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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
OFFSET
0,2
COMMENTS
This is a Riordan array.
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
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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Sep 11 2014
EXTENSIONS
More terms from Chai Wah Wu, Sep 12 2014
STATUS
approved