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Number of defective 3-colorings of an nX4 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order
1

%I #6 Sep 28 2013 18:38:33

%S 3,245,5077,80757,1125333,14461173,175867605,2054728053,23284024533,

%T 257577229557,2794463987157,29833314755445,314218549864917,

%U 3271569607417077,33725758239805653,344669380723927413

%N Number of defective 3-colorings of an nX4 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order

%C Column 4 of A229694

%H R. H. Hardin, <a href="/A229690/b229690.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 27*a(n-1) -243*a(n-2) +729*a(n-3) for n>4.

%F Empirical: g.f. 3*x-x^2*(245-1538*x+3213*x^2) / (9*x-1)^3. - _R. J. Mathar_, Sep 29 2013

%e Some solutions for n=3

%e ..0..0..1..0....0..1..0..2....0..1..2..0....0..1..2..1....0..1..0..2

%e ..1..0..1..2....2..1..0..0....0..1..0..2....0..2..0..2....2..1..0..1

%e ..1..0..0..2....2..0..1..2....0..1..2..1....0..1..1..2....2..0..0..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 27 2013