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

Author

N. J. A. Sloane, Mar 25 2014

Keywords

• nonn
• tabl

Examples

			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
  ...
		

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

See A046899 for a closely related triangle. Cf. A246971.

Programs

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

Extensions

More terms from Chai Wah Wu, Sep 12 2014