%I
%S 297,1647,9126,50571,280233,1552878,8605089,47684079,264235662,
%T 1464230547,8113859721,44961990246,249151530393,1380643622703,
%U 7650672704694,42395294391579,234928490071977,1301828333534622
%N Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.
%H R. H. Hardin, <a href="/A253029/b253029.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n1) + 3*a(n2).
%F Conjectures from _Colin Barker_, Dec 08 2018: (Start)
%F G.f.: 27*x*(11 + 6*x) / (1  5*x  3*x^2).
%F a(n) = (27*2^(n)*((5sqrt(37))^n*(6+sqrt(37)) + (5+sqrt(37))^n*(6+sqrt(37)))) / sqrt(37).
%F (End)
%e Some solutions for n=4:
%e ..0..1..0....0..1..0....0..0..1....0..0..1....0..1..1....0..0..1....0..0..1
%e ..0..2..0....1..0..0....1..0..0....1..1..2....2..1..1....2..1..2....1..2..2
%e ..2..1..2....0..0..1....0..1..1....0..0..2....0..0..2....0..0..1....0..0..1
%e ..0..2..2....0..1..0....0..1..0....1..1..0....0..0..2....0..0..2....1..2..1
%e ..0..1..1....1..0..1....1..0..1....0..0..2....2..2..1....2..1..1....0..2..0
%e ..2..1..2....1..0..0....0..1..1....0..0..2....2..0..2....2..0..2....0..0..1
%Y Column 1 of A253035.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 26 2014
