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

5,2

Links

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

Formula

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

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);

Crossrefs

Column k=5 of A292506.

Cf. A027306, A292549.

Sequence in context: A316404 A333027 A316405 * A316407 A316408 A316409

Adjacent sequences: A316403 A316404 A316405 * A316407 A316408 A316409

Keyword

nonn

Author

Alois P. Heinz, Jul 02 2018

Status

approved