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A207846 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.

%I A207846 #8 Jun 25 2018 15:55:10
%S A207846 6,36,72,180,432,1044,2520,6084,14688,35460,85608,206676,498960,
%T A207846 1204596,2908152,7020900,16949952,40920804,98791560,238503924,
%U A207846 575799408,1390102740,3356004888,8102112516,19560229920,47222572356,114005374632
%N A207846 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.
%C A207846 Row 3 of A207845.
%H A207846 R. H. Hardin, <a href="/A207846/b207846.txt">Table of n, a(n) for n = 1..210</a>
%F A207846 Empirical: a(n) = 2*a(n-1) + a(n-2) for n>3.
%F A207846 Conjectures from _Colin Barker_, Jun 25 2018: (Start)
%F A207846 G.f.: 6*x*(1 + 4*x - x^2) / (1 - 2*x - x^2).
%F A207846 a(n) = 9*(sqrt(2)*((1-sqrt(2))^n*(1+sqrt(2)) + (-1+sqrt(2))*(1+sqrt(2))^n)) for n>2.
%F A207846 (End)
%e A207846 Some solutions for n=4:
%e A207846 ..1..1..1..1....1..1..0..0....1..1..0..1....1..0..1..1....0..1..0..0
%e A207846 ..0..1..0..0....1..0..1..1....0..1..1..1....1..1..0..0....1..0..1..1
%e A207846 ..1..0..1..1....0..1..1..0....1..0..1..0....0..1..1..0....1..1..1..0
%Y A207846 Cf. A207845.
%K A207846 nonn
%O A207846 1,1
%A A207846 _R. H. Hardin_, Feb 21 2012