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%I #10 Dec 05 2017 04:09:31
%S 1,3,6,9,26,74,163,535,1735,4960,15935,51598,159682,507871,1626269,
%T 5134567,16304686,51939793,164789906,523362014,1664172607,5285951875,
%U 16791701819,53363480620,169541243631,538639046154,1711496670766
%N Number of n X 3 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1's.
%C Column 3 of A296115.
%H R. H. Hardin, <a href="/A296110/b296110.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A296110/a296110.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = a(n-1) +3*a(n-2) +15*a(n-3) +2*a(n-4) -18*a(n-5) -36*a(n-6) -21*a(n-7) -25*a(n-8) +3*a(n-9) +11*a(n-10) +6*a(n-11).
%F Empirical formula verified by _Robert Israel_, Dec 04 2017 (see link).
%e Some solutions for n=7
%e ..0..0..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..1..1. .0..1..1
%e ..0..1..1. .0..1..1. .0..1..1. .0..1..1. .1..1..0. .0..1..1. .0..1..1
%e ..0..1..1. .0..1..1. .0..1..1. .0..1..0. .1..1..0. .0..0..1. .1..0..0
%e ..0..0..1. .0..0..0. .0..0..1. .0..1..1. .0..0..0. .0..1..1. .1..1..0
%e ..0..1..0. .1..1..0. .0..1..0. .0..1..1. .0..1..0. .0..0..1. .0..1..0
%e ..1..1..1. .1..1..0. .1..1..0. .0..0..0. .1..1..1. .1..1..0. .0..1..1
%e ..0..1..0. .0..0..0. .1..1..0. .0..0..0. .0..1..0. .1..1..0. .0..1..1
%Y Cf. A296115.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 04 2017
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