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A229581 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

%I A229581 #8 Sep 19 2018 08:50:34
%S A229581 2,28,264,2160,16416,119232,839808,5785344,39191040,262020096,
%T A229581 1733363712,11367641088,74010599424,478892113920,3082323787776,
%U A229581 19747769352192,126009575866368,801195213717504,5077997833420800,32092946307219456
%N A229581 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
%H A229581 R. H. Hardin, <a href="/A229581/b229581.txt">Table of n, a(n) for n = 1..210</a>
%F A229581 Empirical: a(n) = 12*a(n-1) - 36*a(n-2).
%F A229581 Conjectures from _Colin Barker_, Sep 19 2018: (Start)
%F A229581 G.f.: 2*(1 + 2*x) / (1 - 6*x)^2.
%F A229581 a(n) = 2^(n + 1) * 3^(n - 1) * (4*n + 3).
%F A229581 (End)
%e A229581 Some solutions for n=3:
%e A229581 ..0..1..1....0..1..2....0..0..1....0..1..2....0..1..2....0..1..2....0..1..0
%e A229581 ..0..2..1....0..1..2....1..0..2....2..1..0....2..0..1....0..1..0....2..1..0
%e A229581 ..0..2..1....0..2..0....2..1..0....2..2..0....2..2..1....0..1..1....2..2..0
%Y A229581 Column 3 of A229586.
%K A229581 nonn
%O A229581 1,1
%A A229581 _R. H. Hardin_, Sep 26 2013