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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 July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)