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%I #16 Sep 13 2014 15:32:47
%S 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,
%T 26,7,1,3264,1611,732,300,108,33,8,1,12036,5936,2727,1150,437,146,41,
%U 9,1,44722,22047,10214,4398,1736,617,192,50,10,1
%N Triangular array read by rows, arising from enumeration of binary words containing n 0's and k 1's that avoid the pattern 1011101.
%H Chai Wah Wu, <a href="/A239103/b239103.txt">Rows n = 0..15, flattened</a>
%H D. Baccherini, D. Merlini, R. Sprugnoli, <a href="http://dx.doi.org/10.1016/j.disc.2006.07.023">Binary words excluding a pattern and proper Riordan arrays</a>, Discrete Math. 307 (2007), no. 9-10, 1021--1037. MR2292531 (2008a:05003).
%e Triangle begins
%e 1
%e 2 1
%e 6 3 1
%e 20 10 4 1
%e 70 35 15 5 1
%e 248 123 54 20 6 1
%e 894 442 198 78 26 7 1
%e 3264 1611 732 300 108 33 8 1
%e ...
%o (Python)
%o from itertools import combinations
%o A239103_list = []
%o for n in range(16):
%o ....for k in range(n,-1,-1):
%o ........c, d0 = 0, ['0']*(n+k)
%o ........for x in combinations(range(n+k),n):
%o ............d = list(d0)
%o ............for i in x:
%o ................d[i] = '1'
%o ............if not '1011101' in ''.join(d):
%o ................c += 1
%o ........A239103_list.append(c) # _Chai Wah Wu_, Sep 12 2014
%Y See A046899 for a closely related triangle. Cf. A246971.
%K nonn,tabl,more
%O 0,2
%A _N. J. A. Sloane_, Mar 25 2014
%E More terms from _Chai Wah Wu_, Sep 12 2014
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