#This file begins by enumerating 27 of the 16457 (computation interrupted) different equivalence classes for the case of 1 pattern of length 4 and 2 patterns of length 5. #At line 1870, begin samples of attempting to find enumeration schemes for random sets of patterns (1 length four and 2 length five). >SipurF([4,5,5],5,3,10,20,n,N,x,3,2); There all together, 16457, different equivalence classes For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [3, 2, 1, 4, 5]}, {[4, 3, 2, 1], [3, 4, 5, 2, 1], [5, 4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [1, 2, 5, 4, 3], [3, 2, 1, 4, 5]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1], [0, 0, 2, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[2, 1, 3], {[0, 0, 0, 3]}, {}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {1}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {3}], [ [2, 1, 4, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[3, 1, 4, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 2, 4, 1], {[0, 0, 0, 0, 3]}, {3}], [[3, 4, 1, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {2}], [ [4, 2, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[4, 3, 1, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[4, 3, 2, 1], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 479, 2372, 12032, 61856, 320409] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 1, 5, 4, 3], [3, 2, 1, 5, 4]}, {[4, 3, 2, 1], [3, 4, 5, 1, 2], [4, 5, 1, 2, 3]}} the member , {[1, 2, 3, 4], [2, 1, 5, 4, 3], [3, 2, 1, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {[0, 0, 0, 3]}, {}], [[2, 1, 3], {[0, 0, 0, 3], [0, 0, 3, 0]}, {}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3]}, {}], [[3, 2, 1], {[0, 0, 0, 3]}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [ [1, 4, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [ [2, 1, 3, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {3}], [[2, 1, 4, 3], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 3, 0, 0]}, {}], [ [2, 4, 3, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {1}], [ [3, 1, 4, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 0]}, {3}], [ [3, 2, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0], [0, 0, 3, 0, 0]}, {1}], [ [3, 2, 4, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {3}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [4, 1, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 2, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 3, 0, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 3, 1, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 3, 2, 1], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[2, 1, 4, 3, 5], { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [ [2, 1, 5, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {2}], [[2, 5, 1, 3, 4], { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {2}], [ [2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 0, 0]}, {2}], [ [3, 1, 5, 4, 2], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}, {1}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}, {1} ], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 0]}, {2}], [[3, 5, 2, 4, 1], { [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {2} ]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 464, 2151, 10000, 46536, 216611] For the equivalence class of patterns, { {[2, 1, 4, 3], [1, 2, 3, 5, 4], [2, 1, 3, 4, 5]}, {[3, 4, 1, 2], [4, 5, 3, 2, 1], [5, 4, 3, 1, 2]}} the member , {[2, 1, 4, 3], [1, 2, 3, 5, 4], [2, 1, 3, 4, 5]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {[0, 0, 3]}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {[0, 0, 0, 3]}, {}], [[2, 1, 3], {[0, 0, 0, 2], [0, 0, 1, 0]}, {1}], [[2, 3, 1], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[3, 1, 2], {[0, 0, 0, 3]}, {}], [[3, 2, 1], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 2, 4, 3], {[0, 0, 0, 0, 3]}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {2}], [ [1, 3, 4, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {3}], [[1, 4, 2, 3], {[0, 0, 0, 0, 3]}, {2}], [[1, 4, 3, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[2, 3, 4, 1], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [ [2, 4, 3, 1], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 2, 3], {[0, 0, 0, 0, 3]}, {1}], [[4, 1, 3, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 479, 2371, 12010, 61576, 317681] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [1, 