A297390 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

3, 9, 19, 57, 139, 369, 963, 2489, 6523, 16929, 44147, 114953, 299307, 779697, 2030243, 5287833, 13770971, 35864001, 93402579, 243249193, 633503627, 1649849553, 4296752131, 11190160825, 29142853947, 75897603297, 197662332211

Offset: 1

Author

R. H. Hardin, Dec 29 2017

Keywords

• nonn

Examples

			Some solutions for n=5:
..0..1..0. .1..1..0. .0..1..1. .0..0..1. .0..1..1. .0..0..0. .1..0..0
..0..0..1. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .1..0..0. .0..1..0
..1..0..0. .0..1..1. .0..1..1. .0..0..0. .1..1..0. .0..1..0. .0..0..0
..0..1..0. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..0
..0..0..0. .1..1..0. .0..1..1. .1..0..0. .1..1..0. .1..1..0. .0..1..1
		

Links

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

Crossrefs

Column 3 of A297395.

Formula

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

Empirical g.f.: x*(1 + 2*x)*(3 - 2*x^2) / (1 - x - 4*x^2 - 2*x^3 + 4*x^4). - Colin Barker, Feb 28 2019