%I #9 Jul 08 2018 10:48:22
%S 5,76,1326,23248,407832,7154944,125526240,2202232576,38635976064,
%T 677829707776,11891846929920,208630607073280,3660216151873536,
%U 64214845877125120,1126585496573239296,19764820171301257216
%N Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or rightupward antidiagonal neighbors.
%C Column 3 of A209100.
%H R. H. Hardin, <a href="/A209095/b209095.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 20*a(n1)  44*a(n2) + 16*a(n3) for n>4.
%F Conjectures from _Colin Barker_, Jul 08 2018: (Start)
%F G.f.: x*(5  4*x)*(1  4*x + 2*x^2) / ((1  2*x)*(1  18*x + 8*x^2)).
%F a(n) = 2^(n3) + ((9sqrt(73))^n*(25+sqrt(73)) + (9+sqrt(73))^n*(25+sqrt(73))) / (16*sqrt(73)) for n>1.
%F (End)
%e Some solutions for n=4:
%e ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....0..1..2
%e ..1..2..1....1..1..1....1..1..2....2..0..0....1..1..2....1..0..2....1..2..1
%e ..1..0..1....2..0..0....2..0..0....2..1..0....0..0..0....1..1..2....0..2..1
%e ..2..1..2....1..2..2....1..1..1....2..2..2....1..2..0....0..0..1....1..2..2
%Y Cf. A209100.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 05 2012
