cp's OEIS Frontend

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.

%I A316407 #9 Jul 02 2018 16:30:51
%S A316407 1,3,10,33,98,291,826,2284,6185,16471,43156,111446,284517,717486,
%T A316407 1793081,4434929,10887761,26495243,64069055,153761086,366992020,
%U A316407 870215947,2053484109,4818104922,11256015936,26164409278,60583174348,139655557194,320805463602
%N 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.
%H A316407 Alois P. Heinz, <a href="/A316407/b316407.txt">Table of n, a(n) for n = 6..1000</a>
%F A316407 a(n) = [x^n y^6] 1/Product_{j>=1} (1-y*x^j)^A027306(j).
%p A316407 g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
%p A316407 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
%p A316407        binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 7)
%p A316407     end:
%p A316407 a:= n-> coeff(b(n$2), x, 6):
%p A316407 seq(a(n), n=6..34);
%Y A316407 Column k=6 of A292506.
%Y A316407 Cf. A027306, A292549.
%K A316407 nonn
%O A316407 6,2
%A A316407 _Alois P. Heinz_, Jul 02 2018