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A297590 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.

%I A297590 #13 Mar 01 2019 16:32:01
%S A297590 1,3,9,25,69,205,597,1701,4949,14389,41493,120149,348437,1008021,
%T A297590 2917653,8451605,24467733,70830869,205101333,593841429,1719269653,
%U A297590 4977934613,14412904725,41729378581,120820070677,349814724885,1012822636821,2932443592981,8490378131733
%N A297590 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.
%H A297590 Alois P. Heinz, <a href="/A297590/b297590.txt">Table of n, a(n) for n = 0..1000</a> (terms n = 1..210 from R. H. Hardin)
%F A297590 Empirical: a(n) = a(n-1) + 2*a(n-2) + 10*a(n-3) + 4*a(n-4) - 8*a(n-5) - 8*a(n-6).
%F A297590 Empirical g.f.: 1 + x*(3 + 6*x + 10*x^2 - 4*x^3 - 16*x^4 - 8*x^5) / ((1 - x)*(1 - 2*x^2 - 12*x^3 - 16*x^4 - 8*x^5)). - _Colin Barker_, Mar 01 2019
%e A297590 Some solutions for n=7:
%e A297590 ..0..0..0. .0..1..1. .0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..1
%e A297590 ..1..0..0. .0..0..0. .0..1..1. .1..0..0. .0..0..0. .0..1..1. .0..1..0
%e A297590 ..0..1..0. .1..0..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..1..0
%e A297590 ..0..0..0. .0..1..0. .0..1..1. .1..1..0. .0..0..0. .0..0..1. .0..0..1
%e A297590 ..1..0..1. .0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..1..0. .0..0..1
%e A297590 ..1..1..1. .0..1..0. .1..1..0. .0..0..0. .0..1..0. .0..0..0. .0..1..0
%e A297590 ..1..0..0. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0
%Y A297590 Column 3 of A297595.
%K A297590 nonn
%O A297590 0,2
%A A297590 _R. H. Hardin_, Jan 01 2018
%E A297590 a(0)=1 prepended by _Alois P. Heinz_, Mar 01 2019