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%I #9 Jul 02 2018 16:30:09
%S 1,3,10,33,98,270,738,1935,5004,12580,31354,76444,185305,441363,
%T 1046837,2447913,5705753,13143961,30202325,68719396,156034994,
%U 351348607,789783351,1762658134,3928209272,8700183502,19244947618,42340195770,93049476310,203518456343
%N 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.
%H Alois P. Heinz, <a href="/A316405/b316405.txt">Table of n, a(n) for n = 4..1000</a>
%F a(n) = [x^n y^4] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 5)
%p end:
%p a:= n-> coeff(b(n$2), x, 4):
%p seq(a(n), n=4..33);
%Y Column k=4 of A292506.
%Y Cf. A027306, A292549.
%K nonn
%O 4,2
%A _Alois P. Heinz_, Jul 02 2018