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A212234
Number of 0..2 arrays of length 1+2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle)
1
14, 124, 1113, 10002, 89911, 808403, 7269626, 65380788, 588072207, 5289869433, 47586806448, 428105244789, 3851528519268, 34652238703192, 311776035394625, 2805210936456962, 25240510718260791, 227111596463339585
OFFSET
1,1
COMMENTS
Row 2 of A212232
LINKS
FORMULA
a(n) = [x^(2*n)] (1+z+z^2)^(2*n-1)*(1+3*z+5*z^2)/(1-z). - Robert Israel, Mar 06 2018
EXAMPLE
Some solutions for n=3
..0....0....0....1....1....0....1....0....1....0....1....1....0....0....2....1
..0....0....0....1....0....2....1....2....0....2....1....0....0....1....1....1
..1....0....2....0....1....0....0....2....0....1....1....1....0....0....0....2
..2....1....1....2....1....0....2....0....0....0....2....2....2....0....1....0
..0....1....0....1....2....1....0....0....1....2....1....0....1....1....2....1
..2....1....1....0....1....1....1....0....2....0....0....0....0....1....0....0
..0....0....0....2....0....2....1....2....1....1....0....1....0....1....0....2
MAPLE
f:= proc(n) local S;
S:= series((1+z+z^2)^(2*n-1)*(1+3*z+5*z^2)/(1-z), z, 2*n+1);
coeff(S, z, 2*n);
end proc:
map(f, [$1..50]); # Robert Israel, Mar 06 2018
CROSSREFS
Sequence in context: A125377 A147590 A167602 * A155637 A126535 A222647
KEYWORD
nonn
AUTHOR
R. H. Hardin May 06 2012
STATUS
approved