A268784 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

2, 17, 72, 302, 1144, 4207, 14984, 52335, 179854, 610504, 2051436, 6836258, 22622554, 74418562, 243553160, 793537401, 2575357784, 8329124488, 26854438804, 86342760711, 276915214344, 886094782671, 2829527431748, 9018299661270

Offset: 1

Author

R. H. Hardin, Feb 13 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A268789.

Formula

Empirical: a(n) = 2*a(n-1) + 9*a(n-2) - 2*a(n-3) - 33*a(n-4) - 42*a(n-5) - 14*a(n-6) + 10*a(n-7) + 8*a(n-8) - a(n-10).

Empirical g.f.: x*(2 + 13*x + 20*x^2 + 9*x^3 - 8*x^4 - 10*x^5 - 4*x^6) / ((1 + x)^2*(1 - 2*x - 3*x^2 - x^3 + x^4)^2). - Colin Barker, Jan 15 2019