {{[[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [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, {{[[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[4, 0], [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, 1], [2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[4, 1], [2, 0], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 5, 15, 54, 235 Using the scheme, the first, , 31, terms are [1, 1, 2, 5, 15, 54, 235, 1237, 7790, 57581, 489231, 4690254, 49986715, 585372877, 7463687750, 102854072045, 1522671988215, 24093282856182, 405692082526075, 7242076686885157, 136599856992122366, 2714409550073698925, 56674981258436882463, 1240409916125255533662, 28396256038413772845979, 678620228150165566119421, 16899850691078521962602102, 437837828891602558408686125, 11783055965037826523473187271, 328932078330541852123090999302, 9512432153659253937868832744059] For the equivalence class of patterns, {{[[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[4, 0], [2, 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, {{[[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[4, 0], [3, 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], [3, 0], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[4, 0], [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] Out of a total of , 16, cases 14, were successful and , 2, failed Success Rate: , 0.875 Here are the failures {{{[[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]]}}, { {[[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]]}}} {{{[[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]]}}, { {[[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]]}}} "for patterns of lengths: ", [[4, 2]] There all together, 26, different equivalence classes For the equivalence class of patterns, {{[[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 1]]}} the member , {[[1, 1], [2, 0], [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], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 1], [2, 1], [4, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2, 3], {[1, 0, 0, 0], [0, 1, 0, 0]}, {3}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[1, 0, 0], [0, 1, 0]}, {}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 2, 6, 24 Using the scheme, the first, , 31, terms are [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, 304888344611713860501504000000] For the equivalence class of patterns, {{[[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 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, 1], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[4, 1], [3, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 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, {{[[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [2, 0], [1, 1]]}} the member , {[[1, 1], [2, 0], [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, {{[[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 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, 0], [2, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 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, 1], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 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], [2, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [2, 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, 0], [2, 1], [4, 0], [3, 1]]}, {[[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [2, 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, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [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, {{[[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[1, 1], [4, 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, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [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, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[1, 0], [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], [3, 1], [4, 1], [2, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[1, 0], [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, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[2, 1], [3, 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, {{[[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 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], [3, 1], [2, 0]]}, {[[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[4, 0], [1, 1], [2, 1], [3, 0]]}} the member , {[[1, 0], [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, {{[[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[4, 1], [1, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [3, 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], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[1, 0], [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, {{[[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [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], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 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], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [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, 0], [1, 0], [3, 1]]}, {[[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 1], [4, 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, {{[[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [4, 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] Out of a total of , 26, cases 25, were successful and , 1, failed Success Rate: , 0.962 Here are the failures {{{[[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[4, 1], [2, 0], [3, 0], [1, 1]]}}} {{{[[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[4, 1], [2, 0], [3, 0], [1, 1]]}}} "for patterns of lengths: ", [[4, 3]] There all together, 16, different equivalence classes For the equivalence class of patterns, {{[[3, 1], [2, 0], [4, 1], [1, 1]]}, {[[2, 1], [4, 1], [3, 0], [1, 1]]}, {[[4, 1], [1, 1], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [4, 1], [2, 0], [3, 1]]}, {[[4, 1], [2, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 1], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 1], [4, 1]]}} the member , {[[3, 1], [2, 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, {{[[3, 0], [4, 1], [2, 1], [1, 1]]}, {[[3, 1], [4, 0], [2, 1], [1, 1]]}, {[[1, 1], [2, 1], [4, 1], [3, 0]]}, {[[1, 1], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 1], [4, 1]]}, {[[4, 1], [3, 1], [1, 1], [2, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 1]]}} the member , {[[3, 0], [4, 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, {{[[3, 1], [2, 1], [4, 1], [1, 0]]}, {[[2, 1], [4, 1], [3, 1], [1, 0]]}, {[[3, 1], [1, 1], [2, 1], [4, 0]]}, {[[4, 0], [1, 1], [3, 1], [2, 1]]}, {[[1, 0], [3, 1], [4, 1], [2, 1]]}, {[[1, 0], [4, 1], [2, 1], [3, 1]]}, {[[4, 0], [2, 1], [1, 1], [3, 1]]}, {[[2, 1], [3, 1], [1, 1], [4, 0]]}} the member , {[[3, 1], [2, 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, {{[[1, 0], [3, 1], [2, 1], [4, 1]]}, {[[1, 1], [3, 1], [2, 1], [4, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 1]]}, {[[4, 1], [2, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 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, {{[[1, 0], [2, 1], [3, 1], [4, 1]]}, {[[1, 1], [2, 1], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 1]]}, {[[4, 1], [3, 1], [2, 1], [1, 0]]}} the member , {[[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], [2, 1], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 1], [4, 1]]}, {[[4, 1], [3, 1], [2, 0], [1, 1]]}, {[[4, 1], [3, 0], [2, 1], [1, 1]]}} the member , {[[1, 1], [2, 1], [3, 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], [3, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 1]]}, {[[1, 1], [4, 1], [3, 1], [2, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [2, 1], [1, 1], [4, 1]]}, {[[3, 1], [2, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 1], [4, 1], [1, 1]]}, {[[2, 1], [3, 1], [4, 0], [1, 1]]}} the member , {[[4, 1], [1, 1], [2, 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, {{[[4, 1], [1, 1], [2, 0], [3, 1]]}, {[[1, 1], [4, 1], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [4, 1], [1, 1]]}} the member , {[[4, 1], [1, 1], [2, 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, {{[[2, 1], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [4, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 1], [4, 1], [2, 1]]}, {[[3, 1], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [4, 1], [1, 1], [3, 1]]}} the member , {[[2, 1], [4, 1], [1, 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, {{[[4, 0], [1, 1], [2, 1], [3, 1]]}, {[[1, 0], [4, 1], [3, 1], [2, 1]]}, {[[3, 1], [2, 1], [1, 1], [4, 0]]}, {[[2, 1], [3, 1], [4, 1], [1, 0]]}} the member , {[[4, 0], [1, 1], [2, 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], [2, 1], [4, 0], [1, 1]]}, {[[2, 0], [4, 1], [3, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 1], [4, 1]]}, {[[1, 1], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [4, 0], [2, 1], [3, 1]]}, {[[4, 1], [1, 0], [3, 1], [2, 1]]}, {[[4, 1], [2, 1], [1, 1], [3, 0]]}, {[[2, 1], [3, 1], [1, 0], [4, 1]]}} the member , {[[3, 1], [2, 1], [4, 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], [3, 1], [2, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 1], [4, 1]]}, {[[4, 1], [2, 0], [3, 1], [1, 1]]}, {[[4, 1], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 1], [3, 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, {{[[3, 0], [4, 1], [1, 1], [2, 1]]}, {[[3, 1], [4, 1], [1, 1], [2, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 1]]}, {[[3, 1], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [1, 1], [4, 1], [3, 1]]}, {[[2, 1], [1, 1], [4, 1], [3, 0]]}, {[[2, 1], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [4, 1], [3, 1]]}} the member , {[[3, 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, {{[[2, 1], [4, 0], [3, 1], [1, 1]]}, {[[4, 1], [1, 1], [3, 1], [2, 0]]}, {[[1, 1], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [4, 1], [2, 1], [3, 0]]}, {[[4, 1], [2, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [2, 1], [4, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 1], [4, 1]]}} the member , {[[2, 1], [4, 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], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 1], [3, 0], [4, 1]]}, {[[4, 1], [3, 0], [1, 1], [2, 1]]}} the member , {[[3, 1], [4, 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, {{[[3, 1], [4, 1], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [4, 1], [3, 1]]}, {[[2, 1], [1, 1], [3, 1], [4, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 1]]}} the member , {[[3, 1], [4, 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] Out of a total of , 16, cases 16, were successful and , 0, failed Success Rate: , 1. Here are the failures {} {}