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Number of defective 4-colorings of an n X 5 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
1

%I #8 Apr 27 2021 21:34:12

%S 20,1312,23964,360912,5068384,68447552,900320160,11614790144,

%T 147614682208,1853886660416,23058698415136,284513215031168,

%U 3486867165130720,42487662072402880,515141200042010528

%N Number of defective 4-colorings of an n X 5 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.

%C Column 5 of A229479.

%H R. H. Hardin, <a href="/A229476/b229476.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 44*a(n-1) - 838*a(n-2) + 9452*a(n-3) - 73265*a(n-4) + 422560*a(n-5) - 1882320*a(n-6) + 6531392*a(n-7) - 17307072*a(n-8) + 32474112*a(n-9) - 31011840*a(n-10) - 38977536*a(n-11) + 220663808*a(n-12) - 419692544*a(n-13) + 332922880*a(n-14) + 233046016*a(n-15) - 839122944*a(n-16) + 788529152*a(n-17) - 268435456*a(n-18) for n > 19.

%e Some solutions for n=3:

%e 0 1 0 2 0 0 1 2 0 3 0 1 2 1 0 0 0 1 2 3

%e 3 2 3 1 2 3 0 3 1 2 3 3 0 2 1 3 2 3 0 1

%e 1 1 2 0 3 0 2 0 3 1 1 2 3 0 3 1 0 1 3 2

%Y Cf. A229479.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 24 2013