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A207590 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.

%I A207590 #8 Mar 05 2018 10:00:21
%S A207590 6,36,60,144,324,756,1728,3996,9180,21168,48708,112212,258336,594972,
%T A207590 1369980,3154896,7264836,16729524,38524032,88712604,204284700,
%U A207590 470422512,1083276612,2494544148,5744373984,13228006428,30461128380,70145147664
%N A207590 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.
%C A207590 Row 3 of A207589.
%H A207590 R. H. Hardin, <a href="/A207590/b207590.txt">Table of n, a(n) for n = 1..210</a>
%F A207590 Empirical: a(n) = a(n-1) + 3*a(n-2) for n>4.
%F A207590 Conjectures from _Colin Barker_, Mar 05 2018: (Start)
%F A207590 G.f.: 6*x*(1 + 5*x + x^2 - 4*x^3) / (1 - x - 3*x^2).
%F A207590 a(n) = (2^(1-n)*((1-sqrt(13))^n*(-35+13*sqrt(13)) + (1+sqrt(13))^n*(35+13*sqrt(13)))) / (9*sqrt(13)) for n>2.
%F A207590 (End)
%e A207590 Some solutions for n=4:
%e A207590 ..0..1..1..0....1..1..0..0....1..1..0..1....0..1..1..1....1..1..1..1
%e A207590 ..1..0..1..0....1..0..1..0....0..1..1..1....1..0..1..0....1..0..1..0
%e A207590 ..0..1..0..0....0..1..1..0....1..0..1..0....0..1..0..1....0..1..0..1
%Y A207590 Cf. A207589.
%K A207590 nonn
%O A207590 1,1
%A A207590 _R. H. Hardin_, Feb 19 2012