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A296315 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

%I A296315 #8 Feb 23 2019 04:21:31
%S A296315 3,11,32,96,295,902,2747,8380,25577,78021,238029,726211,2215568,
%T A296315 6759403,20622067,62915288,191946374,585603549,1786600798,5450687951,
%U A296315 16629344149,50733978916,154782809780,472222339285,1440689299042,4395356771500
%N A296315 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.
%H A296315 R. H. Hardin, <a href="/A296315/b296315.txt">Table of n, a(n) for n = 1..210</a>
%F A296315 Empirical: a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 3*a(n-4) - 3*a(n-6) + a(n-7) - 3*a(n-9) + a(n-11).
%F A296315 Empirical g.f.: x*(3 + 8*x + 9*x^2 + 2*x^3 - 4*x^4 - 2*x^5 + 2*x^6 - 3*x^7 - 3*x^8 + x^9 + x^10) / ((1 + x^2 - x^3)*(1 - x - 5*x^2 - 4*x^3 + x^4 - x^5 - 2*x^6 + x^7 + x^8)). - _Colin Barker_, Feb 23 2019
%e A296315 Some solutions for n=5:
%e A296315 ..0..0..0. .0..1..1. .0..1..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0
%e A296315 ..0..0..0. .0..0..0. .0..1..0. .0..0..1. .0..1..0. .0..0..0. .1..1..0
%e A296315 ..0..0..0. .1..0..0. .0..0..0. .0..1..0. .1..0..0. .1..0..0. .0..0..0
%e A296315 ..0..0..0. .1..0..1. .0..0..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1
%e A296315 ..1..1..0. .0..1..0. .0..1..1. .0..1..0. .1..0..0. .0..1..1. .0..0..1
%Y A296315 Column 3 of A296320.
%K A296315 nonn
%O A296315 1,1
%A A296315 _R. H. Hardin_, Dec 10 2017