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A295913 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.

%I A295913 #10 May 02 2023 15:24:56
%S A295913 5,13,39,115,337,993,2919,8587,25257,74289,218511,642715,1890449,
%T A295913 5560465,16355255,48106475,141497817,416194129,1224171199,3600711835,
%U A295913 10590941633,31151630513,91627743527,269508954923,792719257161,2331662118065
%N A295913 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.
%H A295913 R. H. Hardin, <a href="/A295913/b295913.txt">Table of n, a(n) for n = 1..210</a>
%F A295913 Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-4).
%F A295913 Empirical g.f.: x*(5 + 3*x - 2*x^2 - 2*x^3) / (1 - 2*x - 3*x^2 + 2*x^4). - _Colin Barker_, Feb 22 2019
%e A295913 Some solutions for n=7:
%e A295913 ..0..0..1. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1
%e A295913 ..0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..0..0. .1..0..1. .0..1..1
%e A295913 ..0..1..0. .0..0..0. .0..1..1. .1..0..1. .0..1..1. .0..0..0. .0..0..0
%e A295913 ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .1..0..1
%e A295913 ..0..0..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..0
%e A295913 ..0..0..0. .1..1..0. .0..0..0. .1..0..0. .1..0..0. .0..0..0. .0..0..0
%e A295913 ..1..0..0. .0..0..0. .0..0..1. .0..0..1. .0..0..1. .0..0..1. .0..0..0
%Y A295913 Column 3 of A295918.
%K A295913 nonn
%O A295913 1,1
%A A295913 _R. H. Hardin_, Nov 29 2017