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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.
2
1, 3, 10, 33, 83, 230, 568, 1451, 3439, 8384, 19390, 45708, 103770, 238855, 534400, 1208485, 2672043, 5959769, 13051586, 28792488, 62551270, 136760659, 295115360, 640444498, 1374092646, 2963283862, 6326402780, 13569867602, 28846140436, 61586022487, 130422459008
OFFSET
3,2
LINKS
FORMULA
a(n) = [x^n y^3] 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, 4)
end:
a:= n-> coeff(b(n$2), x, 3):
seq(a(n), n=3..33);
CROSSREFS
Column k=3 of A292506.
Sequence in context: A174798 A042039 A080697 * A333027 A316405 A316406
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2018
STATUS
approved