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%I #11 Dec 01 2017 03:00:08
%S 3,15,41,120,465,1472,4667,16230,53266,173851,584543,1934414,6378634,
%T 21232506,70378723,232896476,772967540,2562676394,8490559710,
%U 28155930393,93345299815,309390211243,1025742299033,3400526966741,11272379148340
%N Number of n X 3 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1's.
%C Column 3 of A295943.
%H R. H. Hardin, <a href="/A295938/b295938.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A295938/a295938.pdf">Maple-assisted proof of formula</a>
%F Empirical: a(n) = a(n-1) + 3*a(n-2) + 18*a(n-3) + a(n-4) - 19*a(n-5) - 36*a(n-6) - 13*a(n-7) + 5*a(n-8) + 10*a(n-9).
%F Empirical formula confirmed by _Robert Israel_, Nov 30 2017 (see link).
%e Some solutions for n=7:
%e 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0
%e 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0
%e 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1
%e 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0
%e 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0
%e 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0
%e 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0
%Y Cf. A295943.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2017