A268761 - OEIS

%I #8 Jan 14 2019 09:02:01

%S 2,15,56,223,762,2607,8500,27411,86622,270955,838224,2573015,7841538,

%T 23759463,71619436,214933915,642504870,1914023267,5684288136,

%U 16834582623,49732758858,146587890015,431177727396,1265883329827,3710027613934

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

%H R. H. Hardin, <a href="/A268761/b268761.txt">Table of n, a(n) for n = 1..210</a>

%F 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).

%F 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

%e Some solutions for n=4:

%e ..1..0..1. .0..1..1. .1..0..0. .1..0..1. .0..1..0. .1..1..0. .0..0..0

%e ..0..0..1. .0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0

%e ..0..0..0. .0..0..0. .1..0..1. .0..1..0. .0..0..0. .0..0..0. .1..0..1

%e ..0..0..0. .0..0..0. .0..0..1. .0..0..1. .0..0..1. .0..1..0. .1..0..0

%Y Column 3 of A268766.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2016