%I #8 Jul 05 2018 08:04:14
%S 5,68,1059,16608,260856,4098492,64398564,1011891888,15899856696,
%T 249834571632,3925652965344,61683823050048,969238512405216,
%U 15229654196873472,239303704937730624,3760181449823927808
%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 left-upward diagonal neighbors.
%C Column 3 of A208567.
%H R. H. Hardin, <a href="/A208562/b208562.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 22*a(n-1) - 110*a(n-2) + 180*a(n-3) - 60*a(n-4) for n>5.
%F Empirical g.f.: x*(5 - 42*x + 113*x^2 - 110*x^3 + 30*x^4) / (1 - 22*x + 110*x^2 - 180*x^3 + 60*x^4). - _Colin Barker_, Jul 05 2018
%e Some solutions for n=4:
%e ..0..0..0....0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..2
%e ..1..1..1....2..1..2....0..1..1....0..1..2....2..1..2....2..1..0....1..2..0
%e ..1..0..0....2..0..0....1..2..0....2..0..1....2..0..2....2..0..1....0..1..0
%e ..1..2..2....0..2..1....1..2..1....0..1..0....2..0..1....2..0..2....2..0..1
%Y Cf. A208567.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 28 2012