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%I #7 Feb 25 2019 09:21:53
%S 1,6,21,56,178,609,1997,6511,21494,71021,234110,771936,2546839,
%T 8401997,27715289,91426922,301604833,994943072,3282138566,10827217153,
%U 35717165621,117824839843,388684058778,1282202639897,4229768507606
%N Number of n X 2 0..1 arrays with each 1 adjacent to 2, 3 or 4 king-move neighboring 1s.
%H R. H. Hardin, <a href="/A296821/b296821.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 5*a(n-3) - 2*a(n-4) - 10*a(n-5) - 8*a(n-6).
%F Empirical g.f.: x*(1 + 3*x + 3*x^2 - 12*x^3 - 18*x^4 - 8*x^5) / (1 - 3*x - 5*x^3 + 2*x^4 + 10*x^5 + 8*x^6). - _Colin Barker_, Feb 25 2019
%e Some solutions for n=7:
%e ..1..1. .0..0. .1..1. .1..1. .1..0. .1..1. .1..1. .0..1. .1..0. .0..1
%e ..1..0. .0..0. .0..1. .1..0. .1..1. .1..0. .0..1. .1..1. .1..1. .1..1
%e ..1..0. .0..0. .1..1. .0..0. .1..0. .1..1. .1..1. .0..1. .0..1. .0..0
%e ..1..0. .0..0. .0..0. .0..0. .1..1. .1..0. .0..1. .0..0. .0..0. .0..0
%e ..1..0. .1..0. .1..1. .1..0. .1..1. .0..0. .1..1. .1..1. .0..1. .1..0
%e ..0..1. .1..1. .1..1. .1..1. .0..0. .0..1. .0..0. .0..1. .1..1. .1..1
%e ..1..1. .0..0. .0..1. .1..1. .0..0. .1..1. .0..0. .1..1. .0..0. .0..1
%Y Column 2 of A296827.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 21 2017
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