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)

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

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