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A299592 Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A299592 #11 Feb 15 2018 12:17:15
%S A299592 8,8,19,53,113,256,541,1148,2488,5349,11453,24617,52916,113605,243988,
%T A299592 524156,1125805,2417997,5193737,11155712,23961101,51466060,110544232,
%U A299592 237437573,509991637,1095411153,2352832580,5053645925,10854721796
%N A299592 Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A299592 Column 5 of A299595.
%H A299592 R. H. Hardin, <a href="/A299592/b299592.txt">Table of n, a(n) for n = 1..210</a>
%F A299592 Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.
%F A299592 Empirical g.f.: x*(8 + 3*x^2 + 2*x^3 + 9*x^4 + 33*x^5 + 10*x^6 - 14*x^7 - 10*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Feb 15 2018
%e A299592 Some solutions for n=5:
%e A299592 ..0..0..1..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..1..0..0
%e A299592 ..0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0. .0..0..0..0..1
%e A299592 ..0..0..0..0..0. .1..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0
%e A299592 ..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..0
%e A299592 ..0..0..1..0..0. .0..1..0..0..0. .0..1..0..0..0. .0..0..0..1..0
%Y A299592 Cf. A299595.
%K A299592 nonn
%O A299592 1,1
%A A299592 _R. H. Hardin_, Feb 13 2018