"for patterns of lengths: ", [[3, 1], [4, 0]] There all together, 71, different equivalence classes For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 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, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 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], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [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, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [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], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [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], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 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, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 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], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [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, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 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], [3, 1]], %2}, {[[1, 0], [2, 0], [3, 1]], %1}, {[[1, 1], [2, 0], [3, 0]], %2}, {[[1, 1], [2, 0], [3, 0]], %1}, {[[3, 0], [2, 0], [1, 1]], %2}, {[[3, 0], [2, 0], [1, 1]], %1}, {[[3, 1], [2, 0], [1, 0]], %2}, {[[3, 1], [2, 0], [1, 0]], %1}} %1 := [[3, 0], [1, 0], [4, 0], [2, 0]] %2 := [[2, 0], [4, 0], [1, 0], [3, 0]] the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [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, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 0], [1, 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], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [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, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 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], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [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], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 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], [3, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 0], [1, 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], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[2, 1], {[0, 0, 1], [0, 1, 0]}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 0]}, {1}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[2, 1, 3], {[0, 0, 0, 0]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 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, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [4, 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], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [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, {{%2, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%1, [[4, 0], [2, 0], [1, 0], [3, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [4, 0], [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], [2, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [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], [2, 1], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [4, 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], [2, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 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]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 0], [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, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 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]], [[3, 0], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [1, 0], [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], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 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, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 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, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[2, 1], {[0, 0, 1], [0, 1, 0]}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 0]}, {1}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[2, 1, 3], {[0, 0, 0, 0]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 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] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[4, 0], [3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 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, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 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], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[4, 0], [2, 0], [3, 0], [1, 0]] %2 := [[1, 0], [3, 0], [2, 0], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [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, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [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, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [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], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [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, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 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, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[3, 0], [4, 0], [1, 0], [2, 0]] %2 := [[2, 0], [1, 0], [4, 0], [3, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 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], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [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, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 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]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %1}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[2, 0], [4, 0], [1, 0], [3, 0]] %2 := [[3, 0], [1, 0], [4, 0], [2, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [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, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 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]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [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, 0], [3, 0], [2, 1]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %1}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[3, 0], [1, 0], [4, 0], [2, 0]] %2 := [[2, 0], [4, 0], [1, 0], [3, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 0], [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, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [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, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 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]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[2, 0], [1, 0], [4, 0], [3, 0]] %2 := [[3, 0], [4, 0], [1, 0], [2, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 0], [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, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 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, 0], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [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], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [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, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [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, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[1, 0], [3, 0], [2, 0], [4, 0]] %2 := [[4, 0], [2, 0], [3, 0], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 0], [1, 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, 0], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [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, 0], [2, 1]], %2}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[3, 0], [1, 1], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0], [4, 0]] %2 := [[4, 0], [3, 0], [2, 0], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[2, 1], {[0, 0, 1], [0, 1, 0]}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 0]}, {1}, {}], [[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[2, 1, 3], {[0, 0, 0, 0]}, {1}, {}], [[], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1, 3, 2], {[1, 0, 0, 0]}, {2}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[1, 2, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {3}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[3, 1, 2], {[0, 1, 0, 0]}, {2}, {3}], [[1, 2], {[0, 1, 0]}, {1}, {}], [[2, 1], {}, {}, {2}], [[3, 2, 1], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 1, 2], {[0, 1, 0, 0], [1, 0, 0, 0]}, {2}, {3}], [[1, 2], {}, {1}, {}], [[2, 1], {[1, 0, 0]}, {}, {2}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 0]]}, has a scheme of depth , 5 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {2}, {}], [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}, {}], [[1, 3, 2], {[1, 0, 0, 0]}, {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {}, {}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {5}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2, 4, 5], {[1, 0, 0, 0, 0, 0]}, {4}, {}], [[1, 3, 2, 5, 4], {[1, 0, 0, 0, 0, 0]}, {2, 3}, {}], [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[1, 4, 2, 5, 3], {[1, 0, 0, 0, 0, 0]}, {2, 3}, {}], [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {3}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 23, 103 Using the scheme, the first, , 31, terms are [1, 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] Out of a total of , 71, cases 59, were successful and , 12, failed Success Rate: , 0.831 Here are the failures {{{%4, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 0]]}, {%1, [[4, 0], [3, 0], [1, 0], [2, 0]]}}, { {%4, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%3, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 0]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 0]]}}, {{%4, %5}, {%3, %5}, {%2, %6}, {%1, %6}}, { {%4, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%4, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%3, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 0], [1, 0]]}}, { {%4, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%1, [[3, 0], [2, 0], [1, 0], [4, 0]]}}, {{%4, %8}, {%4, %7}, {%3, %8}, {%3, %7}, {%2, %8}, {%2, %7}, {%1, %8}, {%1, %7}}, { {%4, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%3, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [4, 0], [1, 0]]}}, { {%4, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 0]]}}, {{%4, %6}, {%3, %6}, {%2, %5}, {%1, %5}}, { {%4, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%3, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%2, [[1, 0], [2, 0], [3, 0], [4, 0]]}, {%1, [[1, 0], [2, 0], [3, 0], [4, 0]]}}} %1 := [[3, 1], [1, 0], [2, 0]] %2 := [[2, 0], [3, 0], [1, 1]] %3 := [[2, 0], [1, 0], [3, 1]] %4 := [[1, 1], [3, 0], [2, 0]] %5 := [[2, 0], [1, 0], [4, 0], [3, 0]] %6 := [[3, 0], [4, 0], [1, 0], [2, 0]] %7 := [[3, 0], [1, 0], [4, 0], [2, 0]] %8 := [[2, 0], [4, 0], [1, 0], [3, 0]] {{{%4, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 0]]}, {%1, [[4, 0], [3, 0], [1, 0], [2, 0]]}}, { {%4, [[2, 0], [1, 0], [3, 0], [4, 0]]}, {%3, [[1, 0], [2, 0], [4, 0], [3, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 0]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 0]]}}, {{%4, %5}, {%3, %5}, {%2, %6}, {%1, %6}}, { {%4, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%4, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%3, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 0], [1, 0]]}}, { {%4, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%1, [[3, 0], [2, 0], [1, 0], [4, 0]]}}, {{%4, %8}, {%4, %7}, {%3, %8}, {%3, %7}, {%2, %8}, {%2, %7}, {%1, %8}, {%1, %7}}, { {%4, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%4, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 0], [2, 0], [1, 0], [4, 0]]}, {%3, [[1, 0], [4, 0], [3, 0], [2, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [4, 0], [1, 0]]}}, { {%4, [[3, 0], [2, 0], [4, 0], [1, 0]]}, {%4, [[4, 0], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [4, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [1, 0], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 0]]}, {%2, [[3, 0], [1, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 0]]}}, {{%4, %6}, {%3, %6}, {%2, %5}, {%1, %5}}, { {%4, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%3, [[4, 0], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%3, [[4, 0], [3, 0], [2, 0], [1, 0]]}, {%2, [[1, 0], [2, 0], [3, 0], [4, 0]]}, {%1, [[1, 0], [2, 0], [3, 0], [4, 0]]}}} %1 := [[3, 1], [1, 0], [2, 0]] %2 := [[2, 0], [3, 0], [1, 1]] %3 := [[2, 0], [1, 0], [3, 1]] %4 := [[1, 1], [3, 0], [2, 0]] %5 := [[2, 0], [1, 0], [4, 0], [3, 0]] %6 := [[3, 0], [4, 0], [1, 0], [2, 0]] %7 := [[3, 0], [1, 0], [4, 0], [2, 0]] %8 := [[2, 0], [4, 0], [1, 0], [3, 0]] "for patterns of lengths: ", [[3, 1], [4, 1]] There all together, 240, different equivalence classes For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 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, {{%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%2, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 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], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 15, 52 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [1, 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, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 24, 120 Using the scheme, the first, , 31, terms are [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, 8841761993739701954543616000000] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [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, { {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 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], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 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], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 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, { {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, has a scheme of depth , 5 here it is: {[[3, 1, 2], {[0, 0, 0, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 1, 3], {}, {1}, {3}], [[1, 3, 2], {}, {}, {3}], [[1, 4, 3, 2], {}, {3}, {4}], [[3, 5, 4, 1, 2], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[2, 5, 3, 1, 4], {[0, 0, 0, 0, 0, 0]}, {4}, {}], [[2, 4, 3, 1], {}, {}, {}], [[2, 3, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}], [[3, 2, 1], {}, {2}, {}], [[3, 5, 4, 2, 1], {}, {4}, {}], [[2, 1], {}, {}, {}], [[2, 4, 3, 1, 5], {}, {1, 2, 3}, {5}], [[1, 3, 2, 4], {}, {2}, {4}], [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 15, 52 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 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], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 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], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [1, 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, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 24, 120 Using the scheme, the first, , 31, terms are [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, 8841761993739701954543616000000] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [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], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 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], [3, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 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], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [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, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 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], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 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], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [1, 0, 0]}, {2}, {}]} 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], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 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], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 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], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 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], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 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], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 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], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[1, 0], [4, 0], [2, 0], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 1], [2, 0]]}, {%2, [[2, 1], [3, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 1], [2, 0], [4, 0]]}, {%1, [[2, 0], [4, 1], [3, 0], [1, 0]]}, {%1, [[3, 1], [2, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [2, 0], [1, 1], [3, 0]]}, {%1, [[4, 0], [1, 0], [3, 0], [2, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 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, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 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], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [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, { {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 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], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 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, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 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], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 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, { {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [1, 0, 0]}, {2}, {}]} 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 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], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 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], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [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], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 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, 0], [4, 1], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 1]]}, {%2, [[3, 1], [2, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [2, 0], [1, 1], [4, 0]]}, {%1, [[2, 0], [3, 0], [4, 1], [1, 0]]}, {%1, [[2, 1], [3, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [2, 0], [3, 1]]}, {%1, [[4, 0], [1, 1], [2, 0], [3, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 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], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [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], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [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, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 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], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 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, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%2, [[3, 1], [1, 0], [2, 0], [4, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[4, 0], [2, 0], [1, 0], [3, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 15, 52 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%1, [[1, 0], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 1], [4, 0]]}, {%2, [[2, 0], [4, 0], [3, 1], [1, 0]]}, {%2, [[3, 0], [2, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 1], [2, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 1], [4, 0], [2, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 0], [2, 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], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 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], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 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, [[2, 0], [1, 1], [4, 0], [3, 0]]}, {%2, [[2, 1], [1, 0], [4, 0], [3, 0]]}, {%2, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%2, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%1, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%1, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%1, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%1, [[3, 0], [4, 0], [1, 0], [2, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 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, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 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], [3, 0], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[1, 2], {[1, 0, 0]}, {}, {}], [[2, 3, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2, 3], {[1, 0, 0, 0]}, {2}, {}], [[1, 3, 2], {[0, 0, 1, 0], [1, 0, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [3, 0], [2, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [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], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 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, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 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, { {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 3 here it is: {[[1, 3, 2], {}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2, 3], {}, {2}, {3}], [[2, 3, 