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A229600 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229600 #10 Mar 17 2018 05:45:38
%S A229600 0,6,39,202,925,3924,15795,61182,230121,845640,3049407,10825650,
%T A229600 37929141,131403708,450839115,1533738726,5178892545,17371743408,
%U A229600 57926537559,192131864730,634207340493,2084322230820,6822862231779,22252658047182
%N A229600 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C A229600 Column 2 of A229606.
%H A229600 R. H. Hardin, <a href="/A229600/b229600.txt">Table of n, a(n) for n = 1..210</a>
%F A229600 Empirical: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n>5.
%F A229600 Conjectures from _Colin Barker_, Mar 16 2018: (Start)
%F A229600 G.f.: x^2*(6 - 15*x + 13*x^2 - 2*x^3) / (1 - 3*x)^3.
%F A229600 a(n) = 3^(n-5) * (31*n+32*n^2-30) for n>2.
%F A229600 (End)
%e A229600 Some solutions for n=3:
%e A229600   0 1   0 1   0 1   0 0   0 1   0 1   0 1   0 1   0 1   0 1
%e A229600   1 2   2 0   0 1   0 1   1 2   2 1   2 2   1 1   2 2   2 2
%e A229600   1 2   2 0   2 0   1 2   2 2   2 0   1 1   2 0   0 2   2 0
%Y A229600 Cf. A229606.
%K A229600 nonn
%O A229600 1,2
%A A229600 _R. H. Hardin_, Sep 26 2013