%I #8 May 17 2023 12:14:53
%S 3,3,5,8,14,24,40,68,116,196,332,564,956,1620,2748,4660,7900,13396,
%T 22716,38516,65308,110740,187772,318388,539868,915412,1552188,2631924,
%U 4462748,7567124,12830972,21756468,36890716,62552660,106065596,179847028
%N Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.
%C Column 3 of A303719.
%H R. H. Hardin, <a href="/A303714/b303714.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +2*a(n-3) for n>4.
%F Empirical g.f.: 3*x-x^2*(3+2*x+3*x^2)/(-1+x+2*x^3). - _R. J. Mathar_, Apr 30 2018
%e Some solutions for n=5
%e ..0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%e ..0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..0. .0..0..1. .0..0..0
%e ..1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..1
%e ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%e ..0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..1..0. .0..1..0. .0..0..0
%Y Cf. A303719.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 29 2018
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