1], {}, {1}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {}, {}, {2}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 6, 24, 120 Using the scheme, the first, , 31, terms are [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, 8841761993739701954543616000000] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 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, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%2, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%2, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 0], [2, 1]]}, {%1, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%1, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 1], [1, 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, [[2, 0], [3, 0], [4, 1], [1, 0]]}, {%2, [[2, 1], [3, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 1], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 1]]}, {%1, [[1, 0], [4, 1], [3, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 1]]}, {%1, [[3, 0], [2, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [2, 0], [1, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 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], [3, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 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], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 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, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 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, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%2, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%2, [[3, 0], [1, 1], [4, 0], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%1, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%1, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%1, [[3, 0], [1, 0], [4, 0], [2, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [4, 0], [1, 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], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 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, [[2, 0], [4, 0], [3, 1], [1, 0]]}, {%2, [[3, 0], [2, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 1], [2, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 1], [4, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 1], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 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], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [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, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 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, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [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], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [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, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {2}], [[2, 3, 1], {[0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 0], [4, 1], [3, 0], [1, 0]]}, {%2, [[3, 1], [2, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 1], [3, 0]]}, {%1, [[1, 0], [3, 0], [4, 1], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 1]]}, {%1, [[2, 1], [3, 0], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 1], [2, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 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, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%2, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%1, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 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], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 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, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 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], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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, { {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 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, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%2, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%2, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [1, 0], [2, 0], [4, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 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, { {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 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], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 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], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 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], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 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, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%2, [[3, 0], [4, 0], [1, 0], [2, 1]]}, {%2, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%2, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%1, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%1, [[2, 1], [1, 0], [4, 0], [3, 0]]}, {%1, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%1, [[2, 0], [1, 1], [4, 0], [3, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 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, { {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 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, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [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, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 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, [[3, 0], [4, 1], [2, 0], [1, 0]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 1]]}, {%2, [[4, 0], [3, 0], [1, 1], [2, 0]]}, {%1, [[1, 0], [2, 0], [4, 1], [3, 0]]}, {%1, [[1, 0], [2, 0], [4, 0], [3, 1]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 0]]}, {%1, [[2, 1], [1, 0], [3, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 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], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 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], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 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, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 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, { {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [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, { {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 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], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 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, { {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 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, 1], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 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, 1], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 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, { {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 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, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 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], [3, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 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, 0], [2, 0], [4, 1], [3, 0]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 0]]}, {%1, [[2, 1], [1, 0], [3, 0], [4, 0]]}, {%2, [[3, 0], [4, 1], [2, 0], [1, 0]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 0]]}, {%2, [[4, 0], [3, 0], [1, 1], [2, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 1]]}, {%1, [[1, 0], [2, 0], [4, 0], [3, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [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, { {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 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, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 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], [3, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [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, { {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 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, { {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 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, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 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], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 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, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [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], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 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], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 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], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 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, { {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 0], [2, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 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, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 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], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 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], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 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], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 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, { {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {2}, {3}], [[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 1, 0]}, {}, {2}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 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], [3, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 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, { {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3}], [[1, 2, 3], {}, {2}, {3}], [[1, 2], {}, {}, {2}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 2, 5, 14, 42 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 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], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 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], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [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], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 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, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 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, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [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], [1, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [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], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [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, { {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 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], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 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, { {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 0], [1, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 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, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 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, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [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], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 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, { {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 0], [3, 1]]}} the member , {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 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], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [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], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 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], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 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, { {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 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], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] Out of a total of , 240, cases 229, were successful and , 11, failed Success Rate: , 0.954 Here are the failures {{{%4, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%4, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%3, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%3, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%1, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 0]]}}, { {%4, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%4, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 1], [1, 0], [2, 0], [4, 0]]}, {%3, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%4, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%4, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%4, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%3, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%2, [[3, 0], [4, 0], [1, 0], [2, 1]]}, {%2, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%1, [[2, 0], [1, 1], [4, 0], [3, 0]]}, {%1, [[2, 1], [1, 0], [4, 0], [3, 0]]}}, { {%4, [[4, 1], [1, 0], [2, 0], [3, 0]]}, {%3, [[3, 0], [2, 0], [1, 0], [4, 1]]}, {%2, [[2, 0], [3, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [4, 0], [3, 0], [2, 0]]}}, { {%4, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%4, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}}, { {%3, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%3, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%2, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%2, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%4, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%4, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[4, 1], [3, 0], [1, 0], [2, 0]]}}, { {%3, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%4, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%4, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%1, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [2, 0], [3, 0], [1, 0]]}}, { {%4, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%3, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%2, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 0]]}}} %1 := [[2, 0], [1, 0], [3, 1]] %2 := [[3, 1], [1, 0], [2, 0]] %3 := [[1, 1], [3, 0], [2, 0]] %4 := [[2, 0], [3, 0], [1, 1]] {{{%4, [[2, 0], [4, 1], [1, 0], [3, 0]]}, {%4, [[3, 1], [1, 0], [4, 0], [2, 0]]}, {%3, [[2, 0], [4, 0], [1, 0], [3, 1]]}, {%3, [[3, 0], [1, 0], [4, 1], [2, 0]]}, {%2, [[3, 0], [1, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [4, 0], [1, 1], [3, 0]]}, {%1, [[2, 1], [4, 0], [1, 0], [3, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 0]]}}, { {%4, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%4, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%3, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 0]]}}, { {%4, [[3, 1], [1, 0], [2, 0], [4, 0]]}, {%3, [[3, 0], [2, 0], [4, 1], [1, 0]]}, {%3, [[4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 0], [2, 1]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0]]}, {%4, [[1, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%3, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%2, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%2, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%4, [[1, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 0], [2, 0]]}}, { {%4, [[3, 0], [4, 1], [1, 0], [2, 0]]}, {%4, [[3, 1], [4, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [4, 1], [3, 0]]}, {%3, [[2, 0], [1, 0], [4, 0], [3, 1]]}, {%2, [[3, 0], [4, 0], [1, 0], [2, 1]]}, {%2, [[3, 0], [4, 0], [1, 1], [2, 0]]}, {%1, [[2, 0], [1, 1], [4, 0], [3, 0]]}, {%1, [[2, 1], [1, 0], [4, 0], [3, 0]]}}, { {%4, [[4, 1], [1, 0], [2, 0], [3, 0]]}, {%3, [[3, 0], [2, 0], [1, 0], [4, 1]]}, {%2, [[2, 0], [3, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [4, 0], [3, 0], [2, 0]]}}, { {%4, [[4, 1], [1, 0], [3, 0], [2, 0]]}, {%4, [[4, 1], [2, 0], [1, 0], [3, 0]]}, {%3, [[2, 0], [3, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 0], [2, 0], [4, 1]]}, {%2, [[2, 0], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 0]]}}, { {%3, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%3, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%2, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%2, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%4, [[1, 1], [2, 0], [4, 0], [3, 0]]}, {%4, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[4, 1], [3, 0], [1, 0], [2, 0]]}}, { {%3, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%3, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%2, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%2, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%4, [[1, 1], [3, 0], [2, 0], [4, 0]]}, {%4, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%1, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[4, 1], [2, 0], [3, 0], [1, 0]]}}, { {%4, [[4, 1], [2, 0], [3, 0], [1, 0]]}, {%3, [[1, 0], [3, 0], [2, 0], [4, 1]]}, {%2, [[4, 0], [2, 0], [3, 0], [1, 1]]}, {%1, [[1, 1], [3, 0], [2, 0], [4, 0]]}}, { {%4, [[4, 1], [3, 0], [1, 0], [2, 0]]}, {%3, [[2, 0], [1, 0], [3, 0], [4, 1]]}, {%2, [[3, 0], [4, 0], [2, 0], [1, 1]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 0]]}}} %1 := [[2, 0], [1, 0], [3, 1]] %2 := [[3, 1], [1, 0], [2, 0]] %3 := [[1, 1], [3, 0], [2, 0]] %4 := [[2, 0], [3, 0], [1, 1]] "for patterns of lengths: ", [[3, 1], [4, 2]] There all together, 364, different equivalence classes For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[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, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 1], [1, 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], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 1], [1, 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], [1, 0], [3, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 1], [4, 0], [1, 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], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[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], [1, 0], [3, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 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, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 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, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 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], [3, 0], [2, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [1, 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, 0], [2, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [1, 0], [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, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 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]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 0], [2, 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], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[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], [3, 0], [2, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[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], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [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], [3, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 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, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 0], [3, 1], [1, 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, 0], [3, 0], [2, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 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, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [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], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 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, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 1], [1, 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, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 0], [3, 1], [2, 1], [4, 0]] %2 := [[4, 0], [2, 1], [3, 1], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [4, 1], [3, 0], [1, 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, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 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, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[1, 0], [3, 1], [2, 0]], [[3, 0], [4, 0], [2, 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], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 1], [2, 0], [3, 0], [4, 1]] %2 := [[4, 1], [3, 0], [2, 0], [1, 1]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 0], [2, 1], [3, 1], [4, 0]] %2 := [[4, 0], [3, 1], [2, 1], [1, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 1], [3, 0], [2, 0], [1, 1]] %2 := [[1, 1], [2, 0], [3, 0], [4, 1]] the member , {[[1, 0], [3, 0], [2, 1]], [[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], [3, 0], [2, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [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, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 