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%I #9 Apr 20 2021 15:15:12
%S 1,4,10,27,102,345,1162,4072,14224,49604,173594,607485,2125150,
%T 7436416,26022865,91060814,318652127,1115077417,3902040209,
%U 13654599697,47782246634,167206840944,585115414586,2047524354146,7165006769433
%N Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.
%C Column 3 of A295213.
%H R. H. Hardin, <a href="/A295208/b295208.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A295208/a295208.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 5*a(n-1) -7*a(n-2) +10*a(n-3) -18*a(n-4) +18*a(n-5) -5*a(n-6) -15*a(n-7) +7*a(n-8) -9*a(n-9) +10*a(n-10) -2*a(n-11) +a(n-12).
%F Empirical formula confirmed by _Robert Israel_, Nov 17 2017 (see link).
%e Some solutions for n=7
%e ..1..1..1. .0..1..1. .0..1..1. .1..1..1. .0..1..1. .0..1..1. .1..1..0
%e ..1..1..1. .0..1..1. .0..1..1. .1..0..1. .0..1..1. .0..1..1. .1..1..0
%e ..1..0..1. .0..0..0. .0..1..0. .1..1..1. .0..1..1. .1..1..1. .1..0..0
%e ..1..0..1. .1..1..0. .0..1..0. .1..1..0. .0..0..0. .1..0..1. .1..0..0
%e ..1..1..1. .1..1..0. .1..1..0. .0..0..0. .0..0..0. .1..0..1. .1..1..0
%e ..0..1..1. .1..1..0. .1..1..0. .1..1..1. .0..1..1. .1..1..1. .1..1..0
%e ..0..0..0. .0..0..0. .1..1..0. .1..1..1. .0..1..1. .0..1..1. .0..0..0
%Y Cf. A295213.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 17 2017
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