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A229689 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229689 #9 Apr 28 2021 12:42:28
%S A229689 1,43,626,6732,62856,539568,4377888,34105536,257634432,1899645696,
%T A229689 13735899648,97733495808,686049232896,4760622968832,32708331380736,
%U A229689 222789318524928,1506002505596928,10111798278291456,67486591206162432
%N A229689 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C A229689 Column 3 of A229694.
%H A229689 R. H. Hardin, <a href="/A229689/b229689.txt">Table of n, a(n) for n = 1..210</a>
%F A229689 Empirical: a(n) = 18*a(n-1) -108*a(n-2) +216*a(n-3) for n > 4.
%F A229689 Empirical: g.f. x -x^2*(43-148*x+108*x^2) / (6*x-1)^3. - _R. J. Mathar_, Sep 29 2013
%e A229689 Some solutions for n=3
%e A229689 ..0..0..1....0..0..1....0..1..2....0..1..0....0..1..2....0..1..1....0..1..2
%e A229689 ..2..1..2....2..1..2....0..1..0....2..0..2....1..2..0....0..2..1....1..2..1
%e A229689 ..2..0..2....0..1..0....1..2..2....1..2..0....0..1..0....0..0..1....1..2..1
%Y A229689 Cf. A229694.
%K A229689 nonn
%O A229689 1,2
%A A229689 _R. H. Hardin_, Sep 27 2013