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%I #8 Feb 24 2019 11:03:54
%S 5,21,69,258,963,3493,12860,47305,173498,637397,2341283,8597415,
%T 31576458,115970574,425911328,1564226500,5744847726,21098720647,
%U 77488048294,284585727060,1045180704781,3838572624574,14097695093525,51775756521020
%N Number of n X 3 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.
%H R. H. Hardin, <a href="/A296720/b296720.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 4*a(n-3) - 19*a(n-4) - 14*a(n-5) + 9*a(n-6) + 14*a(n-7) + 6*a(n-8) - 3*a(n-9) - 2*a(n-10).
%F Empirical g.f.: x*(5 + 6*x - 9*x^2 - 32*x^3 - 7*x^4 + 23*x^5 + 20*x^6 + 3*x^7 - 5*x^8 - 2*x^9) / ((1 - x)*(1 - 2*x - 5*x^2 - 9*x^3 + 10*x^4 + 24*x^5 + 15*x^6 + x^7 - 5*x^8 - 2*x^9)). - _Colin Barker_, Feb 24 2019
%e Some solutions for n=5:
%e ..1..0..0. .0..0..0. .0..1..0. .1..1..0. .0..1..0. .1..1..0. .0..0..0
%e ..0..0..1. .1..0..0. .0..1..1. .1..0..0. .0..0..0. .1..0..0. .1..0..1
%e ..0..1..1. .0..0..0. .0..0..0. .0..0..1. .0..1..1. .0..0..1. .0..0..0
%e ..0..1..1. .1..1..1. .1..1..0. .0..1..1. .0..1..0. .1..0..0. .0..0..0
%e ..0..1..0. .1..0..1. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .1..0..1
%Y Column 3 of A296725.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2017
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