%I #7 Aug 03 2018 08:13:01
%S 2,24,270,3024,33858,379080,4244238,47519136,532031490,5956705656,
%T 66692184462,746695862640,8360120691522,93601185534504,
%U 1047973140190350,11733267012473664,131367445887970818,1470809947543386840
%N Number of n X 3 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor.
%C Column 3 of A221087.
%H R. H. Hardin, <a href="/A221082/b221082.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 12*a(n-1) - 9*a(n-2).
%F Conjectures from _Colin Barker_, Aug 03 2018: (Start)
%F G.f.: 2*x / (1 - 12*x + 9*x^2).
%F a(n) = ((-(6-3*sqrt(3))^n + (3*(2+sqrt(3)))^n))/(3*sqrt(3)).
%F (End)
%e Some solutions for n=3:
%e ..0..1..0....0..3..1....1..1..0....0..2..1....0..3..1....0..2..0....0..2..0
%e ..1..3..0....0..1..0....1..2..0....1..1..0....0..2..1....1..1..2....2..2..1
%e ..2..2..0....2..2..0....0..3..1....1..3..0....1..1..0....0..3..0....0..2..0
%Y Cf. A221087.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 01 2013
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