cp's OEIS Frontend

A316404 Number of multisets of exactly three nonempty binary words with a total of n letters such that no word has a majority of 0's.

%I A316404 #9 Jul 02 2018 16:29:49
%S A316404 1,3,10,33,83,230,568,1451,3439,8384,19390,45708,103770,238855,534400,
%T A316404 1208485,2672043,5959769,13051586,28792488,62551270,136760659,
%U A316404 295115360,640444498,1374092646,2963283862,6326402780,13569867602,28846140436,61586022487,130422459008
%N A316404 Number of multisets of exactly three nonempty binary words with a total of n letters such that no word has a majority of 0's.
%H A316404 Alois P. Heinz, <a href="/A316404/b316404.txt">Table of n, a(n) for n = 3..1000</a>
%F A316404 a(n) = [x^n y^3] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p A316404 g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p A316404 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p A316404        binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 4)
%p A316404     end:
%p A316404 a:= n-> coeff(b(n$2), x, 3):
%p A316404 seq(a(n), n=3..33);
%Y A316404 Column k=3 of A292506.
%Y A316404 Cf. A027306, A292549.
%K A316404 nonn
%O A316404 3,2
%A A316404 _Alois P. Heinz_, Jul 02 2018