%I #7 Dec 31 2018 06:08:25
%S 6,15,90,351,2106,10935,65610,378351,2270106,13482855,80897130,
%T 484142751,2904856506,17417978775,104507872650,626946793551,
%U 3761680761306,22569180586695,135415083520170,812482365290751,4874894191744506
%N Number of (n+1) X (3+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.
%H R. H. Hardin, <a href="/A262327/b262327.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n1) + 9*a(n2)  54*a(n3).
%F Conjectures from _Colin Barker_, Dec 31 2018: (Start)
%F G.f.: 3*x*(2  7*x  18*x^2) / ((1  3*x)*(1 + 3*x)*(1  6*x)).
%F a(n) = 3^(n2)*(14 + 2^(2+n)) / 2 for n even.
%F a(n) = 3^(n2)*(28 + 2^(2+n)) / 2 for n odd.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0....0..1..1..0....1..0..0..1....0..0..1..1....1..1..1..1
%e ..0..0..0..0....0..1..1..0....1..1..1..1....0..0..1..1....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..1..1..0....1..0..0..1....1..1..0..0
%e ..1..0..0..1....1..0..0..1....1..0..0..1....1..1..1..1....0..0..1..1
%e ..1..0..0..1....1..0..0..1....1..0..0..1....0..1..1..0....1..1..0..0
%Y Column 3 of A262332.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 18 2015
