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

%I #8 Apr 28 2021 01:23:00

%S 0,202,1496,10227,77620,535671,3723370,25022190,166505166,1090285513,

%T 7066637900,45333775056,288422981684,1821192582307,11424271291526,

%U 71241698297248,441922120307156,2728236364222397,16770150954151850

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

%C Row 4 of A229637.

%H R. H. Hardin, <a href="/A229640/b229640.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) + 21*a(n-2) - 270*a(n-3) - 357*a(n-4) + 2967*a(n-5) + 4906*a(n-6) - 10083*a(n-7) - 18957*a(n-8) + 15750*a(n-9) + 31293*a(n-10) - 13335*a(n-11) - 23929*a(n-12) + 6426*a(n-13) + 7824*a(n-14) - 1336*a(n-15) - 1152*a(n-16) + 96*a(n-17) + 64*a(n-18) for n > 21.

%e Some solutions for n=3:

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Sep 27 2013