A316406 Number of multisets of exactly five nonempty binary words with a total of n letters such that no word has a majority of 0's.

1, 3, 10, 33, 98, 291, 798, 2200, 5804, 15275, 39014, 99214, 247065, 612090, 1492837, 3622213, 8682565, 20711303, 48923317, 115048586, 268374750, 623503251, 1438753371, 3307821910, 7560955644, 17225642730, 39047321794, 88249150462, 198572820286, 445610719629

Offset: 5

Author

Alois P. Heinz, Jul 02 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000

Crossrefs

Column k=5 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, 6)
    end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=5..34);

Formula

a(n) = [x^n y^5] 1/Product_{j>=1} (1-y*x^j)^A027306(j).