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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.
1

%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