%I #8 Mar 07 2018 09:23:03

%S 6,36,78,282,768,2430,7086,21588,64230,193554,579264,1740054,5216502,

%T 15655428,46956702,140885610,422631744,1267935822,3803741790,

%U 11411331636,34233822966,102701747106,308104791168,924315101862,2772944127078

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

%C Row 3 of A208688.

%H R. H. Hardin, <a href="/A208689/b208689.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Mar 07 2018: (Start)

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

%F a(n) = 2^(-n)*(5*6^(2+n) + (75-27*sqrt(5))*(-1+sqrt(5))^n + 3*(-1-sqrt(5))^n*(25+9*sqrt(5))) / 55.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Cf. A208688.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2012