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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.
2
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
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.
Sequence in context: A080697 A316404 A333027 * A316406 A316407 A316408
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2018
STATUS
approved