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 A246971 Triangular array read by rows, arising from enumeration of binary words containing n 0's and k 1's that avoid the pattern 0100010. 2
 1, 2, 1, 6, 3, 1, 20, 10, 4, 1, 70, 35, 15, 5, 1, 248, 126, 56, 21, 6, 1, 894, 457, 210, 84, 28, 7, 1, 3264, 1674, 786, 330, 120, 36, 8, 1, 12036, 6183, 2947, 1280, 495, 165, 45, 9, 1, 44722, 22997, 11080, 4933, 1994, 715, 220, 55, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is a Riordan array. LINKS Chai Wah Wu, Rows n = 0..15, flattened D. Baccherini, D. Merlini, R. Sprugnoli, Binary words excluding a pattern and proper Riordan arrays, Discrete Math. 307 (2007), no. 9-10, 1021--1037. MR2292531 (2008a:05003). EXAMPLE Array begins: 1, 2,1, 6,3,1, 20,10,4,1, 70,35,15,5,1, 248,126,56,21,6,1, 894,457,210,84,28,7,1, 3264,1674,786,330,120,36,8,1, ... PROG (Python) from itertools import combinations A246971_list = [] for n in range(10): ....for k in range(n, -1, -1): ........c, d0 = 0, ['0']*(n+k) ........for x in combinations(range(n+k), n): ............d = list(d0) ............for i in x: ................d[i] = '1' ............if not '0100010' in ''.join(d): ................c += 1 ........A246971_list.append(c) # Chai Wah Wu, Sep 12 2014 CROSSREFS Cf. A239103. Sequence in context: A187888 A239102 A239103 * A092392 A128741 A175757 Adjacent sequences: A246968 A246969 A246970 * A246972 A246973 A246974 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Sep 11 2014 EXTENSIONS More terms from Chai Wah Wu, Sep 12 2014 STATUS approved

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Last modified November 28 05:25 EST 2023. Contains 367394 sequences. (Running on oeis4.)