A316409 Number of multisets of exactly eight 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, 826, 2320, 6342, 17133, 45504, 119580, 310416, 798196, 2033289, 5136803, 12878647, 32056022, 79277444, 194822462, 476101571, 1156995495, 2797803485, 6731961588, 16126628466, 38459836055, 91355046531, 216126089962, 509445131238

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Formula

a(n) = [x^n y^8] 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, 9)
    end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=8..36);

Crossrefs

Column k=8 of A292506.

Cf. A027306, A292549.

Sequence in context: A316406 A316407 A316408 * A316410 A316411 A292549

Adjacent sequences: A316406 A316407 A316408 * A316410 A316411 A316412

Keyword

nonn

Author

Alois P. Heinz, Jul 02 2018

Status

approved