3, 2, 5, 4]}, {[1, 2, 3, 4], [2, 1, 4, 3, 5], [3, 2, 1, 4, 5]}, {[4, 3, 2, 1], [3, 4, 5, 2, 1], [4, 5, 2, 3, 1]}, {[4, 3, 2, 1], [5, 3, 4, 1, 2], [5, 4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [1, 2, 5, 4, 3], [1, 3, 2, 5, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {1}], [[1, 2, 3], {[0, 0, 0, 1], [0, 0, 2, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {4}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1, 2}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1, 2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 482, 2430, 12732, 68634, 378155] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [1, 5, 3, 4, 2]}, {[1, 2, 3, 4], [3, 2, 1, 4, 5], [4, 2, 3, 1, 5]}, {[4, 3, 2, 1], [2, 4, 3, 5, 1], [3, 4, 5, 2, 1]}, {[4, 3, 2, 1], [5, 1, 3, 2, 4], [5, 4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [3, 2, 1, 4, 5], [4, 2, 3, 1, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {}, {2}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3], {}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {}, {}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2], {}, {3}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 2, 4, 1], {}, {3}], [[3, 4, 1, 2], {}, {2}], [[3, 4, 2, 1], {}, {2}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {}, {3}], [[4, 2, 1, 3], {}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1]}, {1}], [[4, 3, 1, 2], {}, {1}], [[4, 3, 2, 1], {}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[2, 5, 1, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[2, 5, 1, 4, 3], {}, {4}], [[3, 5, 1, 4, 2], {}, {2}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 1]}, {2}], [[4, 2, 1, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[5, 2, 1, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {1} ], [[5, 2, 1, 4, 3], {}, {4}], [[5, 3, 1, 4, 2], {[0, 0, 0, 0, 0, 1]}, {1}], [[5, 3, 2, 4, 1], {[0, 0, 0, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 477, 2345, 11795, 60145, 309389] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [2, 1, 3, 5, 4]}, {[1, 2, 3, 4], [2, 1, 3, 5, 4], [3, 2, 1, 4, 5]}, {[4, 3, 2, 1], [3, 4, 5, 2, 1], [4, 5, 3, 1, 2]}, {[4, 3, 2, 1], [4, 5, 3, 1, 2], [5, 4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [1, 2, 5, 4, 3], [2, 1, 3, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1], [0, 0, 2, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[2, 1, 3], {[0, 0, 0, 2]}, {3}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {1}], [[3, 2, 1], {}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {2}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {}], [[3, 4, 2, 1, 5], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0]}, {5} ], [[3, 5, 2, 1, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0]}, {5}], [[4, 5, 2, 1, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {5}], [ [4, 5, 3, 1, 2], {[0, 0, 0, 0, 0, 3], [0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 0, 2], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 1, 2, 0, 0], [0, 0, 2, 0, 0, 1], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {3} ], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 3]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 478, 2363, 12008, 62185, 326519] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [2, 1, 4, 3, 5]}, {[1, 2, 3, 4], [1, 3, 2, 5, 4], [3, 2, 1, 4, 5]}, {[4, 3, 2, 1], [3, 4, 5, 2, 1], [5, 3, 4, 1, 2]}, {[4, 3, 2, 1], [4, 5, 2, 3, 1], [5, 4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [1, 3, 2, 5, 4], [3, 2, 1, 4, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {1}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3], {[0, 0, 0, 0, 2]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 4, 2], {[0, 0, 0, 0, 2]}, {1}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 2, 4, 1], {}, {}], [[3, 4, 1, 2], {}, {1}], [[3, 4, 2, 1], {}, {2}], [[4, 2, 1, 3], {}, {1}], [[4, 3, 1, 2], {}, {1}], [[4, 3, 2, 1], {}, {1}], [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[3, 2, 5, 1, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {3} ], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 2]}, {1}], [[4, 3, 5, 1, 2], {}, {1}], [[4, 3, 5, 2, 1], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 479, 2378, 12148, 63235, 333454] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [2, 1, 5, 4, 3]}, {[1, 2, 3, 4], [3, 2, 1, 4, 5], [3, 2, 1, 5, 4]}, {[4, 