A268776 Number of n X 3 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.

7, 26, 91, 316, 1031, 3354, 10615, 33344, 103339, 317958, 970515, 2945172, 8888719, 26705714, 79909167, 238257768, 708129267, 2098664158, 6203795403, 18296271036, 53845375703, 158159174410, 463734769895, 1357486034320, 3967761581627

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) - a(n-4) + 12*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(7 - 2*x - 27*x^2 + 12*x^3 + 8*x^4 - 4*x^5) / (1 - 2*x - 3*x^2 + 2*x^3)^2. - Colin Barker, Jan 15 2019

Example

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

Crossrefs

Column 3 of A268781.

Sequence in context: A372611 A279761 A245750 * A050476 A026617 A240261

Adjacent sequences: A268773 A268774 A268775 * A268777 A268778 A268779

Keyword

nonn

Author

R. H. Hardin, Feb 13 2016

Status

approved