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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A212232

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences:  A212231 A212232 A212233 * A212235 A212236 A212237

KEYWORD

nonn

AUTHOR

R. H. Hardin May 06 2012

STATUS

approved

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Last modified February 24 13:13 EST 2021. Contains 341569 sequences. (Running on oeis4.)