

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
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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. 910, 10211037. 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