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, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 0], [3, 1], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 1], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[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]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [3, 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, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 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, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [2, 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, 0], [3, 0], [2, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 1], [2, 0], [3, 0], [1, 1]] %2 := [[1, 1], [3, 0], [2, 0], [4, 1]] the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 0], [4, 1], [1, 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, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [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, 0], [2, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}} %1 := [[4, 0], [2, 1], [3, 1], [1, 0]] %2 := [[1, 0], [3, 1], [2, 1], [4, 0]] the member , {[[1, 0], [3, 0], [2, 1]], [[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], [3, 0], [2, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 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, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 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]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 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, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 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, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [2, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [2, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [2, 1], [4, 1], [1, 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, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 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, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [2, 1], [4, 0], [1, 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, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 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], [2, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [2, 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], [3, 0], [2, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 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]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [1, 1], [2, 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, 0], [3, 0], [2, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 0], [4, 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], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [3, 0], [2, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, { {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 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, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 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]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [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]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 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]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 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, { {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 0], [2, 1], [1, 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, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 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], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 1], [1, 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, 0], [3, 0], [2, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 1], [3, 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, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 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]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[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, 0], [1, 0], [3, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[3, 1], [4, 1], [2, 0], [1, 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, 0], [3, 0], [2, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 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, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [3, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 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, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 0], [3, 1], [1, 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, 1], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[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, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 1], [1, 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, 1], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 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], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 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], [3, 1], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[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, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 0], [2, 1], [1, 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, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 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, 0], [3, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[4, 0], [3, 1], [2, 1], [1, 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, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[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], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 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, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 0], [4, 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], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [2, 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], [1, 0], [3, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 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, 0], [3, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 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], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 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], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 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], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 1], [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], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [2, 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], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1, 3], {}, {}, {3}], [[2, 1, 3, 4], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {3, 4}], [[3, 2, 1], {}, {2}, {3, 4}], [[3, 2, 4, 1], {}, {1, 2}, {4, 5}], [[2, 1, 4, 3], {}, {1, 2}, {4, 5}], [[2, 1], {}, {}, {2, 3}], [[3, 1, 4, 2], {}, {1, 2}, {4, 5}]} 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, { {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[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, {{%1, [[1, 1], [4, 1], [3, 0], [2, 0]]}, {%2, [[2, 1], [3, 0], [4, 0], [1, 1]]}, {%2, [[2, 0], [3, 0], [4, 1], [1, 1]]}, {%2, [[4, 1], [1, 0], [2, 0], [3, 1]]}, {%2, [[4, 1], [1, 1], [2, 0], [3, 0]]}, {%1, [[3, 1], [2, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [2, 0], [1, 1], [4, 1]]}, {%1, [[1, 1], [4, 0], [3, 0], [2, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [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, { {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 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, [[2, 1], [1, 0], [3, 0], [4, 1]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 1]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 1]]}, {%2, [[3, 0], [4, 1], [2, 0], [1, 1]]}, {%2, [[4, 1], [3, 0], [1, 0], [2, 1]]}, {%2, [[4, 1], [3, 0], [1, 1], [2, 0]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 1]]}, {%1, [[1, 1], [2, 0], [4, 1], [3, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%1, [[2, 1], [1, 0], [3, 1], [4, 0]]}, {%1, [[2, 0], [1, 1], [3, 1], [4, 0]]}, {%2, [[3, 1], [4, 0], [2, 1], [1, 0]]}, {%2, [[3, 0], [4, 1], [2, 1], [1, 0]]}, {%2, [[4, 0], [3, 1], [1, 1], [2, 0]]}, {%2, [[4, 0], [3, 1], [1, 0], [2, 1]]}, {%1, [[1, 0], [2, 1], [4, 1], [3, 0]]}, {%1, [[1, 0], [2, 1], [4, 0], [3, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 1], [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], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[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, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[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, { {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [2, 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, [[2, 1], [3, 0], [1, 0], [4, 1]]}, {%2, [[3, 0], [1, 1], [2, 0], [4, 1]]}, {%1, [[3, 1], [2, 0], [4, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 0], [2, 1]]}, {%1, [[4, 1], [2, 0], [1, 1], [3, 0]]}, {%2, [[1, 1], [3, 0], [4, 1], [2, 0]]}, {%2, [[1, 1], [4, 0], [2, 0], [3, 1]]}, {%1, [[2, 0], [4, 1], [3, 0], [1, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 1], [3, 0], [1, 1], [4, 0]]}, {%2, [[3, 1], [1, 1], [2, 0], [4, 0]]}, {%1, [[3, 1], [2, 0], [4, 1], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 0], [2, 1]]}, {%1, [[4, 0], [2, 0], [1, 1], [3, 1]]}, {%2, [[1, 0], [3, 0], [4, 1], [2, 1]]}, {%2, [[1, 0], [4, 1], [2, 0], [3, 1]]}, {%1, [[2, 1], [4, 1], [3, 0], [1, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [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], [1, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 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, [[2, 0], [3, 0], [1, 1], [4, 1]]}, {%2, [[3, 1], [1, 0], [2, 0], [4, 1]]}, {%1, [[3, 0], [2, 0], [4, 1], [1, 1]]}, {%1, [[4, 1], [1, 1], [3, 0], [2, 0]]}, {%1, [[4, 1], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 1], [3, 0], [4, 0], [2, 1]]}, {%2, [[1, 1], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 0], [1, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [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, {{%2, [[2, 0], [3, 1], [1, 1], [4, 0]]}, {%2, [[3, 1], [1, 0], [2, 1], [4, 0]]}, {%1, [[3, 0], [2, 1], [4, 1], [1, 0]]}, {%1, [[4, 0], [1, 1], [3, 1], [2, 0]]}, {%1, [[4, 0], [2, 1], [1, 0], [3, 1]]}, {%2, [[1, 0], [3, 1], [4, 0], [2, 1]]}, {%2, [[1, 0], [4, 1], [2, 1], [3, 0]]}, {%1, [[2, 1], [4, 0], [3, 1], [1, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [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, [[2, 0], [3, 1], [1, 0], [4, 1]]}, {%2, [[3, 0], [1, 0], [2, 1], [4, 1]]}, {%1, [[3, 0], [2, 1], [4, 0], [1, 1]]}, {%1, [[4, 1], [1, 0], [3, 1], [2, 0]]}, {%1, [[4, 1], [2, 1], [1, 0], [3, 0]]}, {%2, [[1, 1], [3, 1], [4, 0], [2, 0]]}, {%2, [[1, 1], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [4, 0], [3, 1], [1, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [2, 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, [[2, 1], [3, 1], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 1], [2, 1], [4, 0]]}, {%1, [[3, 1], [2, 1], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [3, 1], [2, 1]]}, {%1, [[4, 0], [2, 1], [1, 1], [3, 0]]}, {%2, [[1, 0], [3, 1], [4, 1], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 1], [3, 1]]}, {%1, [[2, 0], [4, 1], [3, 1], [1, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 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, { {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 0], [3, 1], [4, 1], [1, 0]]}, {%2, [[2, 1], [3, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [2, 1], [3, 1]]}, {%2, [[4, 0], [1, 1], [2, 1], [3, 0]]}, {%1, [[3, 0], [2, 1], [1, 1], [4, 0]]}, {%1, [[3, 1], [2, 1], [1, 0], [4, 0]]}, {%1, [[1, 0], [4, 0], [3, 1], [2, 1]]}, {%1, [[1, 0], [4, 1], [3, 1], [2, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[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, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 1], [4, 0], [1, 1], [3, 0]]}, {%2, [[2, 0], [4, 1], [1, 0], [3, 1]]}, {%2, [[3, 0], [1, 0], [4, 1], [2, 1]]}, {%2, [[3, 1], [1, 1], [4, 0], [2, 0]]}, {%1, [[3, 1], [1, 0], [4, 1], [2, 0]]}, {%1, [[3, 0], [1, 1], [4, 0], [2, 1]]}, {%1, [[2, 0], [4, 0], [1, 1], [3, 1]]}, {%1, [[2, 1], [4, 1], [1, 0], [3, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 0], [4, 0], [1, 1], [3, 1]]}, {%2, [[2, 1], [4, 1], [1, 0], [3, 0]]}, {%2, [[3, 1], [1, 0], [4, 1], [2, 0]]}, {%2, [[3, 0], [1, 1], [4, 0], [2, 1]]}, {%1, [[3, 0], [1, 0], [4, 1], [2, 1]]}, {%1, [[3, 1], [1, 1], [4, 0], [2, 0]]}, {%1, [[2, 1], [4, 0], [1, 1], [3, 0]]}, {%1, [[2, 0], [4, 1], [1, 0], [3, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 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, [[2, 1], [4, 0], [3, 0], [1, 1]]}, {%2, [[3, 0], [2, 0], [4, 1], [1, 1]]}, {%2, [[4, 1], [1, 1], [3, 0], [2, 0]]}, {%2, [[4, 1], [2, 0], [1, 0], [3, 1]]}, {%1, [[1, 1], [3, 0], [4, 0], [2, 1]]}, {%1, [[1, 1], [4, 1], [2, 0], [3, 0]]}, {%1, [[2, 0], [3, 0], [1, 1], [4, 1]]}, {%1, [[3, 1], [1, 0], [2, 0], [4, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 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, [[2, 1], [4, 0], [3, 1], [1, 0]]}, {%2, [[3, 0], [2, 1], [4, 1], [1, 0]]}, {%2, [[4, 0], [1, 1], [3, 1], [2, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 1]]}, {%1, [[1, 0], [3, 1], [4, 0], [2, 1]]}, {%1, [[1, 0], [4, 1], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 1], [4, 0]]}, {%1, [[3, 1], [1, 0], [2, 1], [4, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 0], [4, 0], [3, 1], [1, 1]]}, {%2, [[3, 0], [2, 1], [4, 0], [1, 1]]}, {%2, [[4, 1], [1, 0], [3, 1], [2, 0]]}, {%2, [[4, 1], [2, 1], [1, 0], [3, 0]]}, {%1, [[1, 1], [3, 1], [4, 0], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 0], [4, 1]]}, {%1, [[3, 0], [1, 0], [2, 1], [4, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 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, [[2, 0], [4, 1], [3, 1], [1, 0]]}, {%2, [[3, 1], [2, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 1], [2, 1]]}, {%2, [[4, 0], [2, 1], [1, 1], [3, 0]]}, {%1, [[1, 0], [3, 1], [4, 1], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 1], [3, 1]]}, {%1, [[2, 1], [3, 1], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 1], [2, 1], [4, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[2, 0], [4, 1], [3, 0], [1, 1]]}, {%2, [[3, 1], [2, 0], [4, 0], [1, 1]]}, {%2, [[4, 1], [1, 0], [3, 0], [2, 1]]}, {%2, [[4, 1], [2, 0], [1, 1], [3, 0]]}, {%1, [[1, 1], [3, 0], [4, 1], [2, 0]]}, {%1, [[1, 1], [4, 0], [2, 0], [3, 1]]}, {%1, [[2, 1], [3, 0], [1, 0], [4, 1]]}, {%1, [[3, 0], [1, 1], [2, 0], [4, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 0], [4, 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, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 1], [3, 1], [2, 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, [[2, 1], [4, 1], [3, 0], [1, 0]]}, {%2, [[3, 1], [2, 0], [4, 1], [1, 0]]}, {%2, [[4, 0], [1, 1], [3, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 1], [3, 1]]}, {%1, [[3, 1], [1, 1], [2, 0], [4, 0]]}, {%1, [[1, 0], [3, 0], [4, 1], [2, 1]]}, {%1, [[1, 0], [4, 1], [2, 0], [3, 1]]}, {%1, [[2, 1], [3, 0], [1, 1], [4, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[3, 1], [2, 0], [1, 0], [4, 1]]}, {%2, [[3, 0], [2, 0], [1, 1], [4, 1]]}, {%1, [[4, 1], [1, 0], [2, 0], [3, 1]]}, {%1, [[4, 1], [1, 1], [2, 0], [3, 0]]}, {%2, [[1, 1], [4, 0], [3, 0], [2, 1]]}, {%2, [[1, 1], [4, 1], [3, 0], [2, 0]]}, {%1, [[2, 1], [3, 0], [4, 0], [1, 1]]}, {%1, [[2, 0], [3, 0], [4, 1], [1, 1]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[3, 1], [2, 0], [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], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 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, [[3, 0], [2, 1], [1, 1], [4, 0]]}, {%2, [[3, 1], [2, 1], [1, 0], [4, 0]]}, {%1, [[4, 0], [1, 0], [2, 1], [3, 1]]}, {%1, [[4, 0], [1, 1], [2, 1], [3, 0]]}, {%2, [[1, 0], [4, 0], [3, 1], [2, 1]]}, {%2, [[1, 0], [4, 1], [3, 1], [2, 0]]}, {%1, [[2, 0], [3, 1], [4, 1], [1, 0]]}, {%1, [[2, 1], [3, 1], [4, 0], [1, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 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, { {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[4, 1], [2, 0], [3, 1], [1, 0]]}, {%2, [[4, 0], [2, 0], [3, 1], [1, 1]]}, {%2, [[4, 0], [2, 1], [3, 0], [1, 1]]}, {%2, [[4, 1], [2, 1], [3, 0], [1, 0]]}, {%1, [[1, 1], [3, 0], [2, 1], [4, 0]]}, {%1, [[1, 0], [3, 0], [2, 1], [4, 1]]}, {%1, [[1, 0], [3, 1], [2, 0], [4, 1]]}, {%1, [[1, 1], [3, 1], [2, 0], [4, 0]]}} %1 := [[3, 0], [2, 1], [1, 0]] %2 := [[1, 0], [2, 1], [3, 0]] the member , {[[1, 0], [2, 1], [3, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 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, { {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[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, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 0], [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], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[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, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 0], [1, 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], [2, 1], [3, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 0]], [[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, { {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 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, [[3, 1], [4, 0], [2, 0], [1, 1]]}, {%2, [[3, 0], [4, 1], [2, 0], [1, 1]]}, {%2, [[4, 1], [3, 0], [1, 0], [2, 1]]}, {%2, [[4, 1], [3, 0], [1, 1], [2, 0]]}, {%1, [[1, 1], [2, 0], [4, 0], [3, 1]]}, {%1, [[1, 1], [2, 0], [4, 1], [3, 0]]}, {%1, [[2, 1], [1, 0], [3, 0], [4, 1]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 1]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 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], [3, 1], [1, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, {{%2, [[3, 1], [4, 0], [2, 1], [1, 0]]}, {%2, [[3, 0], [4, 1], [2, 1], [1, 0]]}, {%2, [[4, 0], [3, 1], [1, 1], [2, 0]]}, {%2, [[4, 0], [3, 1], [1, 0], [2, 1]]}, {%1, [[1, 0], [2, 1], [4, 1], [3, 0]]}, {%1, [[1, 0], [2, 1], [4, 0], [3, 1]]}, {%1, [[2, 1], [1, 0], [3, 1], [4, 0]]}, {%1, [[2, 0], [1, 1], [3, 1], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 0], [2, 1], [1, 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, { {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 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, { {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 1]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 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, { {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[1, 0], [2, 1], [3, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}} the member , {[[3, 0], [2, 1], [1, 0]], [[4, 0], [2, 1], [3, 1], [1, 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, [[4, 1], [2, 0], [3, 1], [1, 0]]}, {%2, [[4, 0], [2, 0], [3, 1], [1, 1]]}, {%2, [[4, 0], [2, 1], [3, 0], [1, 1]]}, {%2, [[4, 1], [2, 1], [3, 0], [1, 0]]}, {%1, [[1, 1], [3, 0], [2, 1], [4, 0]]}, {%1, [[1, 0], [3, 0], [2, 1], [4, 1]]}, {%1, [[1, 0], [3, 1], [2, 0], [4, 1]]}, {%1, [[1, 1], [3, 1], [2, 0], [4, 0]]}} %1 := [[1, 0], [2, 1], [3, 0]] %2 := [[3, 0], [2, 1], [1, 0]] the member , {[[3, 0], [2, 1], [1, 0]], [[4, 1], [2, 0], [3, 1], [1, 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, 1], [1, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[1, 0], [3, 0], [2, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [1, 1], [3, 0], [2, 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, 1], [1, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[1, 0], [3, 1], [2, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[2, 1], [1, 0], [3, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[2, 0], [1, 1], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 0], [1, 1], [2, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[2, 1], [3, 0], [1, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[2, 0], [3, 1], [1, 0]], [[4, 0], [2, 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, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [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, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [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]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [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, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 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, { {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [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], [2, 0], [3, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [1, 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], [2, 0], [3, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [2, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [2, 0], [3, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 0], [2, 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], [2, 