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Number of defective 3-colorings of an n X 5 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
1

%I #8 Apr 27 2021 20:58:46

%S 16,112,1588,19276,221096,2451728,26566266,283010776,2975590424,

%T 30959068528,319352065652,3270635802440,33292532186562,

%U 337120240897408,3398161294369868,34116704260522692,341314436219045264

%N Number of defective 3-colorings of an n X 5 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

%C Column 5 of A229534.

%H R. H. Hardin, <a href="/A229531/b229531.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 28*a(n-1) - 286*a(n-2) + 1290*a(n-3) - 2373*a(n-4) + 304*a(n-5) + 3551*a(n-6) - 2846*a(n-7) - 546*a(n-8) + 1308*a(n-9) - 505*a(n-10) + 76*a(n-11) - 4*a(n-12) for n > 13.

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A229534.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 25 2013