3, 2, 1], [3, 4, 5, 1, 2], [3, 4, 5, 2, 1]}, {[4, 3, 2, 1], [4, 5, 1, 2, 3], [5, 4, 1, 2, 3]}} the member , {[1, 2, 3, 4], [3, 2, 1, 4, 5], [3, 2, 1, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 2]}, {1}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 0, 2]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2], {}, {3}], [[3, 2, 4, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {1}], [[3, 4, 1, 2], {}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2]}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {3} ], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 2]}, {3}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[2, 5, 1, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 2]}, {2}], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 0, 2]}, {3}], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {1} ], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 2]}, {2}], [ [3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 474, 2291, 11211, 55140, 271759] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 2, 5, 4, 3], [3, 2, 1, 5, 4]}, {[1, 2, 3, 4], [2, 1, 5, 4, 3], [3, 2, 1, 4, 5]}, {[4, 3, 2, 1], [3, 4, 5, 1, 2], [5, 4, 1, 2, 3]}, {[4, 3, 2, 1], [3, 4, 5, 2, 1], [4, 5, 1, 2, 3]}} the member , {[1, 2, 3, 4], [1, 2, 5, 4, 3], [3, 2, 1, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1], [0, 0, 2, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {}], [[2, 1, 3], {[0, 0, 0, 3]}, {}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {}], [[3, 2, 1], {[0, 0, 0, 3]}, {}], [[1, 3, 2, 4], { [0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 0, 1, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [ [1, 4, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {3}], [ [2, 1, 4, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [ [3, 1, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 2, 0], [0, 0, 1, 1, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 1, 4, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {3}], [[3, 2, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {1}], [ [3, 2, 4, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {3}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [ [4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {1}], [ [4, 1, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [ [4, 2, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 2, 3, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 3, 1, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [ [4, 3, 2, 1], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[2, 1, 4, 3, 5], { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {3}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0]}, {3}], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {3}], [[2, 4, 1, 3, 5], { [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {2}], [[2, 5, 1, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 2, 0, 0]}, {2}], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {2}], [[3, 1, 5, 4, 2], { [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 1, 2, 0, 0], [0, 0, 2, 0, 0, 1], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {3}], [ [3, 2, 5, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {3}], [[3, 5, 1, 4, 2], { [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 1, 2, 0, 0], [0, 0, 2, 0, 0, 1], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {2}], [ [3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 470, 2235, 10723, 51632, 248970] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 2, 5, 4], [2, 1, 3, 5, 4]}, {[1, 2, 3, 4], [2, 1, 3, 5, 4], [2, 1, 4, 3, 5]}, {[4, 3, 2, 1], [4, 5, 2, 3, 1], [4, 5, 3, 1, 2]}, {[4, 3, 2, 1], [4, 5, 3, 1, 2], [5, 3, 4, 1, 2]}} the member , {[1, 2, 3, 4], [1, 3, 2, 5, 4], [2, 1, 3, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {[0, 0, 0, 2]}, {3}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {1}], [[3, 2, 1], {}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {2}], [[3, 4, 1, 2], {}, {1}], [[3, 4, 2, 1], {}, {}], [[3, 4, 2, 1, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[3, 5, 2, 1, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0]}, {5}], [[4, 5, 2, 1, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {5}], [[4, 5, 3, 1, 2], {}, {3}], [[4, 5, 3, 2, 1], {}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 480, 2397, 12371, 65336, 350918] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 