A316405 Number of multisets of exactly four nonempty binary words with a total of n letters such that no word has a majority of 0's.

1, 3, 10, 33, 98, 270, 738, 1935, 5004, 12580, 31354, 76444, 185305, 441363, 1046837, 2447913, 5705753, 13143961, 30202325, 68719396, 156034994, 351348607, 789783351, 1762658134, 3928209272, 8700183502, 19244947618, 42340195770, 93049476310, 203518456343

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Formula

a(n) = [x^n y^4] 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, 5)
    end:
a:= n-> coeff(b(n$2), x, 4):
seq(a(n), n=4..33);

Crossrefs

Column k=4 of A292506.

Cf. A027306, A292549.

Sequence in context: A080697 A316404 A333027 * A316406 A316407 A316408

Adjacent sequences: A316402 A316403 A316404 * A316406 A316407 A316408

Keyword

nonn

Author

Alois P. Heinz, Jul 02 2018

Status

approved