%I #8 Mar 05 2018 10:00:21

%S 6,36,60,144,324,756,1728,3996,9180,21168,48708,112212,258336,594972,

%T 1369980,3154896,7264836,16729524,38524032,88712604,204284700,

%U 470422512,1083276612,2494544148,5744373984,13228006428,30461128380,70145147664

%N 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 Row 3 of A207589.

%H R. H. Hardin, <a href="/A207590/b207590.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-2) for n>4.

%F Conjectures from _Colin Barker_, Mar 05 2018: (Start)

%F G.f.: 6*x*(1 + 5*x + x^2 - 4*x^3) / (1 - x - 3*x^2).

%F 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 (End)

%e Some solutions for n=4:

%e ..0..1..1..0....1..1..0..0....1..1..0..1....0..1..1..1....1..1..1..1

%e ..1..0..1..0....1..0..1..0....0..1..1..1....1..0..1..0....1..0..1..0

%e ..0..1..0..0....0..1..1..0....1..0..1..0....0..1..0..1....0..1..0..1

%Y Cf. A207589.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2012