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 A239103 Triangular array read by rows, arising from enumeration of binary words containing n 0's and k 1's that avoid the pattern 1011101. 3
 1, 2, 1, 6, 3, 1, 20, 10, 4, 1, 70, 35, 15, 5, 1, 248, 123, 54, 20, 6, 1, 894, 442, 198, 78, 26, 7, 1, 3264, 1611, 732, 300, 108, 33, 8, 1, 12036, 5936, 2727, 1150, 437, 146, 41, 9, 1, 44722, 22047, 10214, 4398, 1736, 617, 192, 50, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 Triangle begins 1 2 1 6 3 1 20 10 4 1 70 35 15 5 1 248 123 54 20 6 1 894 442 198 78 26 7 1 3264 1611 732 300 108 33 8 1 ... PROG (Python) from itertools import combinations A239103_list = [] for n in range(16): ....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 '1011101' in ''.join(d): ................c += 1 ........A239103_list.append(c) # Chai Wah Wu, Sep 12 2014 CROSSREFS See A046899 for a closely related triangle. Cf. A246971. Sequence in context: A180281 A187888 A239102 * A246971 A092392 A128741 Adjacent sequences:  A239100 A239101 A239102 * A239104 A239105 A239106 KEYWORD nonn,tabl,more AUTHOR N. J. A. Sloane, Mar 25 2014 EXTENSIONS More terms from Chai Wah Wu, Sep 12 2014 STATUS approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)