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%I #13 Nov 26 2017 13:59:45
%S 5,20,83,338,1425,6080,26249,114298,501405,2211832,9799095,43554852,
%T 194071913,866357594,3872915901,17331341902,77618369051,347815345000,
%U 1559266623743,6992481752642,31365036076887,140713926545922
%N Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1s.
%C Column 3 of A295606.
%H R. H. Hardin, <a href="/A295601/b295601.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A295601/a295601_1.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = 7*a(n-1) - 9*a(n-2) - 11*a(n-3) + 14*a(n-4) - 53*a(n-5) + 19*a(n-6) + 42*a(n-7) - 23*a(n-8) + 72*a(n-9) + 36*a(n-10) - 25*a(n-11) - 12*a(n-12).
%F Formula confirmed by _Robert Israel_, Nov 24 2017 (see link).
%e Some solutions for n=7:
%e 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0
%e 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0
%e 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0
%e 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0
%e 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0
%e 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1
%e 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0
%Y Cf. A295606.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 24 2017
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