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

Author

N. J. A. Sloane, Sep 11 2014

Keywords

• nonn
• tabl

Comments

This is a Riordan array.

Examples

			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;
  ...
		

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).

Crossrefs

Cf. A239103.

Programs

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

Extensions

More terms from Chai Wah Wu, Sep 12 2014