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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.
3
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
Alois P. Heinz, Rows n = 0..200, flattened (first 16 rows from Chai Wah Wu)
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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Mar 25 2014
EXTENSIONS
More terms from Chai Wah Wu, Sep 12 2014
STATUS
approved