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%I #7 Apr 27 2021 22:20:11
%S 40,1608,28448,535671,9722206,170405645,2902520386,48303362606,
%T 788657935296,12673198849045,200926746561814,3149086238797127,
%U 48865266229013882,751678393470169836,11474405764402402524
%N Number of defective 3-colorings of an n X 6 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C Column 6 of A229637.
%H R. H. Hardin, <a href="/A229635/b229635.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 54*a(n-1) - 1140*a(n-2) + 11637*a(n-3) - 54252*a(n-4) + 33192*a(n-5) + 658756*a(n-6) - 1921212*a(n-7) - 1566516*a(n-8) + 12850374*a(n-9) - 7108644*a(n-10) - 35018232*a(n-11) + 43506046*a(n-12) + 38500440*a(n-13) - 85687812*a(n-14) - 200796*a(n-15) + 75241308*a(n-16) - 31685592*a(n-17) - 25769200*a(n-18) + 20878068*a(n-19) + 213348*a(n-20) - 3655770*a(n-21) + 608916*a(n-22) + 230904*a(n-23) - 61761*a(n-24) - 2790*a(n-25) + 1800*a(n-26) - 125*a(n-27) for n > 30.
%e Some solutions for n=3:
%e 0 1 0 2 0 2 0 1 0 2 0 1 0 1 0 1 2 1 0 1 0 1 0 0
%e 1 2 0 2 1 2 2 1 0 1 0 2 1 2 0 1 0 2 2 1 2 1 2 0
%e 1 2 0 2 0 0 1 2 0 1 0 2 0 2 0 1 0 1 2 0 2 0 2 0
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 27 2013
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