%I #8 Jun 30 2018 14:54:01

%S 4,18,78,336,1446,6222,26772,115194,495654,2132688,9176478,39484326,

%T 169892196,731008002,3145363422,13533793104,58232875254,250562996958,

%U 1078116359028,4638892804266,19960114944246,85883896308432

%N Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

%C Column 3 of A208314.

%H R. H. Hardin, <a href="/A208309/b208309.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 3*a(n-2).

%F Conjectures from _Colin Barker_, Jun 30 2018: (Start)

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

%F a(n) = (2^(-n)*((5-sqrt(13))^n*(-7+sqrt(13)) + (5+sqrt(13))^n*(7+sqrt(13)))) / (3*sqrt(13)).

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208314.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012