0], [3, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [4, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [4, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [1, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [4, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 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, { {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [4, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 1], [1, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [1, 1], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [1, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [4, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [4, 1], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [1, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [4, 1], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 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, { {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 1], [4, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 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, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 1], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [4, 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], [2, 0], [3, 1]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [2, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, 0], [3, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [2, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [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], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [2, 1], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [2, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 1], [2, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [2, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [2, 0], [3, 1]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [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, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [2, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, 0], [2, 0], [3, 1]], [[1, 1], [2, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 1], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 1], [3, 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, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [1, 1], [2, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 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, { {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 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, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [1, 0], [2, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [2, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [2, 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, 0], [2, 0], [3, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [3, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [2, 0], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [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], [2, 0], [3, 1]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [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], [3, 1]], [[1, 0], [3, 0], [2, 1], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [2, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 0], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [3, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [2, 1], [3, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [2, 0], [3, 1]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [3, 1], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [2, 1], [3, 1], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [3, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 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, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [2, 0], [3, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [2, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [3, 0], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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], [2, 0], [3, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 1], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [2, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [3, 0], [2, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 1], [1, 0], [2, 1], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 1], [4, 0], [3, 1], [2, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [1, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [1, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [4, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [1, 0], [2, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 1], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 1], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 1], [4, 1], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 0], [3, 1], [2, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 1], [3, 1], [2, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 0], [2, 1], [1, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 1], [1, 0], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 1], [1, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [2, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 0], [2, 1], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[1, 0], [4, 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], [2, 0], [3, 1]], [[1, 0], [4, 1], [3, 0], [2, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[3, 1], [2, 0], [1, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[2, 1], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[4, 0], [1, 1], [2, 0], [3, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [3, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [3, 0], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [4, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 0], [4, 1], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [1, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [2, 0], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [2, 0], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 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, 0], [3, 1]], [[3, 0], [2, 1], [4, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 1], [2, 1], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 0], [3, 1], [1, 0], [4, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 1], [3, 1], [4, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 1], [4, 0], [2, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 1], [1, 0], [3, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 0], [2, 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], [2, 0], [3, 1]], [[2, 1], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [3, 1], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [2, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [2, 1], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [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], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 1], [2, 1], [4, 0], [3, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 1], [3, 1], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [2, 1], [1, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 1], [3, 0], [4, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 1], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 1], [1, 1], [3, 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, 0], [2, 0], [3, 1]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 0], [4, 0], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [1, 1], [4, 1], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 1], [1, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 0], [1, 0], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [4, 1], [1, 1], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[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, { {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 1], [4, 1], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [4, 1], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 1], [4, 0], [1, 1], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 1], [1, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 1], [1, 0], [4, 1], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [1, 1], [4, 0], [3, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1]], [[4, 0], [2, 1], [1, 1], [3, 0]]}, {[[1, 1], [2, 0], [3, 0]], [[2, 0], [4, 1], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[2, 1], [3, 1], [1, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 1]], [[1, 0], [3, 1], [4, 1], [2, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[3, 0], [1, 1], [2, 1], [4, 0]]}, {[[3, 1], [2, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 1]]}, {[[1, 1], [2, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 1]]}} the member , {[[1, 0], [2, 0], [3, 1]], [[3, 1], [2, 1], [4, 0], [1, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [4, 1], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[3, 0], [4, 0], [1, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[2, 0], [1, 0], [4, 1], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [1, 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, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [1, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 0], [1, 1], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 0], [4, 1], [3, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [4, 0], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 0], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [1, 1], [3, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [4, 1], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 0], [2, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[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, { {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 1], [2, 0], [4, 1], [1, 0]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [1, 1], [3, 0], [2, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 0], [4, 1], [2, 0], [3, 1]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 1], [3, 0], [1, 1], [4, 0]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, {[[2, 0], [1, 0], [3, 1]], [[3, 1], [1, 0], [2, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[2, 1], [4, 0], [3, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [4, 1], [1, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [2, 0], [1, 0], [3, 1]]}, {[[3, 1], [1, 0], [2, 0]], [[4, 1], [1, 1], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [3, 0], [4, 0], [2, 1]]}, {[[1, 1], [3, 0], [2, 0]], [[1, 1], [4, 1], [2, 0], [3, 0]]}} the member , {[[2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 1], [4, 1]]}, has a scheme of depth , 1 here it is: {[[], {}, {}, {}], [[1], {[0, 1], [1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 0, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 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] Out of a total of , 364, cases 355, were successful and , 9, failed Success Rate: , 0.975 Here are the failures {{{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}}, { {%6, [[1, 1], [2, 1], [4, 0], [3, 0]]}, {%5, [[4, 1], [3, 1], [1, 0], [2, 0]]}, {%4, [[3, 0], [4, 0], [2, 1], [1, 1]]}, {%3, [[2, 0], [1, 0], [3, 1], [4, 1]]}}, {{%6, %1}, {%5, %2}, {%4, %2}, {%3, %1}}, { {%6, [[1, 1], [3, 0], [4, 1], [2, 0]]}, {%6, [[1, 1], [4, 0], [2, 0], [3, 1]]}, {%5, [[4, 1], [1, 0], [3, 0], [2, 1]]}, {%5, [[4, 1], [2, 0], [1, 1], [3, 0]]}, {%4, [[2, 0], [4, 1], [3, 0], [1, 1]]}, {%4, [[3, 1], [2, 0], [4, 0], [1, 1]]}, {%3, [[2, 1], [3, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 1], [2, 0], [4, 1]]}}, { {%6, [[1, 1], [3, 1], [4, 0], [2, 0]]}, {%6, [[1, 1], [4, 0], [2, 1], [3, 0]]}, {%5, [[4, 1], [1, 0], [3, 1], [2, 0]]}, {%5, [[4, 1], [2, 1], [1, 0], [3, 0]]}, {%4, [[2, 0], [4, 0], [3, 1], [1, 1]]}, {%4, [[3, 0], [2, 1], [4, 0], [1, 1]]}, {%3, [[2, 0], [3, 1], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 0], [2, 1], [4, 1]]}}, { {%6, [[1, 1], [4, 0], [3, 0], [2, 1]]}, {%6, [[1, 1], [4, 1], [3, 0], [2, 0]]}, {%5, [[4, 1], [1, 0], [2, 0], [3, 1]]}, {%5, [[4, 1], [1, 1], [2, 0], [3, 0]]}, {%4, [[2, 1], [3, 0], [4, 0], [1, 1]]}, {%4, [[2, 0], [3, 0], [4, 1], [1, 1]]}, {%3, [[3, 1], [2, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [2, 0], [1, 1], [4, 1]]}}, { {%6, [[1, 1], [4, 0], [3, 1], [2, 0]]}, {%5, [[4, 1], [1, 0], [2, 1], [3, 0]]}, {%4, [[2, 0], [3, 1], [4, 0], [1, 1]]}, {%3, [[3, 0], [2, 1], [1, 0], [4, 1]]}}, {{[[1, 0], [2, 1], [3, 0]], %2}, {[[3, 0], [2, 1], [1, 0]], %1}}, { {[[1, 0], [2, 0], [3, 1]], %2}, {[[1, 1], [2, 0], [3, 0]], %2}, {[[3, 0], [2, 0], [1, 1]], %1}, {[[3, 1], [2, 0], [1, 0]], %1}}} %1 := [[1, 1], [3, 0], [2, 0], [4, 1]] %2 := [[4, 1], [2, 0], [3, 0], [1, 1]] %3 := [[1, 1], [3, 0], [2, 0]] %4 := [[3, 1], [1, 0], [2, 0]] %5 := [[2, 0], [3, 0], [1, 1]] %6 := [[2, 0], [1, 0], [3, 1]] {{{[[1, 0], [3, 0], [2, 1]], %2}, {[[2, 0], [3, 1], [1, 0]], %1}, {[[1, 0], [3, 1], [2, 0]], %2}, {[[2, 1], [1, 0], [3, 0]], %2}, {[[3, 0], [1, 1], [2, 0]], %1}, {[[2, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 0]], %1}}, { {%6, [[1, 1], [2, 1], [4, 0], [3, 0]]}, {%5, [[4, 1], [3, 1], [1, 0], [2, 0]]}, {%4, [[3, 0], [4, 0], [2, 1], [1, 1]]}, {%3, [[2, 0], [1, 0], [3, 1], [4, 1]]}}, {{%6, %1}, {%5, %2}, {%4, %2}, {%3, %1}}, { {%6, [[1, 1], [3, 0], [4, 1], [2, 0]]}, {%6, [[1, 1], [4, 0], [2, 0], [3, 1]]}, {%5, [[4, 1], [1, 0], [3, 0], [2, 1]]}, {%5, [[4, 1], [2, 0], [1, 1], [3, 0]]}, {%4, [[2, 0], [4, 1], [3, 0], [1, 1]]}, {%4, [[3, 1], [2, 0], [4, 0], [1, 1]]}, {%3, [[2, 1], [3, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 1], [2, 0], [4, 1]]}}, { {%6, [[1, 1], [3, 1], [4, 0], [2, 0]]}, {%6, [[1, 1], [4, 0], [2, 1], [3, 0]]}, {%5, [[4, 1], [1, 0], [3, 1], [2, 0]]}, {%5, [[4, 1], [2, 1], [1, 0], [3, 0]]}, {%4, [[2, 0], [4, 0], [3, 1], [1, 1]]}, {%4, [[3, 0], [2, 1], [4, 0], [1, 1]]}, {%3, [[2, 0], [3, 1], [1, 0], [4, 1]]}, {%3, [[3, 0], [1, 0], [2, 1], [4, 1]]}}, { {%6, [[1, 1], [4, 0], [3, 0], [2, 1]]}, {%6, [[1, 1], [4, 1], [3, 0], [2, 0]]}, {%5, [[4, 1], [1, 0], [2, 0], [3, 1]]}, {%5, [[4, 1], [1, 1], [2, 0], [3, 0]]}, {%4, [[2, 1], [3, 0], [4, 0], [1, 1]]}, {%4, [[2, 0], [3, 0], [4, 1], [1, 1]]}, {%3, [[3, 1], [2, 0], [1, 0], [4, 1]]}, {%3, [[3, 0], [2, 0], [1, 1], [4, 1]]}}, { {%6, [[1, 1], [4, 0], [3, 1], [2, 0]]}, {%5, [[4, 1], [1, 0], [2, 1], [3, 0]]}, {%4, [[2, 0], [3, 1], [4, 0], [1, 1]]}, {%3, [[3, 0], [2, 1], [1, 0], [4, 1]]}}, {{[[1, 0], [2, 1], [3, 0]], %2}, {[[3, 0], [2, 1], [1, 0]], %1}}, { {[[1, 0], [2, 0], [3, 1]], %2}, {[[1, 1], [2, 0], [3, 0]], %2}, {[[3, 0], [2, 0], [1, 1]], %1}, {[[3, 1], [2, 0], [1, 0]], %1}}} %1 := [[1, 1], [3, 0], [2, 0], [4, 1]] %2 := [[4, 1], [2, 0], [3, 0], [1, 1]] %3 := [[1, 1], [3, 0], [2, 0]] %4 := [[3, 1], [1, 0], [2, 0]] %5 := [[2, 0], [3, 0], [1, 1]] %6 := [[2, 0], [1, 0], [3, 1]] "for patterns of lengths: ", [[3, 0], [4, 1]] There all together, 88, different equivalence classes For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[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, 0], [1, 0], [2, 0]], [[4, 0], [1, 1], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[4, 0], [1, 0], [2, 0], [3, 1]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [4, 0], [3, 0], [2, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 1], [2, 0], [1, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 1], [3, 0], [4, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[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], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[4, 0], [2, 1], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 1], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [3, 1], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [2, 1], [4, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[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, 0], [1, 0], [2, 0]], [[4, 0], [1, 0], [3, 0], [2, 1]]}, {[[3, 0], [1, 0], [2, 0]], [[4, 0], [2, 0], [1, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [4, 0], [2, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 1], [3, 0], [1, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 1], [2, 0], [4, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[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, 0], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 0], [2, 1]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [4, 0], [3, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [1, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 1], [1, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 1], [4, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [4, 1], [2, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [1, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[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, { {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}} the member , {[[2, 0], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[0, 0, 1]}, {2}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}} the member , {[[3, 0], [1, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[1, 0], [3, 0], [2, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1, 3], {[1, 0, 0, 0]}, {1}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 1, 0, 0], [1, 0, 0, 0]}, {}, {3}], [[1, 2], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [[1, 2, 3], {}, {2}, {}], [[3, 1, 2], {[0, 1, 0, 0], [1, 0, 0, 0]}, {2}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {1}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {3}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [ [1, 4, 2, 3], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}, {4} ], [[2, 3, 1, 4], {[1, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}, {}], [ [2, 4, 1, 3], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}, {4} ]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 18, 47 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 18, 47, 138, 436, 1438, 4871, 16806, 58797, 208024, 742913, 2674454, 9694860, 35357686, 129644807, 477638718, 1767263209, 6564120440, 24466267041, 91482563662, 343059613673, 1289904147348, 4861946401477, 18367353072178, 69533550916031, 263747951750388, 1002242216651397] For the equivalence class of patterns, {{[[1, 1], [3, 0], [4, 0], [2, 0]], %2}, {[[1, 1], [4, 0], [2, 0], [3, 0]], %2}, {[[2, 0], [3, 0], [1, 0], [4, 1]], %2}, {[[3, 0], [1, 0], [2, 0], [4, 1]], %2}, {[[2, 0], [4, 0], [3, 0], [1, 1]], %1}, {[[3, 0], [2, 0], [4, 0], [1, 1]], %1}, {[[4, 1], [1, 0], [3, 0], [2, 0]], %1}, {[[4, 1], [2, 0], [1, 0], [3, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [3, 0], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}, {3}], [[1, 2], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}], [[1, 2, 3], {}, {1}, {}], [[1, 3, 2], {[0, 1, 0, 0], [1, 0, 0, 0]}, {1}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {3}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {3}, {4}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0]}, {3}, {}], [ [2, 4, 1, 3], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}, {4} ]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 9, 23, 65 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, 290512, 1033412, 3707852, 13402697, 48760367, 178405157, 656043857, 2423307047, 8987427467, 33453694487, 124936258127, 467995871777, 1757900019101, 6619846420553, 24987199492705, 94520750408709, 358268702159069, 1360510918810437] For the equivalence class of patterns, {{[[1, 0], [4, 1], [2, 0], [3, 0]], %2}, {[[1, 0], [3, 0], [4, 0], [2, 1]], %2}, {[[2, 0], [3, 0], [1, 1], [4, 0]], %2}, {[[3, 1], [1, 0], [2, 0], [4, 0]], %2}, {[[2, 1], [4, 0], [3, 0], [1, 0]], %1}, {[[3, 0], [2, 0], [4, 1], [1, 0]], %1}, {[[4, 0], [1, 1], [3, 0], [2, 0]], %1}, {[[4, 0], [2, 0], [1, 0], [3, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[1, 0], [3, 0], [4, 0], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 2], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}, {}], [[1, 3, 4, 2], %2, {1}, {}], [[2, 1, 4, 3], %2, {1}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[3, 1, 4, 2], %2, {1}, {}], [[2, 3, 4, 1], %1, {4}, {4}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 1, 3], {[1, 0, 0, 0]}, {}, {}], [[2, 1, 3, 4], %1, {2}, {4}], [[2, 4, 1, 3], %2, {1}, {}], [[3, 4, 1, 2], %2, {1}, {}], [[2, 3, 1, 4], %1, {3}, {4}], [[1, 3, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2, 3], {[0, 0, 1, 0], [0, 0, 0, 1]}, {}, {3}], [[3, 1, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} %1 := {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]} %2 := {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 5, 3, 0 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 5, 3, 0, 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, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [2, 0], [1, 0], [4, 1]], [[3, 0], [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, 0], [1, 0], [4, 1], [3, 0]], %2}, {[[2, 0], [1, 0], [4, 0], [3, 1]], %2}, {[[2, 1], [1, 0], [4, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [4, 0], [3, 0]], %2}, {[[3, 0], [4, 1], [1, 0], [2, 0]], %1}, {[[3, 0], [4, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [4, 0], [1, 0], [2, 1]], %1}, {[[3, 1], [4, 0], [1, 0], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [1, 