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Number of defective 3-colorings of a 4 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
1

%I #10 Apr 08 2021 00:29:58

%S 0,336,6732,80757,848937,8186713,75035643,663220698,5704874295,

%T 48038840103,397625913450,3244798314423,26164241721531,

%U 208829737022022,1652110212078675,12969730076956551,101126149198462638

%N Number of defective 3-colorings of a 4 X n 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%C Row 4 of A229694.

%H R. H. Hardin, <a href="/A229697/b229697.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 27*a(n-1) - 288*a(n-2) + 1557*a(n-3) - 4644*a(n-4) + 8073*a(n-5) - 8343*a(n-6) + 5022*a(n-7) - 1620*a(n-8) + 216*a(n-9) for n > 17.

%e Some solutions for n=3:

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 27 2013