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%I #11 Jun 25 2017 17:19:05
%S 2,15,716,83440,18171918,6423127757,3376465219485,2486327138729353,
%T 2454996141671330713,3143641561804718358884,5084413934903476204054959,
%U 10166624612435356414640715276,24691194409056203926713355839051
%N Number of n X 3 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
%H Andrew Howroyd, <a href="/A208051/b208051.txt">Table of n, a(n) for n = 1..100</a> (first 20 terms from R. H. Hardin)
%e Some solutions for n=4
%e ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
%e ..2..3..1....2..3..1....2..3..2....2..3..1....2..3..2....2..3..4....2..3..1
%e ..0..2..0....0..4..5....0..4..0....1..0..2....0..1..4....0..5..0....4..5..3
%e ..1..3..1....5..3..4....1..2..1....2..3..0....2..0..1....1..2..1....0..6..4
%Y Column 3 of A208054.
%Y Column 6 of A216460 and column 6 of A216612.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 22 2012