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.

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

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