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%I #9 Apr 11 2023 13:38:12
%S 3,11,34,116,391,1304,4374,14645,49051,164353,550580,1844483,6179157,
%T 20700471,69348050,232320799,778290532,2607326895,8734723380,
%U 29261921589,98029444240,328405359664,1100180474788,3685680030204,12347280822238
%N Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 3 or 4 1's.
%C Column 3 of A295551.
%H R. H. Hardin, <a href="/A295546/b295546.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A295546/a295546.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 5*a(n-1) -6*a(n-2) +2*a(n-3) -3*a(n-4) +12*a(n-5) -24*a(n-6) +a(n-7) +17*a(n-8) -3*a(n-9) +6*a(n-10) +8*a(n-11) +5*a(n-12) -15*a(n-13) +12*a(n-14) -9*a(n-15) +2*a(n-16) -a(n-17).
%F Empirical formula confirmed by _Robert Israel_, Nov 23 2017 (see link).
%e Some solutions for n=5
%e ..1..0..0. .0..0..1. .1..0..1. .0..1..0. .1..1..1. .0..0..0. .1..0..1
%e ..1..0..0. .0..0..1. .1..0..1. .1..1..1. .0..1..0. .0..1..0. .1..0..1
%e ..0..0..0. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .1..1..1. .0..0..0
%e ..0..1..0. .1..1..0. .1..1..0. .0..0..1. .1..1..0. .0..0..0. .0..1..0
%e ..1..1..1. .0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0. .1..1..1
%Y Cf. A295551.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 23 2017
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