1], [4, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, {{[[2, 0], [4, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [4, 0], [1, 1], [3, 0]], %2}, {[[3, 0], [1, 0], [4, 0], [2, 1]], %2}, {[[3, 1], [1, 0], [4, 0], [2, 0]], %2}, {[[2, 0], [4, 0], [1, 0], [3, 1]], %1}, {[[2, 1], [4, 0], [1, 0], [3, 0]], %1}, {[[3, 0], [1, 0], [4, 1], [2, 0]], %1}, {[[3, 0], [1, 1], [4, 0], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [4, 1], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 0, 1], [1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 0], [3, 0], [4, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 0], [4, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 5 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {}, {3}], [[1, 2], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[1, 0, 0, 0]}, {}, {}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 4, 1, 3], { [0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[3, 1, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [ [3, 4, 1, 5, 2], {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}, {4}], [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[1, 2, 3, 4], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {2}, {4}], [[2, 3, 1, 5, 4], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[3, 4, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {3}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 5, 4, 4 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4] For the equivalence class of patterns, {{[[2, 0], [4, 0], [3, 0], [1, 1]], %2}, {[[3, 0], [2, 0], [4, 0], [1, 1]], %2}, {[[4, 1], [1, 0], [3, 0], [2, 0]], %2}, {[[4, 1], [2, 0], [1, 0], [3, 0]], %2}, {[[1, 1], [3, 0], [4, 0], [2, 0]], %1}, {[[1, 1], [4, 0], [2, 0], [3, 0]], %1}, {[[2, 0], [3, 0], [1, 0], [4, 1]], %1}, {[[3, 0], [1, 0], [2, 0], [4, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [4, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, {{[[2, 1], [4, 0], [3, 0], [1, 0]], %2}, {[[3, 0], [2, 0], [4, 1], [1, 0]], %2}, {[[4, 0], [1, 1], [3, 0], [2, 0]], %2}, {[[4, 0], [2, 0], [1, 0], [3, 1]], %2}, {[[1, 0], [4, 1], [2, 0], [3, 0]], %1}, {[[1, 0], [3, 0], [4, 0], [2, 1]], %1}, {[[2, 0], [3, 0], [1, 1], [4, 0]], %1}, {[[3, 1], [1, 0], [2, 0], [4, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [4, 1], [1, 0]], [[3, 0], [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, 1], [1, 0], [2, 0]], %1}, {[[3, 0], [4, 0], [1, 1], [2, 0]], %1}, {[[3, 0], [4, 0], [1, 0], [2, 1]], %1}, {[[2, 0], [1, 0], [4, 1], [3, 0]], %2}, {[[2, 0], [1, 0], [4, 0], [3, 1]], %2}, {[[2, 1], [1, 0], [4, 0], [3, 0]], %2}, {[[2, 0], [1, 1], [4, 0], [3, 0]], %2}, {[[3, 1], [4, 0], [1, 0], [2, 0]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[3, 0], [4, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [4, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [4, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[4, 0], [2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0], [4, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[4, 0], [2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [ [1, 3, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[3, 1, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {}], [[2, 3, 1], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 4, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 4, 0, 0, 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], [2, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 1, 4, 3], %1, {1}, {}], [[3, 2, 4, 1], {[0, 0, 0, 0, 0]}, {1}, {}], [[3, 1, 4, 2], %1, {1}, {}], [[2, 4, 1, 3], %1, {1}, {}], [[3, 4, 1, 2], %1, {1}, {}], [[1, 3, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [ [3, 1, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[1, 0, 0, 0], [0, 0, 0, 1]}, {}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {}, {}], [[1, 2], {[0, 0, 1]}, {}, {}]} %1 := {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 4, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 4, 0, 0, 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, 0], [2, 0], [4, 1], [3, 0]]}, {%2, [[1, 0], [2, 0], [4, 0], [3, 1]]}, {%2, [[2, 0], [1, 1], [3, 0], [4, 0]]}, {%2, [[2, 1], [1, 0], [3, 0], [4, 0]]}, {%1, [[3, 0], [4, 1], [2, 0], [1, 0]]}, {%1, [[3, 1], [4, 0], [2, 0], [1, 0]]}, {%1, [[4, 0], [3, 0], [1, 1], [2, 0]]}, {%1, [[4, 0], [3, 0], [1, 0], [2, 1]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [3, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [ [1, 3, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[3, 1, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {}], [[2, 3, 1], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 4, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 4, 0, 0, 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], [2, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {}, {}], [ [1, 3, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[3, 1, 2], {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[2, 1, 3], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}], [[1, 2], {[0, 0, 1]}, {}, {}], [[2, 3, 1], {[1, 0, 0, 0], [0, 0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 4, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 4, 0, 0, 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, 0], [3, 0], [4, 1], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 0], [3, 1]]}, {%2, [[2, 1], [3, 0], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 1], [2, 0], [4, 0]]}, {%1, [[2, 0], [4, 1], [3, 0], [1, 0]]}, {%1, [[3, 1], [2, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [3, 0], [2, 1]]}, {%1, [[4, 0], [2, 0], [1, 1], [3, 0]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [3, 0], [4, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, {{%2, [[1, 0], [3, 1], [4, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [2, 1], [3, 0]]}, {%2, [[2, 0], [3, 1], [1, 0], [4, 0]]}, {%2, [[3, 0], [1, 0], [2, 1], [4, 0]]}, {%1, [[2, 0], [4, 0], [3, 1], [1, 0]]}, {%1, [[3, 0], [2, 1], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 0], [3, 1], [2, 0]]}, {%1, [[4, 0], [2, 1], [1, 0], [3, 0]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [3, 1], [4, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, {{%2, [[1, 0], [4, 1], [3, 0], [2, 0]]}, {%2, [[1, 0], [4, 0], [3, 0], [2, 1]]}, {%2, [[3, 0], [2, 0], [1, 1], [4, 0]]}, {%2, [[3, 1], [2, 0], [1, 0], [4, 0]]}, {%1, [[2, 0], [3, 0], [4, 1], [1, 0]]}, {%1, [[2, 1], [3, 0], [4, 0], [1, 0]]}, {%1, [[4, 0], [1, 1], [2, 0], [3, 0]]}, {%1, [[4, 0], [1, 0], [2, 0], [3, 1]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[1, 0], [4, 1], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, {{%2, [[2, 0], [3, 0], [4, 1], [1, 0]]}, {%2, [[2, 1], [3, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 1], [2, 0], [3, 0]]}, {%2, [[4, 0], [1, 0], [2, 0], [3, 1]]}, {%1, [[1, 0], [4, 1], [3, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [3, 0], [2, 1]]}, {%1, [[3, 0], [2, 0], [1, 1], [4, 0]]}, {%1, [[3, 1], [2, 0], [1, 0], [4, 0]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[2, 0], [3, 0], [4, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [4, 0], [3, 1], [2, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[3, 0], [2, 1], [1, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[2, 0], [3, 1], [4, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, {{%2, [[2, 0], [4, 0], [3, 1], [1, 0]]}, {%2, [[3, 0], [2, 1], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 1], [2, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 0]]}, {%1, [[1, 0], [3, 1], [4, 0], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 1], [3, 0]]}, {%1, [[2, 0], [3, 1], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 0], [2, 1], [4, 0]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[2, 0], [4, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, {{%2, [[2, 0], [4, 1], [3, 0], [1, 0]]}, {%2, [[3, 1], [2, 0], [4, 0], [1, 0]]}, {%2, [[4, 0], [1, 0], [3, 0], [2, 1]]}, {%2, [[4, 0], [2, 0], [1, 1], [3, 0]]}, {%1, [[1, 0], [3, 0], [4, 1], [2, 0]]}, {%1, [[1, 0], [4, 0], [2, 0], [3, 1]]}, {%1, [[2, 1], [3, 0], [1, 0], [4, 0]]}, {%1, [[3, 0], [1, 1], [2, 0], [4, 0]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[2, 0], [4, 1], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[4, 0], [3, 1], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [2, 1], [4, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 1], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[3, 0], [4, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}], [[2, 1], {[1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, {{%2, [[3, 0], [4, 1], [2, 0], [1, 0]]}, {%2, [[3, 1], [4, 0], [2, 0], [1, 0]]}, {%2, [[4, 0], [3, 0], [1, 1], [2, 0]]}, {%2, [[4, 0], [3, 0], [1, 0], [2, 1]]}, {%1, [[1, 0], [2, 0], [4, 1], [3, 0]]}, {%1, [[1, 0], [2, 0], [4, 0], [3, 1]]}, {%1, [[2, 0], [1, 1], [3, 0], [4, 0]]}, {%1, [[2, 1], [1, 0], [3, 0], [4, 0]]}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 0], [2, 0], [1, 0]], [[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], [2, 0], [1, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[4, 0], [2, 0], [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], [2, 0], [1, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [2, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}], [[1, 2], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {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, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [4, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [4, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 0], [1, 0], [4, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [4, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 0], [1, 0], [3, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 1], [1, 0], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 1], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {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], [3, 0], [1, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [4, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {1}, {}], [[1, 2], {[0, 1, 0]}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 9, 21, 51 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 25669818476, 73007772802, 208023278209, 593742784829, 1697385471211] For the equivalence class of patterns, { {[[2, 0], [3, 0], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [3, 0], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {}, {3}], [[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [ [2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}, {}] , [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {3}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {3}, {4}], [[3, 4, 2, 1], {[0, 0, 0, 1, 0]}, {3}, {4}], [[1, 2], {[0, 1, 0]}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 9, 23, 65 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, 290512, 1033412, 3707852, 13402697, 48760367, 178405157, 656043857, 2423307047, 8987427467, 33453694487, 124936258127, 467995871777, 1757900019101, 6619846420553, 24987199492705, 94520750408709, 358268702159069, 1360510918810437] For the equivalence class of patterns, { {[[2, 0], [4, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 0], [4, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {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], [3, 0], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [3, 0], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 5 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {}, {3}], [[1, 2, 4, 3], {[0, 0, 0, 0, 0]}, {1}, {}], [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[2, 3, 1, 5, 4], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1, 2}, {}], [[3, 4, 2, 1], {[0, 0, 0, 1, 0]}, {3}, {}], [ [1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {2}, {4} ], [[2, 3, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[3, 4, 1, 5, 2], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[1, 2], {[0, 1, 0]}, {}, {}], [[2, 3, 1, 4, 5], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {4}, {5}], [ [3, 4, 2, 5, 1], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [ [2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {}, {4}] } Naively, we would expect the sequence to begin , 1, 1, 2, 4, 9, 23, 65 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, 290512, 1033412, 3707852, 13402697, 48760367, 178405157, 656043857, 2423307047, 8987427467, 33453694487, 124936258127, 467995871777, 1757900019101, 6619846420553, 24987199492705, 94520750408709, 358268702159069, 1360510918810437] For the equivalence class of patterns, { {[[2, 0], [4, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 1], [4, 0], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [4, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [1, 1], [4, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[2, 0], [4, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [4, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {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, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 0], [4, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[4, 0], [1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[3, 0], [2, 0], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [4, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [2, 0], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 3 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[3, 2, 1], {[0, 0, 0, 0]}, {1}, {}], [[2, 1], {}, {}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [2, 0], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 5 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[3, 2, 1], {}, {}, {3}], [[2, 1], {}, {}, {}], [[3, 2, 4, 1, 5], { [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {3}, {}], [ [3, 2, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}] , [[4, 3, 1, 2], {[0, 1, 0, 0, 0]}, {3}, {4}], [[4, 3, 2, 1], {}, {2}, {4}], [[4, 3, 5, 1, 2], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {4}, {5}], [[3, 2, 5, 1, 4], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 0]}, {3}, {}], [[4, 3, 5, 2, 1], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {4}, {5}], [ [2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}, {}] , [[2, 1, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {}, {}], [[4, 2, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}, {4}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {}, {4}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 18, 47 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 18, 47, 138, 436, 1438, 4871, 16806, 58797, 208024, 742913, 2674454, 9694860, 35357686, 129644807, 477638718, 1767263209, 6564120440, 24466267041, 91482563662, 343059613673, 1289904147348, 4861946401477, 18367353072178, 69533550916031, 263747951750388, 1002242216651397] For the equivalence class of patterns, { {[[3, 0], [4, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [4, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [4, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [4, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[3, 0], [2, 0], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [2, 0], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 4 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {}, {}], [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 1, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {}, {3}], [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {3}, {}], [ [2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}, {4} ], [[3, 2, 1], {}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 9, 23, 65 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, 290512, 1033412, 3707852, 13402697, 48760367, 178405157, 656043857, 2423307047, 8987427467, 33453694487, 124936258127, 467995871777, 1757900019101, 6619846420553, 24987199492705, 94520750408709, 358268702159069, 1360510918810437] For the equivalence class of patterns, { {[[3, 0], [4, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[3, 0], [4, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 2 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2], {[0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 8, 16, 32 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912] For the equivalence class of patterns, { {[[4, 0], [2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 0], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [2, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[4, 0], [2, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 4 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {}], [[3, 2, 1], {}, {2}, {}], [[2, 1], {}, {}, {}], [ [3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {4}, {4} ], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {2}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {3}, {4}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {2}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {}, {3}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 9, 23, 65 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 9, 23, 65, 197, 626, 2056, 6918, 23714, 82500, 290512, 1033412, 3707852, 13402697, 48760367, 178405157, 656043857, 2423307047, 8987427467, 33453694487, 124936258127, 467995871777, 1757900019101, 6619846420553, 24987199492705, 94520750408709, 358268702159069, 1360510918810437] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [2, 0], [3, 1], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [3, 1], [2, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 0]], [[4, 0], [2, 1], [3, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 1], [3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 1], [2, 0], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0], [4, 1]]}} the member , {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 0], [1, 1]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[2, 0], [1, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[2, 0], [3, 0], [1, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[3, 0], [1, 0], [2, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[1, 0], [3, 0], [2, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 1, 0]}, {1}, {}], [[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 4, 7, 11, 16 Using the scheme, the first, , 31, terms are [1, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436] For the equivalence class of patterns, { {[[3, 0], [2, 0], [1, 0]], [[4, 0], [3, 0], [2, 1], [1, 0]]}, {[[3, 0], [2, 0], [1, 0]], [[4, 0], [3, 1], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [2, 0], [3, 1], [4, 0]]}, {[[1, 0], [2, 0], [3, 0]], [[1, 0], [2, 1], [3, 0], [4, 0]]}} the member , {[[3, 0], [2, 0], [1, 0]], [[4, 0], [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] Out of a total of , 88, cases 84, were successful and , 4, failed Success Rate: , 0.955 Here are the failures {{{[[1, 1], [2, 0], [4, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}}, { {[[1, 1], [2, 0], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}}, { {[[1, 1], [4, 0], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}}, { {[[2, 0], [4, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}}} {{{[[1, 1], [2, 0], [4, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}}, { {[[1, 1], [2, 0], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}}, { {[[1, 1], [4, 0], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}}, { {[[2, 0], [4, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 0], [2, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}}} "for patterns of lengths: ", [[3, 0], [4, 2]] There all together, 136, different equivalence classes For the equivalence class of patterns, { {[[1, 1], [3, 1], [2, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 1], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [2, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [2, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 1], [3, 1], [2, 0], [4, 0]], [[1, 0], [3, 0], [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, 0], [2, 1], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 1], [2, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [2, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 1], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [2, 1], [4, 1]], [[1, 0], [3, 0], [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], [2, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [3, 1], [2, 1], [4, 0]], [[1, 0], [3, 0], [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, { {[[3, 0], [2, 0], [4, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [1, 1], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [2, 0], [4, 1], [1, 1]], [[1, 0], [3, 0], [2, 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, { {[[3, 0], [2, 1], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [1, 1], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[3, 0], [2, 1], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [3, 1], [4, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [4, 0], [1, 1]], [[1, 0], [3, 0], [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, { {[[3, 1], [2, 1], [4, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 1], [1, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [4, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [2, 