%I #9 Aug 05 2018 08:21:13
%S 0,6,30,144,672,3108,14328,65976,303672,1397520,6431136,29594352,
%T 136184256,626677152,2883768672,13270180608,61065117312,281002082880,
%U 1293081432192,5950345861248,27381582408576,126001256419584
%N Number of n X 3 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2.
%C Column 3 of A221400.
%H R. H. Hardin, <a href="/A221397/b221397.txt">Table of n, a(n) for n = 1..41</a>
%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) -2*a(n-3).
%F Empirical g.f.: 6*x^2*(1 - x) / (1 - 6*x + 6*x^2 + 2*x^3). - _Colin Barker_, Aug 05 2018
%e Some solutions for n=3:
%e ..0..2..0....1..2..0....0..2..0....0..2..0....1..2..0....0..2..1....0..2..1
%e ..1..2..0....0..2..1....0..2..2....1..2..1....1..2..1....0..2..1....2..2..0
%e ..1..2..1....0..2..1....1..2..0....1..2..0....0..2..0....1..2..0....0..2..0
%Y Cf. A221400.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 15 2013