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%I #8 Feb 23 2019 09:56:39
%S 4,12,29,85,248,664,1897,5385,14924,42180,118869,332765,937088,
%T 2635856,7400673,20815825,58523540,164457532,462389261,1299858917,
%U 3653657736,10271361928,28873923801,81164992281,228166526044,641398040884
%N Number of n X 2 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.
%H R. H. Hardin, <a href="/A296645/b296645.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 3*a(n-2) + 9*a(n-3) - 4*a(n-4) - 12*a(n-5) - 4*a(n-6).
%F Empirical g.f.: x*(4 + 8*x + 5*x^2 - 16*x^3 - 16*x^4 - 4*x^5) / (1 - x - 3*x^2 - 9*x^3 + 4*x^4 + 12*x^5 + 4*x^6). - _Colin Barker_, Feb 23 2019
%e Some solutions for n=7:
%e ..0..0. .0..1. .0..0. .0..0. .0..0. .0..0. .1..0. .1..0. .0..0. .1..0
%e ..1..0. .0..0. .0..1. .1..0. .0..0. .0..0. .0..1. .0..0. .0..1. .1..0
%e ..0..0. .1..0. .0..1. .0..0. .1..1. .0..1. .0..0. .0..1. .0..1. .0..0
%e ..1..1. .1..0. .1..1. .0..0. .1..1. .0..0. .0..0. .0..0. .1..1. .0..0
%e ..0..0. .0..0. .1..0. .0..0. .0..0. .0..1. .1..0. .0..0. .0..1. .0..0
%e ..1..1. .1..1. .0..1. .1..1. .0..0. .0..0. .0..0. .0..0. .0..1. .0..1
%e ..1..1. .1..1. .0..0. .0..0. .0..1. .1..0. .1..1. .1..1. .0..0. .0..1
%Y Column 2 of A296651.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 17 2017
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