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%I #9 Jan 15 2019 09:09:38
%S 4,11,26,65,148,343,766,1709,3752,8195,17746,38233,81916,174767,
%T 371366,786437,1660240,3495259,7340026,15379121,32156324,67108871,
%U 139810126,290805085,603979768,1252698803,2594876066,5368709129,11095332172
%N Number of n X 2 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.
%H R. H. Hardin, <a href="/A268775/b268775.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4).
%F Conjectures from _Colin Barker_, Jan 15 2019: (Start)
%F G.f.: x*(4 + 3*x - 8*x^2 - 4*x^3) / ((1 + x)^2*(1 - 2*x)^2).
%F a(n) = ((-1)^(1+n) + 2^(2+n) + ((-1)^n+2^(1+n))*n) / 3.
%F (End)
%e Some solutions for n=4:
%e ..0..0. .0..0. .0..1. .0..1. .1..0. .0..0. .0..0. .1..0. .1..1. .0..0
%e ..0..0. .1..1. .1..0. .0..0. .0..0. .1..1. .0..0. .0..0. .0..0. .0..1
%e ..0..1. .0..0. .0..0. .1..1. .0..0. .0..0. .1..0. .0..1. .0..1. .0..0
%e ..1..0. .1..0. .1..0. .0..0. .1..0. .0..1. .1..0. .1..0. .0..0. .1..0
%Y Column 2 of A268781.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 13 2016
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