A283409 Number of n X 2 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors.

4, 16, 61, 236, 912, 3525, 13624, 52656, 203513, 786568, 3040048, 11749641, 45411804, 175514464, 678355061, 2621810068, 10133171296, 39164225421, 151367869744, 585029621920, 2261111681777, 8739089177552, 33776164295072

Offset

1,1

Links

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

Formula

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

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

Example

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

Crossrefs

Column 2 of A283415.

Sequence in context: A206570 A206790 A283858 * A192468 A364921 A365835

Adjacent sequences: A283406 A283407 A283408 * A283410 A283411 A283412

Keyword

nonn

Author

R. H. Hardin, Mar 07 2017

Status

approved