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Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
1

%I #8 Jan 15 2019 09:14:26

%S 1,5,17,48,131,338,850,2091,5061,12095,28608,67095,156244,361652,

%T 832757,1908885,4358285,9915728,22489147,50862918,114743814,258261695,

%U 580072917,1300393467,2910078592,6501783407,14504787560,32313853992,71896385513

%N Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

%H R. H. Hardin, <a href="/A268783/b268783.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 + 3*x + 4*x^2 + x^3) / (1 - x - 2*x^2 - x^3)^2. - _Colin Barker_, Jan 15 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A268789.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 13 2016