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%I #9 Jun 16 2017 08:12:54
%S 0,7680,228096,6298560,162171072,4032737280,97662620160,2320483572864,
%T 54321921368064,1256772873968640,28798595015489856,654681579415674048,
%U 14783463288895694400,331920615489235774848,7415532825963054368832
%N Number of defective 3-colorings of an n X 6 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
%C Column 6 of A229510.
%H R. H. Hardin, <a href="/A229508/b229508.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 50*a(n-1) -715*a(n-2) +324*a(n-3) +50175*a(n-4) -180630*a(n-5) -940491*a(n-6) +4556250*a(n-7) +2329155*a(n-8) -27398736*a(n-9) +13286025*a(n-10) +47829690*a(n-11) -43046721*a(n-12) for n>13.
%F Empirical g.f.: 192*x^2*(40 - 812*x + 2005*x^2 + 40851*x^3 - 164547*x^4 - 625725*x^5 + 3177063*x^6 + 1119015*x^7 - 16522785*x^8 + 8109396*x^9 + 26926344*x^10 - 23914845*x^11) / ((1 - 25*x + 90*x^2 - 81*x^3)^2*(1 - 45*x^2 - 81*x^3)^2). - _Colin Barker_, Jun 16 2017
%e Some solutions for n=3
%e ..0..1..2..0..2..0....0..1..2..0..2..0....0..1..2..2..1..2....0..1..2..1..2..1
%e ..0..1..2..0..2..0....2..1..2..0..2..1....2..0..0..0..0..0....2..1..2..0..0..1
%e ..0..0..2..0..1..1....0..0..2..0..0..0....2..1..2..2..2..1....0..1..1..1..2..1
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 25 2013
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