A316408 Number of multisets of exactly seven 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, 6297, 16989, 44828, 117352, 302429, 773496, 1954845, 4905939, 12195457, 30123762, 73825711, 179891662, 435427632, 1048510795, 2510267189, 5981859208, 14182293004, 33482368279, 78690956088, 184229429914, 429570180998

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

a(n) = [x^n y^7] 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, 8)
    end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=7..35);

Crossrefs

Column k=7 of A292506.

Cf. A027306, A292549.

Sequence in context: A316405 A316406 A316407 * A316409 A316410 A316411

Adjacent sequences: A316405 A316406 A316407 * A316409 A316410 A316411

Keyword

nonn

Author

Alois P. Heinz, Jul 02 2018

Status

approved