2, 5, 4], [2, 1, 5, 4, 3]}, {[1, 2, 3, 4], [2, 1, 4, 3, 5], [3, 2, 1, 5, 4]}, {[4, 3, 2, 1], [3, 4, 5, 1, 2], [4, 5, 2, 3, 1]}, {[4, 3, 2, 1], [4, 5, 1, 2, 3], [5, 3, 4, 1, 2]}} the member , {[1, 2, 3, 4], [2, 1, 4, 3, 5], [3, 2, 1, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {}, {}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 3]}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 0, 2]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3], {[0, 0, 0, 0, 1]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2], {}, {3}], [[3, 2, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {1}], [ [3, 2, 4, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 3, 0]}, {3}], [[3, 4, 1, 2], {}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 1, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 2, 1], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[2, 5, 1, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 2]}, {2}], [ [3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 3, 0, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 471, 2248, 10818, 52207, 252200] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 2, 5, 4], [3, 2, 1, 5, 4]}, {[1, 2, 3, 4], [2, 1, 4, 3, 5], [2, 1, 5, 4, 3]}, {[4, 3, 2, 1], [3, 4, 5, 1, 2], [5, 3, 4, 1, 2]}, {[4, 3, 2, 1], [4, 5, 1, 2, 3], [4, 5, 2, 3, 1]}} the member , {[1, 2, 3, 4], [1, 3, 2, 5, 4], [3, 2, 1, 5, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 3]}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 1, 4, 3], {[0, 0, 0, 0, 2]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 1, 4, 2], {[0, 0, 0, 0, 2]}, {3}], [[3, 2, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {1}], [ [3, 2, 4, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {3}], [[3, 4, 1, 2], {}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [ [4, 1, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 1, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 2, 1], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 473, 2277, 11081, 54143, 264932] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 5, 2, 4], [1, 4, 2, 5, 3]}, {[1, 2, 3, 4], [2, 4, 1, 3, 5], [3, 1, 4, 2, 5]}, {[4, 3, 2, 1], [3, 5, 2, 4, 1], [4, 2, 5, 3, 1]}, {[4, 3, 2, 1], [5, 2, 4, 1, 3], [5, 3, 1, 4, 2]}} the member , {[1, 2, 3, 4], [1, 3, 5, 2, 4], [1, 4, 2, 5, 3]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[1, 3, 2], {[0, 0, 1, 1]}, {2}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1]}, {}], [[2, 4, 1, 3], {[0, 0, 0, 1, 1]}, {1, 2}], [[3, 4, 1, 2], {}, {1, 2}], [[3, 4, 2, 1], {}, {3}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {3}], [[2, 3, 1, 5, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {4} ], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 5, 1, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {3} ], [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {4} ], [[2, 4, 5, 1, 3], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {1} ], [[3, 4, 1, 5, 2], {[0, 0, 0, 0, 0, 1]}, {4}], [[3, 4, 2, 5, 1], {[0, 0, 0, 0, 0, 1]}, {3}], [[3, 4, 5, 1, 2], {[0, 0, 0, 0, 0, 1]}, {1}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 1]}, {4}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 481, 2419, 12657, 68244, 376651] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 5, 2, 4], [2, 4, 1, 3, 5]}, {[1, 2, 3, 4], [1, 4, 2, 5, 3], [3, 1, 4, 2, 5]}, {[4, 3, 2, 1], [3, 5, 2, 4, 1], [5, 2, 4, 1, 3]}, {[4, 3, 2, 1], [4, 2, 5, 3, 1], [5, 3, 1, 4, 2]}} the member , {[1, 2, 3, 4], [1, 3, 5, 2, 4], [2, 4, 1, 3, 5]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}], [[1, 3, 2], {}, {2}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[1, 2, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 3, 4, 1], {[0, 0, 0, 0, 1]}, {3}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1]}, {1, 2}], [[3, 4, 1, 2], {}, {1, 2}], [[3, 4, 2, 1], {}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 481, 2420, 12678, 68517, 379496] For the equivalence class of patterns, { {[1, 2, 3, 4], [1, 3, 5, 2, 4], [3, 1, 4, 2, 5]}, {[1, 2, 3, 4], [1, 4, 2, 5, 3], [2, 4, 1, 3, 5]}, {[4, 3, 2, 1], [3, 5, 2, 4, 1], [5, 3, 1, 4, 2]}, {[4, 3, 2, 1], [4, 2, 5, 3, 1], [5, 2, 4, 1, 3]}} the member , {[1, 2, 3, 4], [1, 4, 2, 5, 3], [2, 4, 1, 3, 5]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {[0, 0, 1, 1]}, {2}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {[0, 