1], [4, 0], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[3, 1], [4, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [4, 1], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 1], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [4, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 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, { {[[3, 1], [4, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [4, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 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, { {[[3, 0], [4, 0], [1, 1], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 1], [4, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 1], [4, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [4, 0], [1, 1], [2, 1]], [[1, 0], [3, 0], [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], [2, 1], [4, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [4, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 1], [2, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [4, 0], [3, 1]], [[1, 0], [3, 0], [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], [2, 1], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [2, 1], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [3, 1], [4, 1]], [[2, 0], [1, 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, { {[[1, 1], [2, 0], [4, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 1], [2, 0], [4, 1], [3, 0]], [[1, 0], [3, 0], [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], [2, 0], [4, 1], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]], [[3, 0], [1, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [4, 1], [3, 1]], [[1, 0], [3, 0], [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, { {[[3, 0], [4, 1], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [4, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [4, 1], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 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, { {[[3, 1], [4, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 0], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [4, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [4, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 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, { {[[3, 1], [4, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [4, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [4, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [4, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[3, 0], [4, 0], [2, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 1], [4, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 1], [4, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 0], [2, 1], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [4, 0], [2, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 3, 2], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1], {[0, 0, 1, 0]}, {}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {3}, {}], [[1, 2, 3], {[0, 0, 1, 0], [0, 1, 0, 0]}, {1}, {3, 4}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1, 2}, {4, 5}], [ [2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1, 2}, {4, 5}], [[1, 2], {[0, 1, 0]}, {}, {2, 3}], [[3, 4, 2, 1], {[0, 0, 0, 1, 0]}, {1, 2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 2, 5, 14 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 0], [4, 1], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [4, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [4, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [4, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [4, 1], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[3, 0], [4, 1], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 0], [3, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [1, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [4, 1], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 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, 0], [2, 1], [3, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 0], [2, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 0], [4, 1]], [[1, 0], [3, 0], [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], [2, 1], [3, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1], [4, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 1], [2, 1], [3, 0], [4, 0]], [[1, 0], [3, 0], [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], [2, 0], [3, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 0], [2, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 1], [2, 0], [3, 1], [4, 0]], [[1, 0], [3, 0], [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, { {[[3, 1], [4, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [4, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [1, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [1, 1], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [1, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [4, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 1], [2, 0], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 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, { {[[4, 1], [1, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[3, 0], [2, 1], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 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, { {[[4, 1], [3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 0], [3, 1], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 1], [3, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 0], [3, 1], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 1], [3, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 1], [3, 1], [2, 0], [1, 0]], [[1, 0], [3, 0], [2, 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], [2, 0], [3, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 0], [2, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 1], [2, 0], [3, 0], [4, 1]], [[1, 0], [3, 0], [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, { {[[4, 0], [1, 0], [2, 1], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 0], [3, 1], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 1], [4, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 1], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [1, 0], [2, 1], [3, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [1, 1], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 0], [3, 1], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 1], [4, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [1, 1], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [1, 1], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [4, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[4, 0], [1, 1], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [1, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[3, 0], [2, 0], [1, 1], [4, 1]], [[2, 0], [3, 0], [1, 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, { {[[4, 1], [1, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [4, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[2, 1], [3, 0], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 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, { {[[4, 1], [1, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 1], [4, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [2, 1], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [2, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [1, 0], [4, 1]], [[2, 0], [3, 0], [1, 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, { {[[4, 0], [3, 1], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [3, 1], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [3, 1], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 0], [2, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [2, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [3, 1], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [3, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [3, 0], [2, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 1], [3, 0], [2, 0], [1, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [1, 0], [3, 1], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 1], [1, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [4, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [4, 1], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 1], [4, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [1, 0], [3, 1], [2, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [1, 1], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [4, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 1], [4, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [1, 1], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [1, 1], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [4, 1], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 1], [2, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [4, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [1, 1], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 1], [1, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 1], [3, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [2, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 1], [2, 0], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 0], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 1], [2, 1], [3, 0], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [2, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [3, 0], [4, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[3, 0], [1, 1], [2, 0], [4, 1]], [[2, 0], [3, 0], [1, 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, { {[[4, 0], [2, 0], [1, 1], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 1], [2, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [1, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [4, 1], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[4, 0], [2, 0], [1, 1], [3, 1]], [[1, 0], [3, 0], [2, 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, { {[[4, 0], [2, 1], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 1], [3, 1], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 0], [2, 1], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 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, { {[[4, 1], [2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [2, 0], [3, 1], [1, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [2, 0], [4, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 1], [2, 0], [4, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 1], [4, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [3, 0], [2, 1], [4, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 1], [3, 0], [1, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 1], [3, 0], [1, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[4, 1], [2, 0], [3, 1], [1, 0]], [[1, 0], [3, 0], [2, 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, 0], [2, 0], [3, 1], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [2, 1], [3, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 0], [3, 1], [4, 1]], [[1, 0], [3, 0], [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], [2, 1], [3, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 0], [2, 1], [3, 1], [4, 0]], [[1, 0], [3, 0], [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], [2, 0], [4, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [3, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [3, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 0], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [2, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [2, 0], [4, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[1, 1], [2, 0], [4, 1], [3, 0]], [[2, 0], [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, { {[[1, 0], [2, 0], [4, 1], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 1], [2, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [2, 0], [4, 1], [3, 1]], [[2, 0], [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, { {[[1, 0], [2, 1], [4, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [2, 1], [4, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [3, 1], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [3, 1], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 0], [2, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [2, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [3, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [3, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [2, 1], [4, 1], [3, 0]], [[2, 0], [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, { {[[1, 1], [2, 1], [4, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 0], [2, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[3, 0], [4, 0], [2, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 1, 0]}, {1}, {}], [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 3, 1], {[0, 0, 1, 0], [0, 1, 0, 0]}, {}, {3}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1, 2}, {}], [[1, 2], {}, {}, {2, 3}], [[1, 2, 3], {}, {2}, {3, 4}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {3}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1, 2}, {4, 5}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}, {3, 4}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 2, 5, 14 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[1, 1], [3, 0], [4, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 1], [2, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 1], [3, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 0], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 1], [3, 0], [4, 0], [2, 1]], [[2, 0], [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, { {[[1, 1], [3, 0], [4, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 1], [3, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 1], [3, 0], [1, 1]], [[3, 0], [1, 0], [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, 0], [4, 1], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 1], [3, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 1], [2, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 0], [4, 1], [2, 1]], [[2, 0], [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, { {[[1, 0], [3, 1], [4, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 1], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 1], [4, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 1], [1, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 1], [4, 1], [2, 0]], [[2, 0], [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, { {[[1, 0], [3, 1], [4, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 0], [3, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [4, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [3, 1], [4, 0], [2, 1]], [[2, 0], [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, { {[[1, 1], [3, 1], [4, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 0], [2, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [2, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 0], [3, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [3, 1], [1, 1]], [[3, 0], [1, 0], [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, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 1], [3, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 1], [2, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [4, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 0], [1, 1], [4, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [3, 0], [4, 0], [1, 1]], [[3, 0], [1, 0], [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], [1, 0], [3, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [3, 1], [4, 0], [1, 1]], [[3, 0], [1, 0], [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, 0], [3, 1], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [2, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 1], [4, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [3, 1], [4, 0], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [4, 0], [3, 1], [2, 1]], [[2, 0], [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, { {[[1, 0], [4, 1], [3, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 0], [4, 1], [1, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 1], [4, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[1, 0], [4, 1], [3, 0], [2, 1]], [[2, 0], [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], [4, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 1], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [4, 0], [3, 1]], [[2, 0], [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], [4, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 0], [1, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [1, 0], [4, 1], [3, 0]], [[2, 0], [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, 0], [1, 0], [4, 1], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 1], [4, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [1, 0], [4, 1], [3, 1]], [[2, 0], [1, 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], [3, 0], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [3, 0], [4, 1], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [1, 1], [2, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [2, 0], [1, 1], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 1], [3, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [4, 0], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [3, 0], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 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], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [2, 0], [1, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [3, 0], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 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, 1], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [3, 1], [4, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 0], [2, 1], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [1, 1], [2, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 0], [4, 0], [3, 1], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [4, 1], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [2, 1], [1, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 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, 1], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 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], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [4, 0], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 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, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [4, 0], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 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, 0], [1, 1], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [1, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [1, 1], [3, 1]], [[2, 0], [3, 0], [1, 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], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 1], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 1], [3, 0]], [[2, 0], [3, 0], [1, 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], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [4, 1], [1, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 1], [1, 0], [3, 1]], [[2, 0], [3, 0], [1, 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, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [1, 0], [4, 1], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[2, 0], [4, 0], [1, 1], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [4, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 1], [4, 0], [2, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [4, 1], [1, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [4, 0], [1, 1], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[3, 0], [1, 0], [4, 1], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [4, 1], [1, 0], [3, 0]], [[2, 0], [3, 0], [1, 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], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 0], [4, 1], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 1], [3, 0], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 0], [1, 1], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 1], [2, 0], [3, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [3, 0], [4, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [4, 0], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 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], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 1], [1, 0], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 0], [2, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [3, 1], [4, 0], [2, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [4, 1], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [4, 0], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 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, 0], [3, 1], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [2, 1], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 1], [2, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [2, 1], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 0], [2, 1], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [3, 1], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 1], [4, 0], [2, 0]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 1], [4, 0], [2, 1], [3, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 0], [3, 1], [1, 1]], [[2, 0], [3, 