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A229681 Number of defective 3-colorings of an n X 4 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229681 #11 Apr 28 2021 01:23:52
%S A229681 0,360,10896,186576,2700432,35485776,437924880,5169543120,59031049104,
%T A229681 656886585168,7159989801744,76729919248080,810700618461840,
%U A229681 8463178886657616,87441690785378832,895373932606109136
%N A229681 Number of defective 3-colorings of an n X 4 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C A229681 Column 4 of A229685.
%H A229681 R. H. Hardin, <a href="/A229681/b229681.txt">Table of n, a(n) for n = 1..210</a>
%F A229681 Empirical: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 6.
%F A229681 Conjectures from _Colin Barker_, Jun 16 2017: (Start)
%F A229681 G.f.: 24*x^2*(15 + 49*x - 839*x^2 + 2007*x^3 - 1296*x^4) / (1 - 9*x)^3.
%F A229681 a(n) = 16*3^(2*n-7)*(-449 + 60*n + 256*n^2) for n > 3.
%F A229681 (End)
%e A229681 Some solutions for n=3:
%e A229681   0 1 1 0     0 0 1 2     0 1 0 2     0 0 0 1     0 1 1 0
%e A229681   2 2 0 1     1 1 1 1     2 1 2 2     0 2 2 2     0 0 0 2
%e A229681   1 1 0 1     2 2 2 0     2 1 1 0     1 1 1 2     2 2 1 2
%K A229681 nonn
%O A229681 1,2
%A A229681 _R. H. Hardin_, Sep 27 2013