"There are ", 10, " pattern sets of type ", [2, 2, 2] "They fall into ", 5, " trivial pattern classes." "---------------------------------------------" "For the equivalence class ", {{[0, 0], [0, 1], [1, 0]}}, " the pattern set ", {[0, 0], [0, 1], [1, 0]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 1], [[1], 0]}], [[1], {1}, {[[0, 0], 1]}]] "First ", 15, " terms of the counting sequence are ", [2, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000] "First ", 15, " rows of the 0s triangle are: " [1, 1] [2, 0, 0] [6, 0, 0, 0] [24, 0, 0, 0, 0] [120, 0, 0, 0, 0, 0] [720, 0, 0, 0, 0, 0, 0] [5040, 0, 0, 0, 0, 0, 0, 0] [40320, 0, 0, 0, 0, 0, 0, 0, 0] [362880, 0, 0, 0, 0, 0, 0, 0, 0, 0] [3628800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [39916800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [479001600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [6227020800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [87178291200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1307674368000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 0], [1, 2], [2, 1]}}, " the pattern set ", {[0, 0], [1, 2], [2, 1]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[0], 1], [[2], 0]}], [[1], {1}, {[[0, 0], 2], [[0, 1], 0], [[1, 0], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "First ", 15, " rows of the 0s triangle are: " [1, 1] [0, 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, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [1, 0], [1, 2]}, {[0, 1], [1, 0], [2, 1]}}, " the pattern set ", {[0, 1], [1, 0], [1, 2]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[1], 0]}], [[1], {1}, {[[0, 0], 1], [[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 0, 1] [1, 0, 0, 1] [1, 0, 0, 0, 1] [1, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 1], [1, 2], [2, 1]}, {[1, 0], [1, 2], [2, 1]}}, " the pattern set ", {[0, 1], [1, 2], [2, 1]}, " has the scheme ", [[[], {}, {}], [[0], {1}, {[[1], 0]}], [[1], {1}, {[[0, 1], 0], [[1, 0], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] "First ", 15, " rows of the 0s triangle are: " [1, 1] [0, 2, 1] [0, 0, 3, 1] [0, 0, 0, 4, 1] [0, 0, 0, 0, 5, 1] [0, 0, 0, 0, 0, 6, 1] [0, 0, 0, 0, 0, 0, 7, 1] [0, 0, 0, 0, 0, 0, 0, 8, 1] [0, 0, 0, 0, 0, 0, 0, 0, 9, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 1] [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 1] "---------------------------------------------" "For the equivalence class ", {{[0, 0], [0, 1], [1, 2]}, {[0, 0], [0, 1], [2, 1]}, {[0, 0], [1, 0], [1, 2]}, {[0, 0], [1, 0], [2, 1]} }, " the pattern set ", {[0, 0], [0, 1], [1, 2]}, " has the scheme ", [ [[], {}, {}], [[0], {1}, {[[0], 1], [[1], 0]}], [[1], {1}, {[[0, 0], 2], [[0, 1], 0]}]] "First ", 15, " terms of the counting sequence are ", [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] "First ", 15, " rows of the 0s triangle are: " [1, 1] [1, 2, 0] [1, 3, 0, 0] [1, 4, 0, 0, 0] [1, 5, 0, 0, 0, 0] [1, 6, 0, 0, 0, 0, 0] [1, 7, 0, 0, 0, 0, 0, 0] [1, 8, 0, 0, 0, 0, 0, 0, 0] [1, 9, 0, 0, 0, 0, 0, 0, 0, 0] [1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [1, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] "---------------------------------------------" "Overall, we found schemes for ", 5, " out of ", 5, " trivial classes, for a success rate of ", 1.