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

Author

Alois P. Heinz, Jul 02 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=6 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, 7)
    end:
a:= n-> coeff(b(n$2), x, 6):
seq(a(n), n=6..34);

Formula

a(n) = [x^n y^6] 1/Product_{j>=1} (1-y*x^j)^A027306(j).