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

1,1

Links

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

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

Example

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

Crossrefs

Column 3 of A268789.

Sequence in context: A182876 A056074 A320685 * A338088 A155715 A307851

Adjacent sequences: A268781 A268782 A268783 * A268785 A268786 A268787

Keyword

nonn

Author

R. H. Hardin, Feb 13 2016

Status

approved