A283410 Number of n X 3 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors.

8, 61, 416, 2944, 20744, 146228, 1030788, 7266120, 51219756, 361053936, 2545110952, 17940781184, 126466639652, 891477956620, 6284131129240, 44297566481868, 312258664857680, 2201147411081008, 15516142450416040

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 13*a(n-2) + 10*a(n-3) + a(n-4) + 2*a(n-5) for n>7.

Empirical g.f.: x*(1 + x)*(8 + 13*x - 6*x^2 - 3*x^3 + x^4 - 2*x^5) / (1 - 5*x - 13*x^2 - 10*x^3 - x^4 - 2*x^5). - Colin Barker, Feb 21 2019

Example

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

Crossrefs

Column 3 of A283415.

Sequence in context: A071401 A247535 A283852 * A081907 A278596 A190976

Adjacent sequences: A283407 A283408 A283409 * A283411 A283412 A283413

Keyword

nonn

Author

R. H. Hardin, Mar 07 2017

Status

approved