0, 0, 0, 1]}, {1, 2}], [[3, 4, 1, 2], {}, {1, 2}], [[3, 4, 2, 1], {}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 480, 2404, 12513, 67093, 368227] For the equivalence class of patterns, { {[1, 2, 3, 4], [2, 1, 3, 5, 4], [2, 1, 5, 4, 3]}, {[1, 2, 3, 4], [2, 1, 3, 5, 4], [3, 2, 1, 5, 4]}, {[4, 3, 2, 1], [3, 4, 5, 1, 2], [4, 5, 3, 1, 2]}, {[4, 3, 2, 1], [4, 5, 1, 2, 3], [4, 5, 3, 1, 2]}} the member , {[1, 2, 3, 4], [2, 1, 3, 5, 4], [3, 2, 1, 5, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 1]}, {3}], [[1, 3, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 2]}, {3}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 3]}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 4, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [[1, 4, 3, 2], {[0, 0, 0, 0, 2]}, {2}], [[2, 3, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 2, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {1}], [[3, 4, 1, 2], {}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[4, 1, 2, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 1, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 2, 1], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 471, 2248, 10819, 52219, 252288] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [1, 3, 2, 4, 5]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 2, 4, 3, 5]}, {[3, 4, 2, 1], [5, 4, 2, 3, 1], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [5, 3, 4, 2, 1], [5, 4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [1, 2, 3, 4, 5], [1, 3, 2, 4, 5]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {1}], [[1, 2, 3], {[0, 0, 0, 2], [0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {4}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1, 2}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1, 2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 482, 2430, 12732, 68634, 378155] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [1, 4, 3, 2, 5]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 4, 3, 2, 5]}, {[3, 4, 2, 1], [5, 2, 3, 4, 1], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [5, 2, 3, 4, 1], [5, 4, 3, 2, 1]}} the member , {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 4, 3, 2, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {}, {2}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 3, 4, 2], {}, {3}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 1]}, {2}], [[2, 3, 4, 1], {}, {2}], [[2, 4, 3, 1], {}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[4, 1, 2, 3], {}, {1}], [[4, 1, 3, 2], {}, {1}], [[4, 2, 3, 1], {}, {1}], [[1, 2, 4, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[1, 2, 5, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {3} ], [[1, 2, 5, 4, 3], {[0, 0, 0, 0, 0, 1]}, {3}], [[1, 3, 5, 4, 2], {[0, 0, 0, 0, 0, 1]}, {3}], [[1, 4, 2, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[1, 5, 2, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[1, 5, 2, 4, 3], {[0, 0, 0, 0, 0, 1]}, {2}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 1]}, {2}], [[2, 3, 5, 4, 1], {}, {2}], [[2, 5, 3, 4, 1], {}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 478, 2370, 12127, 63503, 338548] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [1, 5, 3, 4, 2]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [4, 2, 3, 1, 5]}, {[3, 4, 2, 1], [2, 4, 3, 5, 1], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [5, 1, 3, 2, 4], [5, 4, 3, 2, 1]}} the member , {[2, 1, 3, 4], [1, 2, 3, 4, 5], [4, 2, 3, 1, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {}, {2}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 2, 4, 3], {}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 3, 4, 2], {}, {3}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {}, {2}], [[2, 3, 4, 1], {}, {2}], [[2, 4, 3, 1], {}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {}, {}], [[4, 2, 3, 1], {[0, 0, 0, 0, 1]}, {1}], [[1, 4, 2, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[1, 5, 2, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[1, 5, 2, 4, 3], {}, {4}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 1]}, {2}], [[2, 5, 3, 4, 1], {[0, 0, 0, 0, 0, 1]}, {2}], [[4, 1, 2, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[4, 1, 3, 2, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[5, 1, 2, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {1} ], [[5, 1, 2, 4, 3], {}, {4}], [[5, 1, 3, 2, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {1} ], [[5, 1, 3, 4, 2], {[0, 0, 0, 0, 0, 1]}, {1}], [[5, 1, 4, 2, 3], {}, {1}], [[5, 1, 4, 3, 2], {}, {3}], [[5, 2, 3, 4, 1], {[0, 0, 0, 0, 0, 1]}, {1}], [[5, 2, 4, 3, 1], {[0, 0, 0, 0, 0, 1]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 478, 2366, 12053, 62603, 329602] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [2, 1, 3, 4, 5]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 2, 3, 5, 4]}, {[3, 4, 2, 1], [5, 4, 3, 1, 2], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [4, 5, 3, 2, 1], [5, 4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [1, 2, 3, 4, 5], [2, 1, 3, 4, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 2], [0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[2, 1, 3], {[0, 0, 0, 2]}, {3}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {1}], [[3, 2, 1], {}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {2}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {}], [[3, 4, 2, 1, 5], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 0]}, {5} ], [[3, 5, 2, 1, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0]}, {5}], [[4, 5, 2, 1, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {5}], [ [4, 5, 3, 1, 2], {[0, 0, 0, 0, 0, 3], [0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 0, 2], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 1, 2, 0, 0], [0, 0, 2, 0, 0, 1], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {3} ], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 3]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 478, 2363, 12008, 62185, 326519] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [2, 1, 4, 3, 5]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 3, 2, 5, 4]}, {[3, 4, 2, 1], [5, 3, 4, 1, 2], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [4, 5, 2, 3, 1], [5, 4, 3, 2, 1]}} the member , {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 3, 2, 5, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {}, {2}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 2, 4, 3], {[0, 0, 0, 0, 2]}, {3}], [[1, 3, 4, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {2}], [[2, 3, 4, 1], {}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[4, 1, 2, 3], {}, {1}], [[4, 1, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 3, 1], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 477, 2345, 11808, 60402, 312464] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [2, 1, 5, 4, 3]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [3, 2, 1, 5, 4]}, {[3, 4, 2, 1], [3, 4, 5, 1, 2], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [4, 5, 1, 2, 3], [5, 4, 3, 2, 1]}} the member , {[2, 1, 3, 4], [1, 2, 3, 4, 5], [3, 2, 1, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {}, {2}], [[3, 1, 2], {}, {}], [[3, 2, 1], {[0, 0, 0, 2]}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[1, 3, 4, 2], {}, {3}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {[0, 0, 0, 0, 2]}, {2}], [[2, 3, 4, 1], {}, {2}], [[2, 4, 3, 1], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {4}], [[4, 1, 2, 3], {}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2]}, {1}], [[1, 2, 4, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[1, 2, 5, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {3} ], [[1, 2, 5, 4, 3], {[0, 0, 0, 0, 0, 2]}, {3}], [[1, 3, 5, 4, 2], {[0, 0, 0, 0, 0, 2]}, {3}], [[1, 4, 2, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[1, 5, 2, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {2} ], [[1, 5, 2, 4, 3], {[0, 0, 0, 0, 0, 2]}, {2}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 2]}, {2}], [[2, 3, 5, 4, 1], {[0, 0, 0, 0, 0, 2]}, {2}], [[2, 5, 3, 4, 1], {[0, 0, 0, 0, 0, 2]}, {2}], [[4, 1, 2, 3, 5], {[0, 0, 0, 0, 0, 1]}, {5}], [[5, 1, 2, 3, 4], {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}, {1} ], [[5, 1, 2, 4, 3], {[0, 0, 0, 0, 0, 2]}, {1}], [[5, 1, 3, 4, 2], {[0, 0, 0, 0, 0, 2]}, {1}], [[5, 2, 3, 4, 1], {[0, 0, 0, 0, 0, 2]}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 478, 2355, 11854, 60354, 309170] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [3, 2, 1, 4, 5]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [1, 2, 5, 4, 3]}, {[3, 4, 2, 1], [5, 4, 1, 2, 3], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [3, 4, 5, 2, 1], [5, 4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [1, 2, 3, 4, 5], [3, 2, 1, 4, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 2], [0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {}], [[2, 1, 3], {[0, 0, 0, 3]}, {}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {}], [[3, 2, 1], {}, {}], [[1, 3, 2, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {2}], [ [1, 4, 2, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}, {2}], [[1, 4, 3, 2], { [0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {3}], [ [2, 1, 4, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {}], [[2, 3, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {}], [[2, 4, 3, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [ [3, 1, 2, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {1}], [ [3, 1, 4, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {3}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 2, 4, 1], {[0, 0, 0, 0, 2]}, {3}], [[3, 4, 1, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2]}, {2}], [ [4, 1, 2, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0], [0, 0, 1, 0, 0]}, {1}], [[4, 1, 3, 2], { [0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 2, 3, 1], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [ [4, 3, 1, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[4, 3, 2, 1], {}, {1}], [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {3}], [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}, {3} ], [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {3} ], [[2, 4, 1, 3, 5], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {2}], [[2, 5, 1, 3, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 0]}, {2} ], [[2, 5, 1, 4, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {2} ], [[3, 1, 5, 4, 2], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 1, 2, 0, 0], [0, 0, 2, 0, 0, 1], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {3} ], [[3, 2, 5, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0]}, {3}], [[3, 5, 1, 4, 2], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0], [0, 0, 1, 0, 1, 1], [0, 0, 1, 0, 2, 0], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 0, 1, 2, 0, 0], [0, 0, 2, 0, 0, 1], [0, 0, 2, 0, 1, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0]}, {2}], [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0]}, {2}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 471, 2251, 10884, 52936, 258274] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 2, 3, 4, 5], [3, 2, 1, 5, 4]}, {[2, 1, 3, 4], [1, 2, 3, 4, 5], [2, 1, 5, 4, 3]}, {[3, 4, 2, 1], [4, 5, 1, 2, 3], [5, 4, 3, 2, 1]}, {[4, 3, 1, 2], [3, 4, 5, 1, 2], [5, 4, 3, 2, 1]}} the member , {[1, 2, 4, 3], [1, 2, 3, 4, 5], [3, 2, 1, 5, 4]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {[0, 0, 3]}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 0, 2], [0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {2}], [[2, 1, 3], {[0, 0, 0, 3]}, {}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3], [0, 0, 1, 2], [0, 0, 2, 1], [0, 0, 3, 0]}, {1}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {3}], [ [2, 1, 4, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {2}], [[3, 1, 4, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[3, 2, 1, 4], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 0, 3]}, {3}], [[3, 4, 1, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {2}], [ [4, 2, 1, 3], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[4, 3, 1, 2], { [0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0], [0, 0, 1, 0, 2], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0], [0, 0, 2, 0, 1], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0]}, {1}], [[4, 3, 2, 1], {}, {1}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 479, 2371, 12010, 61576, 317681] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 3, 2, 4, 5], [2, 1, 3, 4, 5]}, {[2, 1, 3, 4], [1, 2, 3, 5, 4], [1, 2, 4, 3, 5]}, {[3, 4, 2, 1], [5, 4, 2, 3, 1], [5, 4, 3, 1, 2]}, {[4, 3, 1, 2], [4, 5, 3, 2, 1], [5, 3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4, 5], [2, 1, 3, 4, 5]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {[0, 0, 0, 2]}, {3}], [[2, 3, 1], {[0, 0, 0, 3]}, {}], [[3, 1, 2], {[0, 0, 0, 3]}, {1}], [[3, 2, 1], {}, {1}], [[2, 3, 1, 4], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {2}], [ [2, 4, 1, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {2}], [ [3, 4, 1, 2], {[0, 0, 0, 0, 3], [0, 0, 0, 1, 2], [0, 0, 0, 2, 1], [0, 0, 0, 3, 0]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 0, 3]}, {}], [[3, 4, 2, 1, 5], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 0]}, {5} ], [[3, 5, 2, 1, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0]}, {5}], [[4, 5, 2, 1, 3], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 2, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0], [0, 0, 0, 2, 0, 0]}, {5}], [ [4, 5, 3, 1, 2], {[0, 0, 0, 0, 0, 3], [0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 2, 1], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 0, 2], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 0], [0, 0, 0, 2, 0, 1], [0, 0, 0, 2, 1, 0], [0, 0, 0, 3, 0, 0]}, {3}], [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 3]}, {3}]} Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 478, 2363, 12008, 62185, 326519] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 3, 2, 4, 5], [3, 2, 1, 4, 5]}, {[2, 1, 3, 4], [1, 2, 4, 3, 5], [1, 2, 5, 4, 3]}, {[3, 4, 2, 1], [5, 4, 1, 2, 3], [5, 4, 2, 3, 1]}, {[4, 3, 1, 2], [3, 4, 5, 2, 1], [5, 3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4, 5], [3, 2, 1, 4, 5]}, has a scheme of depth , 4 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 2]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}, {3}], [[3, 1, 4, 2], {[0, 0, 0, 0, 2]}, {3}], [[3, 2, 1, 4], {[0, 0, 0, 0, 1]}, {4}], [[3, 2, 4, 1], {[0, 0, 0, 0, 2]}, {3}], [[3, 4, 1, 2], {[0, 0, 0, 1, 2]}, {2}], [[3, 4, 2, 1], {[0, 0, 0, 0, 2]}, {2}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}], [[4, 1, 3, 2], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 1], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 1, 3], {[0, 0, 0, 0, 2]}, {1}], [[4, 2, 3, 1], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 1, 2], {[0, 0, 0, 0, 2]}, {1}], [[4, 3, 2, 1], {}, {1}] } Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 474, 2290, 11200, 55077, 271577] For the equivalence class of patterns, { {[1, 2, 4, 3], [1, 3, 2, 4, 5], [3, 2, 1, 5, 4]}, {[2, 1, 3, 4], [1, 2, 4, 3, 5], [2, 1, 5, 4, 3]}, {[3, 4, 2, 1], [4, 5, 1, 2, 3], [5, 4, 2, 3, 1]}, {[4, 3, 1, 2], [3, 4, 5, 1, 2], [5, 3, 4, 2, 1]}} the member , {[1, 2, 4, 3], [1, 3, 2, 4, 5], [3, 2, 1, 5, 4]}, has a scheme of depth , 5 here it is: {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[1, 3, 2], {[0, 0, 0, 2]}, {2}], [[2, 1, 3], {}, {}], [[2, 3, 1], {}, {}], [[3, 1, 2], {}, {1}], [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[2, 1, 4, 3], {[0, 0, 0, 0, 2]}, {3}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {2}], [[2, 4, 1, 3], {[0, 0, 0, 0, 2]}, {2}], [[3, 1, 4, 2], {[0, 0, 0, 0, 2]}, {1}], [[3, 2, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], {[0, 0, 0, 1, 2]}, {}], [[3, 4, 1, 2], {[0, 0, 0, 1, 2]}, {1}], [[3, 4, 2, 1], {[0, 0, 0, 1, 2]}, {2}], [[4, 2, 1, 3], {}, {1}], [[4, 3, 1, 2], {}, {1}], [[4, 3, 2, 1], {}, {1}], [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1} ], [[3, 2, 5, 1, 4], {[0, 0, 0, 0, 0, 2], [0, 0, 0, 1, 0, 0]}, {1} ], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 2]}, {1}], [[4, 3, 5, 1, 2], {[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2]}, {1} ], [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 1, 2], [0, 0, 0, 1, 0, 2]}, {1}] } Using the scheme, the first, , 11, terms are [1, 1, 2, 6, 23, 101, 479, 2372, 12032, 61856, 320409] Warning, computation interrupted ############################################################################################################################### ############################################################################################################################### >VatterR4S5(1,2,100,4,2); ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, PATTERNS OF LENGTH 4 AND, 2, PATTERNS OF LENGTH 5 Theorem, 1 The enumeration scheme of permutations avoiding {[2, 1, 3, 4], [1, 2, 3, 5, 4], [1, 2, 5, 3, 4]} is {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [[2, 3, 1], {}, {2}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 2, 4, 3], {[0, 0, 0, 0, 2], [0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {2}], [[1, 3, 4, 2], {[0, 0, 0, 0, 2]}, {3}], [[1, 4, 2, 3], {[0, 0, 0, 0, 2]}, {2}], [[1, 4, 3, 2], {}, {2}], [[2, 3, 4, 1], {[0, 0, 0, 0, 2]}, {2}], [[2, 4, 3, 1], {}, {2}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {1}], [[4, 1, 2, 3], {[0, 0, 0, 0, 2]}, {1}], [[4, 1, 3, 2], {}, {1}], [[4, 2, 3, 1], {}, {1}]} The computation took, 443.096, seconds.