A268761 Number of n X 3 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

2, 15, 56, 223, 762, 2607, 8500, 27411, 86622, 270955, 838224, 2573015, 7841538, 23759463, 71619436, 214933915, 642504870, 1914023267, 5684288136, 16834582623, 49732758858, 146587890015, 431177727396, 1265883329827, 3710027613934

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*(2 + 7*x - 8*x^2 + x^3) / (1 - 2*x - 3*x^2 + 2*x^3)^2. - Colin Barker, Jan 14 2019

Example

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

Crossrefs

Column 3 of A268766.

Sequence in context: A056078 A142861 A305673 * A088979 A265909 A034571

Adjacent sequences: A268758 A268759 A268760 * A268762 A268763 A268764

Keyword

nonn

Author

R. H. Hardin, Feb 13 2016

Status

approved