A316404 Number of multisets of exactly three nonempty binary words with a total of n letters such that no word has a majority of 0's.

1, 3, 10, 33, 83, 230, 568, 1451, 3439, 8384, 19390, 45708, 103770, 238855, 534400, 1208485, 2672043, 5959769, 13051586, 28792488, 62551270, 136760659, 295115360, 640444498, 1374092646, 2963283862, 6326402780, 13569867602, 28846140436, 61586022487, 130422459008

Offset: 3

Author

Alois P. Heinz, Jul 02 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000

Crossrefs

Column k=3 of A292506.

Cf. A027306, A292549.

Programs

Maple

g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
       binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 4)
    end:
a:= n-> coeff(b(n$2), x, 3):
seq(a(n), n=3..33);

Formula

a(n) = [x^n y^3] 1/Product_{j>=1} (1-y*x^j)^A027306(j).