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.

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

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