A269188 Number of n X 2 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

16, 108, 708, 4476, 27684, 168252, 1008804, 5983164, 35170980, 205214268, 1189853604, 6861684156, 39384946596, 225136169532, 1282284719268, 7279841963964, 41210177357988, 232678853273148, 1310648830057380

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 20*a(n-3) - 4*a(n-4) for n>5.

Empirical g.f.: 4*x*(4 - 13*x - 9*x^2 - 4*x^3 + 4*x^4) / (1 - 5*x - 2*x^2)^2. - Colin Barker, Jan 19 2019

Example

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

Crossrefs

Column 2 of A269194.

Sequence in context: A260357 A056001 A163725 * A165558 A337391 A250425

Adjacent sequences: A269185 A269186 A269187 * A269189 A269190 A269191

Keyword

nonn

Author

R. H. Hardin, Feb 20 2016

Status

approved