%I #8 Jan 14 2019 08:40:19
%S 7,32,143,623,2615,10830,44067,177429,707163,2796840,10986379,
%T 42911627,166777091,645395334,2488065863,9559464281,36618142447,
%U 139888931680,533099140807,2027067051095,7692165427919,29135580083054,110168752548843
%N Number of n X 3 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
%H R. H. Hardin, <a href="/A268745/b268745.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + 8*a(n-2) - 24*a(n-3) - 38*a(n-4) + 4*a(n-5) + 12*a(n-6) - a(n-8).
%F Empirical g.f.: x*(7 + 4*x - 41*x^2 - 37*x^3 + 13*x^4 + 6*x^5 + x^6 - x^7) / (1 - 2*x - 6*x^2 + x^4)^2. - _Colin Barker_, Jan 14 2019
%e Some solutions for n=4:
%e ..1..0..1. .0..0..1. .0..0..0. .1..0..1. .0..0..0. .0..0..1. .0..1..0
%e ..1..0..0. .1..0..0. .0..0..1. .0..0..0. .0..1..0. .1..1..0. .0..0..0
%e ..0..0..0. .0..0..0. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%e ..0..0..1. .1..1..0. .0..1..1. .0..1..0. .1..1..0. .0..0..1. .0..1..0
%Y Column 3 of A268750.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 12 2016