A269137 Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

16, 148, 1164, 8532, 59916, 408596, 2727564, 17914580, 116170764, 745617300, 4745165964, 29984668756, 188330955276, 1176750424852, 7319499656844, 45347466532308, 279961285570572, 1722988944076436, 10574188575966348

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 38*a(n-2) + 12*a(n-3) - a(n-4) for n>5.

Empirical g.f.: 4*x*(4 - 11*x - x^2 - x^3 + x^4) / (1 - 6*x + x^2)^2. - Colin Barker, Jan 19 2019

Example

Some solutions for n=4:
..2..0. .3..3. .1..0. .2..2. .3..0. .2..1. .0..0. .0..1. .3..3. .0..1
..2..2. .1..1. .1..1. .2..3. .1..0. .0..1. .0..1. .0..0. .1..1. .0..3
..3..1. .1..3. .3..1. .0..1. .0..1. .1..1. .1..1. .1..2. .1..1. .1..1
..1..1. .3..3. .0..0. .0..1. .0..0. .3..1. .0..2. .0..2. .3..0. .1..0

Crossrefs

Column 2 of A269143.

Sequence in context: A214513 A254952 A178259 * A155657 A135458 A000486

Adjacent sequences: A269134 A269135 A269136 * A269138 A269139 A269140

Keyword

nonn

Author

R. H. Hardin, Feb 20 2016

Status

approved