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A299590 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A299590 #7 Feb 15 2018 12:04:15
%S A299590 3,3,5,11,19,35,65,120,220,404,744,1369,2517,4629,8515,15662,28806,
%T A299590 52982,97450,179239,329671,606359,1115269,2051300,3772928,6939496,
%U A299590 12763724,23476149,43179369,79419241,146074759,268673370,494167370,908915498
%N A299590 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A299590 Column 3 of A299595.
%H A299590 R. H. Hardin, <a href="/A299590/b299590.txt">Table of n, a(n) for n = 1..210</a>
%F A299590 Empirical: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) for n>8.
%F A299590 Empirical g.f.: x*(3 + 2*x^2 - x^4 + x^7) / ((1 + x^2)*(1 - x - x^2 - x^3)). - _Colin Barker_, Feb 15 2018
%e A299590 Some solutions for n=5:
%e A299590 ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..0. .0..0..0. .0..0..0
%e A299590 ..0..0..0. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0
%e A299590 ..0..0..0. .0..0..1. .0..0..0. .1..0..0. .0..0..0. .0..0..1. .0..0..0
%e A299590 ..0..0..0. .0..0..0. .1..0..0. .0..0..0. .0..0..1. .0..0..0. .0..0..0
%e A299590 ..0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%Y A299590 Cf. A299595.
%K A299590 nonn
%O A299590 1,1
%A A299590 _R. H. Hardin_, Feb 13 2018