%I #11 Aug 04 2018 06:40:53

%S 2,10,46,212,976,4492,20672,95128,437752,2014400,9269632,42655888,

%T 196288736,903257824,4156502752,19126892096,88015820416,405020564416,

%U 1863774679808,8576493051520,39466269101440,181611106939904

%N Number of n X 3 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no occupancy greater than 2.

%C Column 3 of A221200.

%H R. H. Hardin, <a href="/A221196/b221196.txt">Table of n, a(n) for n = 1..33</a>

%F Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 2*a(n-3).

%F Empirical g.f.: 2*x*(1 - x - x^2) / (1 - 6*x + 6*x^2 + 2*x^3). - _Colin Barker_, Aug 04 2018

%e Some solutions for n=3:

%e ..0..2..0....0..2..0....1..2..0....1..2..1....1..2..1....1..2..0....0..2..1

%e ..1..2..2....0..2..2....0..2..1....1..2..0....0..2..1....1..2..0....0..2..2

%e ..0..2..0....0..2..1....0..2..1....0..2..0....0..2..0....0..2..1....0..2..0

%Y Cf. A221200.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 04 2013