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A208023 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 0 1 vertically.

%I A208023 #9 Mar 06 2018 15:48:22
%S A208023 6,36,102,279,741,1995,5404,14555,39180,105688,284961,767907,2070021,
%T A208023 5580470,15042195,40547128,109300950,294632265,794208105,2140875657,
%U A208023 5770963528,15556228121,41933454712,113036097920,304700733021
%N A208023 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 0 1 vertically.
%C A208023 Column 3 of A208028.
%H A208023 R. H. Hardin, <a href="/A208023/b208023.txt">Table of n, a(n) for n = 1..210</a>
%F A208023 Empirical: a(n) = a(n-1) + a(n-2) + 8*a(n-3) + 4*a(n-4) + 3*a(n-5) - 5*a(n-6) - a(n-7) + a(n-9) for n>10.
%F A208023 Empirical g.f.: x*(6 + 30*x + 60*x^2 + 93*x^3 + 48*x^4 - 3*x^5 - 50*x^6 - 8*x^7 + 6*x^8 + 9*x^9) / (1 - x - x^2 - 8*x^3 - 4*x^4 - 3*x^5 + 5*x^6 + x^7 - x^9). - _Colin Barker_, Mar 06 2018
%e A208023 Some solutions for n=4:
%e A208023 ..1..0..0....0..1..1....1..1..1....1..1..1....1..1..0....1..0..0....0..1..0
%e A208023 ..0..1..0....0..1..1....1..1..1....0..1..0....0..1..0....0..1..0....1..0..1
%e A208023 ..0..1..1....1..0..0....1..1..0....0..1..0....0..1..1....0..1..1....1..0..1
%e A208023 ..1..1..1....1..0..0....1..0..0....1..0..1....1..1..1....1..0..0....1..1..1
%Y A208023 Cf. A208028.
%K A208023 nonn
%O A208023 1,1
%A A208023 _R. H. Hardin_, Feb 22 2012