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A229680 Number of defective 3-colorings of an n X 3 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229680 #9 Jun 16 2017 08:16:08
%S A229680 0,36,888,10896,108000,959040,7952256,62892288,480370176,3571983360,
%T A229680 26000455680,185993957376,1311390425088,9133778681856,62952545157120,
%U A229680 429958047006720,2913266164432896,19601071637004288,131057481860775936
%N A229680 Number of defective 3-colorings of an n X 3 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C A229680 Column 3 of A229685.
%H A229680 R. H. Hardin, <a href="/A229680/b229680.txt">Table of n, a(n) for n = 1..210</a>
%F A229680 Empirical: a(n) = 18*a(n-1) -108*a(n-2) +216*a(n-3) for n>4.
%F A229680 Empirical: G.f. 12*x^2*(10*x+1)*(10*x-3) / (6*x-1)^3. - _R. J. Mathar_, Sep 29 2013
%F A229680 Empirical a(n) = 2^n*3^(n-3)*(-45 + 4*n + 16*n^2) for n>1. - _Colin Barker_, Jun 16 2017
%e A229680 Some solutions for n=3
%e A229680 ..0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..2....0..1..1
%e A229680 ..1..2..2....1..1..2....0..1..2....2..2..0....0..1..1....2..2..0....2..2..2
%e A229680 ..0..2..2....1..1..2....0..1..0....2..1..0....0..2..1....1..2..0....1..2..0
%K A229680 nonn
%O A229680 1,2
%A A229680 _R. H. Hardin_, Sep 27 2013