A269006 Number of n X 3 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

2, 8, 46, 224, 1066, 4952, 22654, 102416, 458674, 2038328, 8999374, 39512144, 172645498, 751190504, 3256354942, 14069557088, 60610482274, 260412843944, 1116181074286, 4773749750528, 20376053362762, 86813692172216

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 31*a(n-2) + 24*a(n-3) + 21*a(n-4) - 18*a(n-5) - 9*a(n-6).

Empirical g.f.: 2*x*(1 - x)*(1 - 3*x)*(1 - 2*x + 3*x^2) / (1 - 5*x + 3*x^2 + 3*x^3)^2. - Colin Barker, Jan 18 2019

Example

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

Crossrefs

Column 3 of A269011.

Sequence in context: A003091 A119501 A183277 * A266507 A202081 A258315

Adjacent sequences: A269003 A269004 A269005 * A269007 A269008 A269009

Keyword

nonn

Author

R. H. Hardin, Feb 17 2016

Status

approved