A251144 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

53, 87, 143, 247, 433, 777, 1413, 2607, 4863, 9167, 17433, 33417, 64493, 125207, 244303, 478727, 941473, 1857097, 3672373, 7277087, 14444703, 28712287, 57137993, 113812297, 226874333, 452534727, 903105263, 1803032407, 3600922513

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5)..

Empirical g.f.: x*(53 - 72*x - 118*x^2 + 83*x^3 + 74*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

Example

Some solutions for n=4:
..2..1..1..0....0..1..1..1....1..1..1..1....1..0..2..1....0..1..0..1
..1..0..2..1....1..2..0..2....1..1..1..1....2..1..1..0....2..1..2..1
..2..1..1..0....0..1..1..1....2..0..2..0....0..1..1..2....0..1..0..1
..1..0..2..1....2..1..1..1....1..1..1..1....1..2..0..1....1..2..1..2
..2..1..1..0....0..1..1..1....1..1..1..1....0..1..1..2....0..1..0..1

Crossrefs

Column 3 of A251149.

Sequence in context: A001836 A144939 A118149 * A214230 A272367 A119289

Adjacent sequences: A251141 A251142 A251143 * A251145 A251146 A251147

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved