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%I #7 Jan 18 2019 15:00:33
%S 7,27,123,537,2343,10167,43959,189465,814359,3491691,14937987,
%T 63778065,271799175,1156345287,4911870063,20834207313,88251723687,
%U 373358554971,1577691954507,6659543294313,28081651307943,118299768626103
%N Number of n X 3 binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.
%H R. H. Hardin, <a href="/A269070/b269070.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 10*a(n-1) - 31*a(n-2) + 24*a(n-3) + 21*a(n-4) - 18*a(n-5) - 9*a(n-6).
%F Empirical g.f.: x*(7 - 43*x + 70*x^2 - 24*x^3 - 9*x^4 - 9*x^5) / (1 - 5*x + 3*x^2 + 3*x^3)^2. - _Colin Barker_, Jan 18 2019
%e Some solutions for n=4:
%e ..0..0..0. .0..0..1. .0..1..0. .1..0..1. .1..0..1. .1..0..0. .1..0..1
%e ..0..0..0. .0..1..0. .1..0..0. .0..0..0. .0..0..0. .1..0..1. .0..0..0
%e ..1..0..0. .0..0..0. .1..0..0. .1..0..0. .0..1..0. .0..0..0. .0..0..0
%e ..1..0..1. .1..0..1. .0..0..1. .0..0..1. .1..0..0. .0..0..0. .1..1..0
%Y Column 3 of A269075.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 19 2016