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%I #12 Apr 27 2021 21:02:42
%S 6,248,3328,36116,360912,3443856,31875248,288634368,2570642816,
%T 22599003712,196602867456,1695703281408,14520402611968,
%U 123579905038336,1046236716429312,8817070242804736,74007384618897408,618990518429175808
%N Number of defective 4-colorings of an n X 4 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
%H R. H. Hardin, <a href="/A229475/b229475.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 24*a(n-1) - 224*a(n-2) + 1096*a(n-3) - 3360*a(n-4) + 6976*a(n-5) - 9744*a(n-6) + 8704*a(n-7) - 4096*a(n-8) for n > 9.
%F Empirical g.f.: 2*x*(3 + 52*x - 640*x^2 + 2610*x^3 - 6024*x^4 + 7944*x^5 - 2824*x^6 - 4736*x^7 + 10240*x^8) / (1 - 12*x + 40*x^2 - 68*x^3 + 64*x^4)^2. - _Colin Barker_, Sep 18 2018
%e Some solutions for n=4:
%e 0 1 0 2 0 1 2 3 0 1 2 0 0 1 2 3 0 1 2 3
%e 0 3 1 3 3 0 0 1 2 3 1 3 3 0 1 3 2 3 1 2
%e 1 0 2 0 2 1 3 2 0 2 0 2 2 3 0 2 1 2 1 0
%e 3 1 3 2 0 2 1 0 1 3 2 1 0 2 3 1 3 0 3 2
%Y Column 4 of A229479.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 24 2013