0], [1, 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], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 1], [4, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 0], [3, 1], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 1], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 1], [1, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 0], [2, 1], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 1], [4, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 1], [3, 1], [1, 0]], [[2, 0], [3, 0], [1, 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], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 0], [1, 1]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 1], [1, 0], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 1], [2, 0], [1, 1], [3, 0]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 0], [1, 1], [2, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [4, 0], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[2, 1], [3, 0], [1, 0], [4, 1]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 1], [3, 0], [4, 1], [2, 0]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 0], [4, 1], [3, 0], [1, 1]], [[2, 0], [3, 0], [1, 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], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 1], [2, 0], [4, 1], [1, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[4, 0], [1, 1], [3, 0], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[4, 0], [2, 0], [1, 1], [3, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[3, 1], [1, 1], [2, 0], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 1], [3, 0], [1, 1], [4, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[1, 0], [4, 1], [2, 0], [3, 1]], [[1, 0], [3, 0], [2, 0]]}, {[[1, 0], [3, 0], [4, 1], [2, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[2, 1], [4, 1], [3, 0], [1, 0]], [[2, 0], [3, 0], [1, 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, { {[[3, 1], [4, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 1]], [[3, 0], [1, 0], [2, 0]]}, {[[2, 1], [1, 1], [4, 0], [3, 0]], [[2, 0], [1, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1]], [[1, 0], [3, 0], [2, 0]]}} the member , {[[3, 1], [4, 1], [1, 0], [2, 0]], [[2, 0], [3, 0], [1, 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, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[2, 0], [1, 1], [4, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [1, 1], [4, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [4, 0], [1, 1], [2, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[2, 1], [1, 1], [4, 0], [3, 0]], [[3, 0], [2, 0], [1, 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], [3, 0], [1, 0], [4, 1]], %1}, {[[3, 0], [1, 1], [2, 0], [4, 1]], %1}, {[[3, 1], [2, 0], [4, 0], [1, 1]], %2}, {[[4, 1], [1, 0], [3, 0], [2, 1]], %2}, {[[4, 1], [2, 0], [1, 1], [3, 0]], %2}, {[[1, 1], [3, 0], [4, 1], [2, 0]], %1}, {[[2, 0], [4, 1], [3, 0], [1, 1]], %2}, {[[1, 1], [4, 0], [2, 0], [3, 1]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[2, 1], [3, 0], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 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], [3, 0], [1, 1], [4, 0]], %2}, {[[3, 1], [1, 1], [2, 0], [4, 0]], %2}, {[[3, 1], [2, 0], [4, 1], [1, 0]], %1}, {[[4, 0], [1, 1], [3, 0], [2, 1]], %1}, {[[4, 0], [2, 0], [1, 1], [3, 1]], %1}, {[[1, 0], [3, 0], [4, 1], [2, 1]], %2}, {[[1, 0], [4, 1], [2, 0], [3, 1]], %2}, {[[2, 1], [4, 1], [3, 0], [1, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 1], [3, 0], [1, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 0], [3, 0], [1, 1], [4, 1]], %1}, {[[4, 1], [1, 1], [3, 0], [2, 0]], %2}, {[[4, 1], [2, 0], [1, 0], [3, 1]], %2}, {[[3, 1], [1, 0], [2, 0], [4, 1]], %1}, {[[2, 1], [4, 0], [3, 0], [1, 1]], %2}, {[[3, 0], [2, 0], [4, 1], [1, 1]], %2}, {[[1, 1], [4, 1], [2, 0], [3, 0]], %1}, {[[1, 1], [3, 0], [4, 0], [2, 1]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[2, 0], [3, 0], [1, 1], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 1], [4, 0], [1, 1], [3, 0]], %2}, {[[2, 0], [4, 1], [1, 0], [3, 1]], %2}, {[[3, 0], [1, 0], [4, 1], [2, 1]], %2}, {[[3, 1], [1, 1], [4, 0], [2, 0]], %2}, {[[3, 0], [1, 1], [4, 0], [2, 1]], %1}, {[[2, 1], [4, 1], [1, 0], [3, 0]], %1}, {[[2, 0], [4, 0], [1, 1], [3, 1]], %1}, {[[3, 1], [1, 0], [4, 1], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 1], [4, 0], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 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, 0], [1, 1], [3, 1]], %2}, {[[2, 1], [4, 1], [1, 0], [3, 0]], %2}, {[[3, 1], [1, 0], [4, 1], [2, 0]], %2}, {[[3, 0], [1, 1], [4, 0], [2, 1]], %2}, {[[3, 1], [1, 1], [4, 0], [2, 0]], %1}, {[[2, 1], [4, 0], [1, 1], [3, 0]], %1}, {[[2, 0], [4, 1], [1, 0], [3, 1]], %1}, {[[3, 0], [1, 0], [4, 1], [2, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [4, 0], [1, 1], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 0], [4, 1], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 1], [4, 0], [1, 0], [3, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [4, 1], [1, 1], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 1], [4, 0], [3, 0], [1, 1]], %2}, {[[3, 0], [2, 0], [4, 1], [1, 1]], %2}, {[[4, 1], [1, 1], [3, 0], [2, 0]], %2}, {[[4, 1], [2, 0], [1, 0], [3, 1]], %2}, {[[1, 1], [3, 0], [4, 0], [2, 1]], %1}, {[[2, 0], [3, 0], [1, 1], [4, 1]], %1}, {[[1, 1], [4, 1], [2, 0], [3, 0]], %1}, {[[3, 1], [1, 0], [2, 0], [4, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 1], [4, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 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], [3, 1], [1, 0]], %2}, {[[3, 0], [2, 1], [4, 1], [1, 0]], %2}, {[[4, 0], [1, 1], [3, 1], [2, 0]], %2}, {[[4, 0], [2, 1], [1, 0], [3, 1]], %2}, {[[1, 0], [3, 1], [4, 0], [2, 1]], %1}, {[[2, 0], [3, 1], [1, 1], [4, 0]], %1}, {[[1, 0], [4, 1], [2, 1], [3, 0]], %1}, {[[3, 1], [1, 0], [2, 1], [4, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 1], [4, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, 0], [3, 1], [1, 1]], %2}, {[[3, 0], [2, 1], [4, 0], [1, 1]], %2}, {[[4, 1], [1, 0], [3, 1], [2, 0]], %2}, {[[4, 1], [2, 1], [1, 0], [3, 0]], %2}, {[[1, 1], [3, 1], [4, 0], [2, 0]], %1}, {[[1, 1], [4, 0], [2, 1], [3, 0]], %1}, {[[2, 0], [3, 1], [1, 0], [4, 1]], %1}, {[[3, 0], [1, 0], [2, 1], [4, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [4, 0], [3, 1], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 0], [4, 1], [3, 1], [1, 0]], %2}, {[[3, 1], [2, 1], [4, 0], [1, 0]], %2}, {[[4, 0], [1, 0], [3, 1], [2, 1]], %2}, {[[4, 0], [2, 1], [1, 1], [3, 0]], %2}, {[[2, 1], [3, 1], [1, 0], [4, 0]], %1}, {[[1, 0], [3, 1], [4, 1], [2, 0]], %1}, {[[1, 0], [4, 0], [2, 1], [3, 1]], %1}, {[[3, 0], [1, 1], [2, 1], [4, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [4, 1], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 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], [3, 0], [1, 1]], %2}, {[[3, 1], [2, 0], [4, 0], [1, 1]], %2}, {[[4, 1], [1, 0], [3, 0], [2, 1]], %2}, {[[4, 1], [2, 0], [1, 1], [3, 0]], %2}, {[[1, 1], [4, 0], [2, 0], [3, 1]], %1}, {[[1, 1], [3, 0], [4, 1], [2, 0]], %1}, {[[2, 1], [3, 0], [1, 0], [4, 1]], %1}, {[[3, 0], [1, 1], [2, 0], [4, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [4, 1], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 0], [3, 1], [1, 1], [4, 0]], %1}, {[[4, 0], [1, 1], [3, 1], [2, 0]], %2}, {[[4, 0], [2, 1], [1, 0], [3, 1]], %2}, {[[2, 1], [4, 0], [3, 1], [1, 0]], %2}, {[[3, 1], [1, 0], [2, 1], [4, 0]], %1}, {[[3, 0], [2, 1], [4, 1], [1, 0]], %2}, {[[1, 0], [3, 1], [4, 0], [2, 1]], %1}, {[[1, 0], [4, 1], [2, 1], [3, 0]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[2, 0], [3, 1], [1, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 0], [3, 1], [1, 0], [4, 1]], %1}, {[[4, 1], [1, 0], [3, 1], [2, 0]], %2}, {[[4, 1], [2, 1], [1, 0], [3, 0]], %2}, {[[2, 0], [4, 0], [3, 1], [1, 1]], %2}, {[[3, 0], [2, 1], [4, 0], [1, 1]], %2}, {[[3, 0], [1, 0], [2, 1], [4, 1]], %1}, {[[1, 1], [3, 1], [4, 0], [2, 0]], %1}, {[[1, 1], [4, 0], [2, 1], [3, 0]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[2, 0], [3, 1], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 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], [3, 1], [1, 0], [4, 0]], %2}, {[[3, 0], [1, 1], [2, 1], [4, 0]], %2}, {[[4, 0], [1, 0], [3, 1], [2, 1]], %1}, {[[4, 0], [2, 1], [1, 1], [3, 0]], %1}, {[[3, 1], [2, 1], [4, 0], [1, 0]], %1}, {[[1, 0], [3, 1], [4, 1], [2, 0]], %2}, {[[1, 0], [4, 0], [2, 1], [3, 1]], %2}, {[[2, 0], [4, 1], [3, 1], [1, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 1], [3, 1], [1, 0], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [3, 0], [4, 1], [1, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 1], [2, 0], [1, 1], [4, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[2, 1], [3, 0], [4, 1], [1, 0]], [[3, 0], [2, 0], [1, 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], [3, 0], [4, 0], [1, 1]], %2}, {[[2, 0], [3, 0], [4, 1], [1, 1]], %2}, {[[4, 1], [1, 0], [2, 0], [3, 1]], %2}, {[[4, 1], [1, 1], [2, 0], [3, 0]], %2}, {[[3, 1], [2, 0], [1, 0], [4, 1]], %1}, {[[3, 0], [2, 0], [1, 1], [4, 1]], %1}, {[[1, 1], [4, 0], [3, 0], [2, 1]], %1}, {[[1, 1], [4, 1], [3, 0], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 1], [3, 0], [4, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[2, 0], [3, 1], [4, 1], [1, 0]], %2}, {[[2, 1], [3, 1], [4, 0], [1, 0]], %2}, {[[4, 0], [1, 0], [2, 1], [3, 1]], %2}, {[[4, 0], [1, 1], [2, 1], [3, 0]], %2}, {[[3, 0], [2, 1], [1, 1], [4, 0]], %1}, {[[3, 1], [2, 1], [1, 0], [4, 0]], %1}, {[[1, 0], [4, 0], [3, 1], [2, 1]], %1}, {[[1, 0], [4, 1], [3, 1], [2, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[2, 0], [3, 1], [4, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, 1], [4, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [2, 1], [1, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[2, 0], [3, 1], [4, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[2, 1], [4, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [1, 1], [4, 1], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [4, 1], [1, 1], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 1], [1, 0], [4, 0], [2, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[2, 1], [4, 0], [1, 0], [3, 1]], [[3, 0], [2, 0], [1, 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, {{[[3, 1], [2, 0], [1, 0], [4, 1]], %1}, {[[3, 0], [2, 0], [1, 1], [4, 1]], %1}, {[[4, 1], [1, 0], [2, 0], [3, 1]], %2}, {[[4, 1], [1, 1], [2, 0], [3, 0]], %2}, {[[2, 1], [3, 0], [4, 0], [1, 1]], %2}, {[[2, 0], [3, 0], [4, 1], [1, 1]], %2}, {[[1, 1], [4, 1], [3, 0], [2, 0]], %1}, {[[1, 1], [4, 0], [3, 0], [2, 1]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[3, 1], [2, 0], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 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, { {[[3, 1], [4, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 0], [4, 1], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [4, 0], [3, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [4, 1], [3, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 1], [4, 0], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 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, { {[[3, 0], [4, 0], [1, 1], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 1], [4, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 1], [4, 0], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [4, 1], [3, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [4, 0], [1, 1], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 0], [4, 1], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [4, 1], [1, 1], [2, 0]], [[3, 0], [2, 0], [1, 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, {{[[3, 1], [4, 0], [2, 0], [1, 1]], %2}, {[[3, 0], [4, 1], [2, 0], [1, 1]], %2}, {[[4, 1], [3, 0], [1, 0], [2, 1]], %2}, {[[4, 1], [3, 0], [1, 1], [2, 0]], %2}, {[[1, 1], [2, 0], [4, 0], [3, 1]], %1}, {[[1, 1], [2, 0], [4, 1], [3, 0]], %1}, {[[2, 1], [1, 0], [3, 0], [4, 1]], %1}, {[[2, 0], [1, 1], [3, 0], [4, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 1], [4, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 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, {{[[3, 1], [4, 0], [2, 1], [1, 0]], %2}, {[[3, 0], [4, 1], [2, 1], [1, 0]], %2}, {[[4, 0], [3, 1], [1, 1], [2, 0]], %2}, {[[4, 0], [3, 1], [1, 0], [2, 1]], %2}, {[[1, 0], [2, 1], [4, 0], [3, 1]], %1}, {[[1, 0], [2, 1], [4, 1], [3, 0]], %1}, {[[2, 1], [1, 0], [3, 1], [4, 0]], %1}, {[[2, 0], [1, 1], [3, 1], [4, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 1], [4, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, { {[[3, 0], [4, 0], [2, 1], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 1], [4, 0], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 0], [4, 0], [2, 1], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 1], [4, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[3, 1], [4, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 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, {{[[3, 0], [2, 1], [1, 1], [4, 0]], %1}, {[[3, 1], [2, 1], [1, 0], [4, 0]], %1}, {[[4, 0], [1, 0], [2, 1], [3, 1]], %2}, {[[4, 0], [1, 1], [2, 1], [3, 0]], %2}, {[[2, 0], [3, 1], [4, 1], [1, 0]], %2}, {[[2, 1], [3, 1], [4, 0], [1, 0]], %2}, {[[1, 0], [4, 0], [3, 1], [2, 1]], %1}, {[[1, 0], [4, 1], [3, 1], [2, 0]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[3, 0], [2, 1], [1, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 0], [2, 1], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [1, 0], [2, 1], [3, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [3, 1], [4, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 1], [4, 0], [3, 1], [2, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[3, 0], [2, 1], [1, 0], [4, 1]], [[3, 0], [2, 0], [1, 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, {{[[3, 1], [2, 0], [4, 1], [1, 0]], %2}, {[[4, 0], [1, 1], [3, 0], [2, 1]], %2}, {[[4, 0], [2, 0], [1, 1], [3, 1]], %2}, {[[1, 0], [3, 0], [4, 1], [2, 1]], %1}, {[[2, 1], [3, 0], [1, 1], [4, 0]], %1}, {[[3, 1], [1, 1], [2, 0], [4, 0]], %1}, {[[2, 1], [4, 1], [3, 0], [1, 0]], %2}, {[[1, 0], [4, 1], [2, 0], [3, 1]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[3, 1], [2, 0], [4, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, { {[[3, 1], [2, 0], [1, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 0], [1, 1], [2, 0], [3, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 1], [3, 0], [4, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [4, 1], [3, 0], [2, 1]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[3, 1], [2, 0], [1, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[4, 0], [2, 1], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[4, 0], [2, 1], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, { {[[4, 1], [2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [3, 0], [2, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[4, 1], [2, 0], [3, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, has a scheme of depth , 2 here it is: {[[1, 2], {[0, 0, 0]}, {1}, {}], [[1], {[0, 1]}, {}, {}], [[], {}, {}, {}], [[2, 1], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[4, 1], [2, 0], [3, 1], [1, 0]], %2}, {[[4, 0], [2, 0], [3, 1], [1, 1]], %2}, {[[4, 0], [2, 1], [3, 0], [1, 1]], %2}, {[[4, 1], [2, 1], [3, 0], [1, 0]], %2}, {[[1, 0], [3, 1], [2, 0], [4, 1]], %1}, {[[1, 1], [3, 1], [2, 0], [4, 0]], %1}, {[[1, 0], [3, 0], [2, 1], [4, 1]], %1}, {[[1, 1], [3, 0], [2, 1], [4, 0]], %1}} %1 := [[1, 0], [2, 0], [3, 0]] %2 := [[3, 0], [2, 0], [1, 0]] the member , {[[4, 1], [2, 0], [3, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, { {[[4, 1], [3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}} the member , {[[4, 1], [3, 0], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 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, { {[[4, 1], [3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 1], [4, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 1]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[4, 1], [3, 0], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 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, { {[[3, 0], [4, 1], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[3, 1], [4, 0], [1, 0], [2, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 0], [4, 0], [3, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[2, 0], [1, 1], [4, 1], [3, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[3, 0], [4, 1], [1, 1], [2, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[3, 1], [4, 0], [2, 0], [1, 1]], %2}, {[[3, 0], [4, 1], [2, 0], [1, 1]], %2}, {[[4, 1], [3, 0], [1, 0], [2, 1]], %2}, {[[4, 1], [3, 0], [1, 1], [2, 0]], %2}, {[[2, 0], [1, 1], [3, 0], [4, 1]], %1}, {[[1, 1], [2, 0], [4, 1], [3, 0]], %1}, {[[2, 1], [1, 0], [3, 0], [4, 1]], %1}, {[[1, 1], [2, 0], [4, 0], [3, 1]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[3, 1], [4, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[3, 1], [4, 0], [2, 1], [1, 0]], %2}, {[[3, 0], [4, 1], [2, 1], [1, 0]], %2}, {[[4, 0], [3, 1], [1, 1], [2, 0]], %2}, {[[4, 0], [3, 1], [1, 0], [2, 1]], %2}, {[[2, 0], [1, 1], [3, 1], [4, 0]], %1}, {[[1, 0], [2, 1], [4, 1], [3, 0]], %1}, {[[1, 0], [2, 1], [4, 0], [3, 1]], %1}, {[[2, 1], [1, 0], [3, 1], [4, 0]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[3, 1], [4, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 0], [4, 0], [2, 1], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 1], [3, 1], [1, 0], [2, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 0], [1, 0], [3, 1], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 1], [4, 0], [3, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[3, 0], [4, 0], [2, 1], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {1}, {}], [[1, 2, 3], {[0, 0, 0, 0]}, {1}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 0]}, {3}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 1]}, {1, 2}, {}], [[2, 3, 1], {[0, 0, 0, 1]}, {}, {3}], [[3, 4, 1, 2], {[0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1, 2}, {4, 5}], [[2, 4, 1, 3], {[0, 0, 0, 1, 0], [0, 0, 0, 0, 1]}, {1, 2}, {4, 5}], [[1, 2], {[0, 0, 1]}, {}, {2, 3}], [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}, {3, 4}]} Naively, we would expect the sequence to begin , 1, 1, 1, 1, 2, 5, 14 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[3, 1], [4, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 0], [3, 0], [1, 1], [2, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[2, 1], [1, 1], [3, 0], [4, 0]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 0], [2, 0], [4, 1], [3, 1]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[3, 1], [4, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, {{[[4, 1], [2, 0], [3, 1], [1, 0]], %2}, {[[4, 0], [2, 0], [3, 1], [1, 1]], %2}, {[[4, 0], [2, 1], [3, 0], [1, 1]], %2}, {[[4, 1], [2, 1], [3, 0], [1, 0]], %2}, {[[1, 1], [3, 0], [2, 1], [4, 0]], %1}, {[[1, 0], [3, 0], [2, 1], [4, 1]], %1}, {[[1, 0], [3, 1], [2, 0], [4, 1]], %1}, {[[1, 1], [3, 1], [2, 0], [4, 0]], %1}} %1 := [[3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0]] the member , {[[4, 1], [2, 0], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[4, 0], [2, 1], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [3, 1], [2, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[4, 0], [2, 1], [3, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[4, 1], [3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 0], [3, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[4, 1], [3, 0], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[4, 1], [3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 0], [3, 1], [2, 0], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 0], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 0], [3, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[4, 1], [3, 0], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[4, 0], [3, 0], [2, 1], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 0], [3, 1], [4, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[1, 1], [2, 1], [3, 0], [4, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[4, 0], [3, 0], [2, 1], [1, 1]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[4, 0], [3, 1], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 0], [2, 1], [3, 1], [4, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[4, 0], [3, 1], [2, 1], [1, 0]], [[1, 0], [2, 0], [3, 0]]}, has a scheme of depth , 2 here it is: {[[], {}, {}, {}], [[1], {[1, 0]}, {}, {}], [[2, 1], {[0, 0, 0]}, {1}, {}], [[1, 2], {[0, 0, 1], [0, 1, 0], [1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 1, 0, 0, 0, 0 Using the scheme, the first, , 31, terms are [1, 1, 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] For the equivalence class of patterns, { {[[1, 0], [2, 0], [3, 1], [4, 1]], [[1, 0], [2, 0], [3, 0]]}, {[[1, 1], [2, 1], [3, 0], [4, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 0], [3, 0], [2, 1], [1, 1]], [[3, 0], [2, 0], [1, 0]]}, {[[4, 1], [3, 1], [2, 0], [1, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 0], [3, 1], [4, 1]], [[1, 0], [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], [2, 1], [3, 1], [4, 0]], [[1, 0], [2, 0], [3, 0]]}, {[[4, 0], [3, 1], [2, 1], [1, 0]], [[3, 0], [2, 0], [1, 0]]}} the member , {[[1, 0], [2, 1], [3, 1], [4, 