A283488 Number of n X 2 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 2, 12, 64, 312, 1460, 6624, 29394, 128264, 552384, 2353888, 9943896, 41703328, 173822258, 720671156, 2974187392, 12224902712, 50069348140, 204417445696, 832198630882, 3379257614032, 13690075484800, 55344113101440

Offset

1,3

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 16*a(n-3) - 13*a(n-4) - 10*a(n-5) - 13*a(n-6) - 8*a(n-7) - 3*a(n-8) - 2*a(n-9) - a(n-10).

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

Example

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

Crossrefs

Column 2 of A283494.

Sequence in context: A330387 A368760 A272363 * A006646 A087635 A180038

Adjacent sequences: A283485 A283486 A283487 * A283489 A283490 A283491

Keyword

nonn

Author

R. H. Hardin, Mar 08 2017

Status

approved