A316407 Number of multisets of exactly six 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, 2284, 6185, 16471, 43156, 111446, 284517, 717486, 1793081, 4434929, 10887761, 26495243, 64069055, 153761086, 366992020, 870215947, 2053484109, 4818104922, 11256015936, 26164409278, 60583174348, 139655557194, 320805463602

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

a(n) = [x^n y^6] 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, 7)
    end:
a:= n-> coeff(b(n$2), x, 6):
seq(a(n), n=6..34);

Crossrefs

Column k=6 of A292506.

Cf. A027306, A292549.

Sequence in context: A333027 A316405 A316406 * A316408 A316409 A316410

Adjacent sequences: A316404 A316405 A316406 * A316408 A316409 A316410

Keyword

nonn

Author

Alois P. Heinz, Jul 02 2018

Status

approved