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A208502 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 1 1 vertically.

%I A208502 #8 Jul 03 2018 12:40:35
%S A208502 9,81,126,324,828,2124,5436,13932,35676,91404,234108,599724,1536156,
%T A208502 3935052,10079676,25819884,66138588,169418124,433972476,1111644972,
%U A208502 2847534876,7294114764,18684254268,47860713324,122597730396,314040583692
%N A208502 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 1 1 vertically.
%C A208502 Row 4 of A208501.
%H A208502 R. H. Hardin, <a href="/A208502/b208502.txt">Table of n, a(n) for n = 1..210</a>
%F A208502 Empirical: a(n) = a(n-1) + 4*a(n-2) for n>4.
%F A208502 Conjectures from _Colin Barker_, Jul 03 2018: (Start)
%F A208502 G.f.: 9*x*(1 + 8*x + x^2 - 14*x^3) / (1 - x - 4*x^2).
%F A208502 a(n) = (9*2^(-6-n)*((1-sqrt(17))^n*(-109+27*sqrt(17)) + (1+sqrt(17))^n*(109+27*sqrt(17)))) / sqrt(17) for n>2.
%F A208502 (End)
%e A208502 Some solutions for n=4:
%e A208502 ..0..1..0..0....1..1..1..0....1..0..1..0....1..0..1..1....1..1..0..0
%e A208502 ..0..1..1..0....0..1..0..1....1..1..0..1....1..0..1..1....1..0..1..0
%e A208502 ..1..0..1..0....1..0..1..1....0..1..1..1....0..1..0..0....0..1..1..0
%e A208502 ..1..1..0..1....1..1..1..0....1..0..1..0....1..1..1..1....0..1..0..1
%Y A208502 Cf. A208501.
%K A208502 nonn
%O A208502 1,1
%A A208502 _R. H. Hardin_, Feb 27 2012