0]], [[1, 0], [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] Out of a total of , 136, cases 133, were successful and , 3, failed Success Rate: , 0.978 Here are the failures {{{%1, [[1, 0], [3, 0], [2, 0]]}, {%1, [[2, 0], [1, 0], [3, 0]]}, {%2, [[2, 0], [3, 0], [1, 0]]}, {%2, [[3, 0], [1, 0], [2, 0]]}}, { {%2, [[1, 0], [3, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [1, 0], [2, 0]]}, {%2, [[2, 0], [1, 0], [3, 0]]}}, {{%2, [[1, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [2, 0], [1, 0]]}}} %1 := [[1, 1], [3, 0], [2, 0], [4, 1]] %2 := [[4, 1], [2, 0], [3, 0], [1, 1]] {{{%1, [[1, 0], [3, 0], [2, 0]]}, {%1, [[2, 0], [1, 0], [3, 0]]}, {%2, [[2, 0], [3, 0], [1, 0]]}, {%2, [[3, 0], [1, 0], [2, 0]]}}, { {%2, [[1, 0], [3, 0], [2, 0]]}, {%1, [[2, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [1, 0], [2, 0]]}, {%2, [[2, 0], [1, 0], [3, 0]]}}, {{%2, [[1, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [2, 0], [1, 0]]}}} %1 := [[1, 1], [3, 0], [2, 0], [4, 1]] %2 := [[4, 1], [2, 0], [3, 0], [1, 1]] "for patterns of lengths: ", [[4, 0], [5, 1]] There all together, 1934, different equivalence classes For the equivalence class of patterns, { {%2, [[2, 0], [3, 1], [5, 0], [4, 0], [1, 0]]}, {%2, [[3, 0], [2, 0], [4, 1], [5, 0], [1, 0]]}, {%2, [[5, 0], [1, 0], [2, 1], [4, 0], [3, 0]]}, {%2, [[5, 0], [2, 0], [1, 0], [3, 1], [4, 0]]}, {%1, [[1, 0], [4, 0], [5, 0], [3, 1], [2, 0]]}, {%1, [[1, 0], [5, 0], [4, 1], [2, 0], [3, 0]]}, {%1, [[3, 0], [4, 0], [2, 1], [1, 0], [5, 0]]}, {%1, [[4, 0], [3, 1], [1, 0], [2, 0], [5, 0]]}} %1 := [[2, 0], [1, 0], [4, 0], [3, 0]] %2 := [[3, 0], [4, 0], [1, 0], [2, 0]] the member , { [[3, 0], [4, 0], [1, 0], [2, 0]], [[5, 0], [2, 0], [1, 0], [3, 1], [4, 0]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0]}, {1}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}, {}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [ [3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}, {}] , [ [4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}] , [[3, 1, 2, 4], {}, {2}, {}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0]}, {3}, {}], [[1, 3, 2, 4], {}, {1}, {}], [[4, 1, 2, 3], {}, {2}, {}], [[2, 1, 3], {}, {2}, {}], [[2, 3, 1], {[0, 1, 0, 0]}, {}, {}], [[3, 1, 2], {}, {}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0]}, {1}, {}], [[1, 2], {}, {}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0]}, {1}, {}], [[1, 4, 2, 3], {}, {1}, {}], [[1, 3, 2], {}, {}, {}], [[1, 2, 3], {}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 88, 368 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 88, 368, 1584, 6968, 31192, 141656, 651136, 3023840, 14166496, 66876096, 317809216, 1519163456, 7299577216, 35237444736, 170812433536, 831127053696, 4057858988416, 19873611712896, 97609555091456, 480665412429312, 2372681964103168, 11738252228246528, 58192137103545344, 289040850441827328, 1438241007404642304, 7168538977121976320] For the equivalence class of patterns, { {%1, [[4, 1], [3, 0], [5, 0], [2, 0], [1, 0]]}, {%1, [[5, 0], [4, 0], [1, 0], [3, 0], [2, 1]]}, {%1, [[5, 0], [4, 0], [2, 0], [1, 1], [3, 0]]}, {%2, [[1, 0], [2, 0], [4, 0], [5, 1], [3, 0]]}, {%2, [[1, 0], [2, 0], [5, 0], [3, 0], [4, 1]]}, {%2, [[2, 1], [3, 0], [1, 0], [4, 0], [5, 0]]}, {%2, [[3, 0], [1, 1], [2, 0], [4, 0], [5, 0]]}, {%1, [[3, 0], [5, 1], [4, 0], [2, 0], [1, 0]]}} %1 := [[4, 0], [3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0], [4, 0]] the member , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [1, 0], [3, 0], [2, 1]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {}, {}, {}], [[2, 1, 3, 4], {}, {3}, {}], [[3, 2, 1], {[0, 1, 0, 0], [1, 0, 0, 0]}, {2}, {}], [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}, {4}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {}], [[2, 1, 3], {}, {}, {}], [[3, 1, 4, 2], {}, {1, 2}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 90, 394 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890, 95149655201962, 518431875418926, 2832923350929742, 15521467648875090, 85249942588971314, 469286147871837366, 2588758890960637798, 14308406109097843626, 79228031819993134650] For the equivalence class of patterns, {{ [[4, 0], [2, 0], [1, 0], [3, 0]], [[3, 0], [1, 1], [2, 0], [4, 0], [5, 0]]} , { [[4, 0], [1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [5, 0], [3, 0], [4, 1]]} , { [[2, 0], [4, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 0], [5, 1], [3, 0]]} , { [[3, 0], [2, 0], [4, 0], [1, 0]], [[2, 1], [3, 0], [1, 0], [4, 0], [5, 0]]} , { [[3, 0], [1, 0], [2, 0], [4, 0]], [[5, 0], [4, 0], [2, 0], [1, 1], [3, 0]]} , { [[1, 0], [4, 0], [2, 0], [3, 0]], [[5, 0], [4, 0], [1, 0], [3, 0], [2, 1]]} , { [[1, 0], [3, 0], [4, 0], [2, 0]], [[3, 0], [5, 1], [4, 0], [2, 0], [1, 0]]} , { [[2, 0], [3, 0], [1, 0], [4, 0]], [[4, 1], [3, 0], [5, 0], [2, 0], [1, 0]]} } the member , { [[4, 0], [1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [5, 0], [3, 0], [4, 1]]} , has a scheme of depth , 5 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 4, 3, 1], {}, {}, {}], [[3, 2, 1], {}, {2}, {}], [[3, 5, 4, 2, 1], {}, {4}, {}], [[2, 1], {}, {}, {}], [[1, 2], {}, {}, {}], [[1, 3, 2], {}, {}, {}], [[2, 3, 1], {}, {}, {}], [[1, 4, 3, 2], {}, {3}, {}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[3, 2, 4, 1], {}, {1}, {}], [[1, 3, 2, 4], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {2}, {}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {3}, {}], [ [3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}] , [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}, {}], [[5, 2, 3, 1, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}, {4}, {}], [ [4, 2, 3, 1, 5], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [[3, 2, 5, 4, 1], {}, {1}, {}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}, {}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0]}, {4}, {}], [[2, 1, 4, 3, 5], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}, {}], [[3, 1, 5, 4, 2], {[0, 1, 0, 0, 0, 0]}, {1}, {}], [[2, 5, 4, 1, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[2, 4, 3, 1, 5], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {2}, {}], [[3, 5, 4, 1, 2], {[0, 1, 0, 0, 0, 0]}, {3}, {}], [[2, 5, 3, 1, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[5, 3, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}, {}], [[2, 1, 5, 4, 3], {}, {4}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {}, {}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 1, 4, 3], {}, {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}, {}], [[5, 3, 4, 1, 2], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2, 3}, {}], [[2, 1, 3], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 88, 363 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 88, 363, 1507, 6241, 25721, 105485, 430767, 1752945, 7113095, 28797292, 116368938, 469531170, 1892133076, 7617145998, 30638026074, 123145086046, 494663313342, 1985995240464, 7969941119476, 31971818819844, 128214549263032, 514024475597524, 2060262910065740, 8255954041620260, 33077227352665956, 132500624336147295] For the equivalence class of patterns, { {%2, [[1, 0], [3, 0], [5, 0], [4, 1], [2, 0]]}, {%2, [[3, 0], [4, 1], [2, 0], [5, 0], [1, 0]]}, {%2, [[4, 0], [2, 1], [1, 0], [3, 0], [5, 0]]}, {%2, [[5, 0], [1, 0], [4, 0], [2, 1], [3, 0]]}, {%1, [[1, 0], [5, 0], [2, 0], [4, 1], [3, 0]]}, {%1, [[2, 0], [4, 1], [5, 0], [3, 0], [1, 0]]}, {%1, [[3, 0], [2, 1], [4, 0], [1, 0], [5, 0]]}, {%1, [[5, 0], [3, 0], [1, 0], [2, 1], [4, 0]]}} %1 := [[2, 0], [4, 0], [1, 0], [3, 0]] %2 := [[3, 0], [1, 0], [4, 0], [2, 0]] the member , { [[3, 0], [1, 0], [4, 0], [2, 0]], [[5, 0], [1, 0], [4, 0], [2, 1], [3, 0]]} , has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[3, 2, 1], {}, {2}, {}], [[2, 1], {}, {}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}, {}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 90, 394 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890, 95149655201962, 518431875418926, 2832923350929742, 15521467648875090, 85249942588971314, 469286147871837366, 2588758890960637798, 14308406109097843626, 79228031819993134650] For the equivalence class of patterns, {{ [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 1], [3, 0], [2, 0], [1, 0]]} , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [3, 0], [2, 1], [1, 0]]} , { [[1, 0], [2, 0], [3, 0], [4, 0]], [[1, 0], [2, 1], [3, 0], [4, 0], [5, 0]]} , { [[1, 0], [2, 0], [3, 0], [4, 0]], [[1, 0], [2, 0], [3, 0], [4, 1], [5, 0]]} } the member , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [3, 0], [2, 1], [1, 0]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {}, {}, {}], [[2, 1, 3, 4], {}, {3}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {}], [[2, 1, 3], {}, {}, {}], [[3, 1, 4, 2], {}, {1, 2}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {4}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}, {}]} 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, [[1, 0], [3, 0], [5, 1], [4, 0], [2, 0]]}, {%2, [[3, 1], [4, 0], [2, 0], [5, 0], [1, 0]]}, {%2, [[4, 0], [2, 0], [1, 1], [3, 0], [5, 0]]}, {%2, [[5, 0], [1, 0], [4, 0], [2, 0], [3, 1]]}, {%1, [[1, 0], [5, 0], [2, 0], [4, 0], [3, 1]]}, {%1, [[2, 0], [4, 0], [5, 1], [3, 0], [1, 0]]}, {%1, [[3, 1], [2, 0], [4, 0], [1, 0], [5, 0]]}, {%1, [[5, 0], [3, 0], [1, 1], [2, 0], [4, 0]]}} %1 := [[2, 0], [4, 0], [1, 0], [3, 0]] %2 := [[3, 0], [1, 0], [4, 0], [2, 0]] the member , { [[3, 0], [1, 0], [4, 0], [2, 0]], [[5, 0], [1, 0], [4, 0], [2, 0], [3, 1]]} , has a scheme of depth , 3 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[3, 2, 1], {}, {2}, {}], [[2, 1], {}, {}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}, {}], [[2, 1, 3], {[0, 1, 0, 0]}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 90, 394 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098, 1037718, 5293446, 27297738, 142078746, 745387038, 3937603038, 20927156706, 111818026018, 600318853926, 3236724317174, 17518619320890, 95149655201962, 518431875418926, 2832923350929742, 15521467648875090, 85249942588971314, 469286147871837366, 2588758890960637798, 14308406109097843626, 79228031819993134650] For the equivalence class of patterns, {{ [[4, 0], [2, 0], [1, 0], [3, 0]], [[3, 0], [1, 0], [2, 1], [4, 0], [5, 0]]} , { [[4, 0], [1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [5, 0], [3, 1], [4, 0]]} , { [[2, 0], [4, 0], [3, 0], [1, 0]], [[1, 0], [2, 0], [4, 1], [5, 0], [3, 0]]} , { [[3, 0], [2, 0], [4, 0], [1, 0]], [[2, 0], [3, 1], [1, 0], [4, 0], [5, 0]]} , { [[3, 0], [1, 0], [2, 0], [4, 0]], [[5, 0], [4, 0], [2, 1], [1, 0], [3, 0]]} , { [[1, 0], [4, 0], [2, 0], [3, 0]], [[5, 0], [4, 0], [1, 0], [3, 1], [2, 0]]} , { [[1, 0], [3, 0], [4, 0], [2, 0]], [[3, 0], [5, 0], [4, 1], [2, 0], [1, 0]]} , { [[2, 0], [3, 0], [1, 0], [4, 0]], [[4, 0], [3, 1], [5, 0], [2, 0], [1, 0]]} } the member , { [[4, 0], [1, 0], [3, 0], [2, 0]], [[1, 0], [2, 0], [5, 0], [3, 1], [4, 0]]} , has a scheme of depth , 5 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 4, 3, 1], {}, {}, {}], [[3, 2, 1], {}, {2}, {}], [[3, 5, 4, 2, 1], {}, {4}, {}], [[2, 1], {}, {}, {}], [[1, 2], {}, {}, {}], [[1, 3, 2], {}, {}, {}], [[2, 3, 1], {}, {}, {}], [[1, 4, 3, 2], {}, {3}, {}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}, {}], [[3, 2, 4, 1], {}, {1}, {}], [[1, 3, 2, 4], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {2}, {}], [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {3}, {}], [ [3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}] , [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}, {}], [[5, 2, 3, 1, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}, {4}, {}], [ [4, 2, 3, 1, 5], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [[3, 2, 5, 4, 1], {}, {1}, {}], [[5, 2, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}, {}], [[2, 1, 5, 3, 4], {[0, 0, 0, 1, 0, 0]}, {4}, {}], [[2, 1, 4, 3, 5], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}, {}], [[3, 1, 5, 4, 2], {[0, 1, 0, 0, 0, 0]}, {1}, {}], [[2, 5, 4, 1, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[2, 4, 3, 1, 5], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {2}, {}], [[3, 5, 4, 1, 2], {[0, 1, 0, 0, 0, 0]}, {3}, {}], [[2, 5, 3, 1, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[5, 3, 4, 2, 1], {[0, 0, 0, 1, 0, 0]}, {4}, {}], [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}, {}], [[2, 1, 5, 4, 3], {}, {4}, {}], [[3, 1, 2], {[0, 1, 0, 0]}, {}, {}], [[4, 2, 3, 1], {[0, 0, 1, 0, 0]}, {}, {}], [[3, 4, 2, 1], {}, {3}, {}], [[2, 1, 4, 3], {}, {}, {}], [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}, {}], [[5, 3, 4, 1, 2], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {2, 3}, {}], [[2, 1, 3], {}, {}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 88, 363 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 88, 363, 1507, 6241, 25721, 105485, 430767, 1752945, 7113095, 28797292, 116368938, 469531170, 1892133076, 7617145998, 30638026074, 123145086046, 494663313342, 1985995240464, 7969941119476, 31971818819844, 128214549263032, 514024475597524, 2060262910065740, 8255954041620260, 33077227352665956, 132500624336147295] For the equivalence class of patterns, {{ [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 1], [4, 0], [3, 0], [2, 0], [1, 0]]} , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [3, 0], [2, 0], [1, 1]]} , { [[1, 0], [2, 0], [3, 0], [4, 0]], [[1, 1], [2, 0], [3, 0], [4, 0], [5, 0]]} , { [[1, 0], [2, 0], [3, 0], [4, 0]], [[1, 0], [2, 0], [3, 0], [4, 0], [5, 1]]} } the member , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [3, 0], [2, 0], [1, 1]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {}, {}, {}], [[2, 1, 3, 4], {}, {3}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {}], [[2, 1, 3], {}, {}, {}], [[3, 1, 4, 2], {}, {1, 2}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {4}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}, {}]} 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, {{ [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [3, 1], [2, 0], [1, 0]]} , { [[1, 0], [2, 0], [3, 0], [4, 0]], [[1, 0], [2, 0], [3, 1], [4, 0], [5, 0]]} } the member , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [3, 1], [2, 0], [1, 0]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {}, {}, {}], [[2, 1, 3, 4], {}, {3}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {}], [[2, 1, 3], {}, {}, {}], [[3, 1, 4, 2], {}, {1, 2}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {4}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}, {}]} 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, {{ [[4, 0], [2, 0], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [5, 0], [2, 0]]} , { [[4, 0], [1, 0], [3, 0], [2, 0]], [[2, 0], [3, 1], [4, 0], [1, 0], [5, 0]]} , { [[3, 0], [2, 0], [4, 0], [1, 0]], [[1, 0], [5, 0], [2, 0], [3, 1], [4, 0]]} , { [[2, 0], [4, 0], [3, 0], [1, 0]], [[4, 0], [1, 0], [2, 1], [3, 0], [5, 0]]} , { [[3, 0], [1, 0], [2, 0], [4, 0]], [[2, 0], [5, 0], [4, 1], [3, 0], [1, 0]]} , { [[1, 0], [4, 0], [2, 0], [3, 0]], [[4, 0], [3, 1], [2, 0], [5, 0], [1, 0]]} , { [[1, 0], [3, 0], [4, 0], [2, 0]], [[5, 0], [3, 0], [2, 1], [1, 0], [4, 0]]} , { [[2, 0], [3, 0], [1, 0], [4, 0]], [[5, 0], [1, 0], [4, 0], [3, 1], [2, 0]]} } the member , { [[4, 0], [2, 0], [1, 0], [3, 0]], [[1, 0], [3, 0], [4, 1], [5, 0], [2, 0]]} , has a scheme of depth , 5 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0]}, {1}, {}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}, {}], [[3, 1, 2], {}, {}, {}], [[1, 2], {}, {}, {}], [[1, 3, 2], {}, {}, {}], [[2, 3, 1], {}, {}, {}], [[2, 1, 4, 3], {}, {}, {}], [[4, 1, 5, 2, 3], {[0, 1, 0, 0, 0, 0]}, {1}, {}], [[2, 1, 3], {}, {}, {}], [[4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0]}, {3}, {}], [[1, 5, 2, 4, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}, {}], [[3, 5, 1, 2, 4], {[0, 1, 0, 0, 0, 0]}, {3}, {}], [[1, 4, 2, 3, 5], %1, {1}, {}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}, {}], [[2, 5, 3, 4, 1], %2, {1}, {}], [[4, 5, 1, 3, 2], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}, {}], [[1, 5, 2, 3, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {}, {}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 1, 0]}, {3}, {}], [[2, 4, 1, 3], {}, {}, {}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 1, 0]}, {3}, {}], [[2, 1, 5, 3, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}, {}], [[5, 1, 3, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}, {}], [[5, 1, 4, 3, 2], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}, {}], [[3, 4, 1, 2], {}, {}, {}], [[2, 1, 4, 3, 5], %1, {1}, {}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0]}, {}, {}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}, {}], [[4, 1, 3, 2, 5], %1, {1}, {}], [[3, 1, 4, 2], {}, {}, {}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 1, 0]}, {1}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}, {}], [[4, 2, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[3, 4, 1, 2, 5], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}, {}], [[2, 4, 3, 1], {[0, 0, 0, 1, 0]}, {2}, {}], [[5, 1, 4, 2, 3], {[0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}, {}], [[3, 5, 2, 4, 1], %2, {1}, {}], [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}, {}], [[2, 5, 1, 3, 4], {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {3}, {}], [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[2, 3, 1, 4], {[0, 0, 1, 0, 0]}, {1}, {}], [[2, 4, 1, 3, 5], %1, {1}, {}], [[5, 2, 4, 3, 1], %2, {1}, {}], [[3, 4, 2, 1], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}], [[4, 2, 5, 3, 1], %2, {1}, {}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 1, 0]}, {1}, {}], [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}, {}], [[3, 1, 5, 2, 4], {[0, 1, 0, 0, 0, 0]}, {1}, {}], [[4, 1, 5, 3, 2], {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}, {}], [[4, 5, 2, 3, 1], %2, {1}, {}], [[3, 1, 4, 2, 5], %1, {1}, {}], [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}, {}]} %1 := {[0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]} %2 := {[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 86, 338 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 86, 338, 1318, 5106, 19718, 76066, 293398, 1131794, 4366374, 16846018, 64995254, 250765298, 967503814, 3732821922, 14401956182, 55565542354, 214382633062, 827129764994, 3191227078902, 12312373271986, 47503525349126, 183277819294562, 707121393512086, 2728211558369682, 10525969619710886, 40611233423076418] For the equivalence class of patterns, { {%1, [[4, 0], [3, 0], [5, 1], [2, 0], [1, 0]]}, {%1, [[5, 0], [4, 0], [1, 1], [3, 0], [2, 0]]}, {%1, [[5, 0], [4, 0], [2, 0], [1, 0], [3, 1]]}, {%2, [[1, 0], [2, 0], [4, 0], [5, 0], [3, 1]]}, {%2, [[1, 0], [2, 0], [5, 1], [3, 0], [4, 0]]}, {%2, [[2, 0], [3, 0], [1, 1], [4, 0], [5, 0]]}, {%2, [[3, 1], [1, 0], [2, 0], [4, 0], [5, 0]]}, {%1, [[3, 1], [5, 0], [4, 0], [2, 0], [1, 0]]}} %1 := [[4, 0], [3, 0], [2, 0], [1, 0]] %2 := [[1, 0], [2, 0], [3, 0], [4, 0]] the member , { [[4, 0], [3, 0], [2, 0], [1, 0]], [[5, 0], [4, 0], [2, 0], [1, 0], [3, 1]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[1, 2], {}, {1}, {}], [[2, 1], {}, {}, {}], [[2, 1, 3, 4], {}, {3}, {}], [[2, 1, 4, 3], {}, {1, 2}, {}], [[3, 1, 2], {}, {2}, {}], [[2, 1, 3], {}, {}, {}], [[3, 1, 4, 2], {}, {1, 2}, {}], [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {4}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}, {}]} 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, [[2, 1], [3, 0], [5, 0], [4, 0], [1, 0]]}, {%2, [[3, 0], [2, 0], [4, 0], [5, 1], [1, 0]]}, {%2, [[5, 0], [1, 1], [2, 0], [4, 0], [3, 0]]}, {%2, [[5, 0], [2, 0], [1, 0], [3, 0], [4, 1]]}, {%1, [[1, 0], [4, 0], [5, 0], [3, 0], [2, 1]]}, {%1, [[1, 0], [5, 1], [4, 0], [2, 0], [3, 0]]}, {%1, [[3, 0], [4, 0], [2, 0], [1, 1], [5, 0]]}, {%1, [[4, 1], [3, 0], [1, 0], [2, 0], [5, 0]]}} %1 := [[2, 0], [1, 0], [4, 0], [3, 0]] %2 := [[3, 0], [4, 0], [1, 0], [2, 0]] the member , { [[3, 0], [4, 0], [1, 0], [2, 0]], [[5, 0], [2, 0], [1, 0], [3, 0], [4, 1]]} , has a scheme of depth , 4 here it is: {[[1], {}, {}, {}], [[], {}, {}, {}], [[2, 1], {}, {}, {}], [[3, 2, 1], {[0, 0, 1, 0]}, {1}, {}], [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {2}, {}], [[1, 4, 3, 2], {[0, 0, 0, 1, 0]}, {2}, {}], [[3, 4, 1, 2], {[0, 0, 0, 0, 0]}, {1}, {}], [ [3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}, {}] , [ [4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}, {}] , [[3, 1, 2, 4], {}, {2}, {}], [[4, 1, 3, 2], {[0, 0, 0, 1, 0]}, {3}, {}], [[1, 3, 2, 4], {}, {1}, {}], [[4, 1, 2, 3], {}, {2}, {}], [[2, 1, 3], {}, {2}, {}], [[2, 3, 1], {[0, 1, 0, 0]}, {}, {}], [[3, 1, 2], {}, {}, {}], [[2, 3, 1, 4], {[0, 1, 0, 0, 0]}, {1}, {}], [[1, 2], {}, {}, {}], [[2, 4, 1, 3], {[0, 1, 0, 0, 0]}, {1}, {}], [[1, 4, 2, 3], {}, {1}, {}], [[1, 3, 2], {}, {}, {}], [[1, 2, 3], {}, {1}, {}]} Naively, we would expect the sequence to begin , 1, 1, 2, 6, 22, 88, 368 Using the scheme, the first, , 31, terms are [1, 1, 2, 6, 22, 88, 368, 1584, 6968, 31192, 141656, 651136, 3023840, 14166496, 66876096, 317809216, 1519163456, 7299577216, 35237444736, 170812433536, 831127053696, 4057858988416, 19873611712896, 97609555091456, 480665412429312, 2372681964103168, 11738252228246528, 58192137103545344, 289040850441827328, 1438241007404642304, 7168538977121976320]