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A296124 Number of n X 4 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.

%I A296124 #10 Feb 22 2019 15:52:06
%S A296124 1,13,30,74,287,841,2463,7953,24428,74660,233017,721069,2226921,
%T A296124 6907921,21399342,66252970,205308499,636102161,1970540971,6105562057,
%U A296124 18917255184,58610713832,181598709121,562663895105,1743342282089,5401567886229
%N A296124 Number of n X 4 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.
%H A296124 R. H. Hardin, <a href="/A296124/b296124.txt">Table of n, a(n) for n = 1..210</a>
%F A296124 Empirical: a(n) = 3*a(n-1) + a(n-2) + 5*a(n-3) - 18*a(n-4) - 14*a(n-5) + 3*a(n-6) + a(n-7) + a(n-8) - a(n-9).
%F A296124 Empirical g.f.: x*(1 + x)*(1 + 9*x - 19*x^2 - 15*x^3 + 3*x^4 + x^5 + x^6 - x^7) / (1 - 3*x - x^2 - 5*x^3 + 18*x^4 + 14*x^5 - 3*x^6 - x^7 - x^8 + x^9). - _Colin Barker_, Feb 22 2019
%e A296124 Some solutions for n=7:
%e A296124 ..0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..0
%e A296124 ..1..0..1..0. .0..0..1..0. .0..0..0..0. .0..0..1..0. .1..1..1..0
%e A296124 ..1..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..1..1
%e A296124 ..1..0..1..0. .0..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..0..0
%e A296124 ..1..0..0..1. .0..0..1..1. .0..0..0..0. .1..0..0..1. .0..0..0..1
%e A296124 ..0..1..1..0. .1..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..1..1
%e A296124 ..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..1..1..0. .0..0..0..0
%Y A296124 Column 4 of A296128.
%K A296124 nonn
%O A296124 1,2
%A A296124 _R. H. Hardin_, Dec 05 2017