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Number of n X 3 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.
1

%I #9 Dec 04 2017 02:55:23

%S 3,13,30,91,280,785,2319,6816,19796,57991,169568,495194,1447954,

%T 4232103,12368507,36153433,105669553,308852290,902733635,2638539016,

%U 7712024753,22541039139,65883825698,192567918338,562845326527,1645106908766

%N Number of n X 3 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

%C Column 3 of A296019.

%H R. H. Hardin, <a href="/A296014/b296014.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A296014/a296014.pdf">Maple-assisted proof of formula</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-2) + 11*a(n-3) - 3*a(n-4) - 11*a(n-5) - 27*a(n-6) + a(n-7) + 6*a(n-8) + 7*a(n-9) + a(n-10).

%F Empirical formula confirmed by _Robert Israel_, Dec 03 2017 (see link).

%e Some solutions for n=5:

%e 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0

%e 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0

%e 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

%e 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0

%e 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1

%Y Cf. A296019.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 02 2017