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%I #8 Apr 27 2021 21:09:10
%S 0,1188,11184,185808,2451728,34811238,463976296,6218438820,
%T 81495355792,1062456887518,13702092455116,175680546862100,
%U 2237595650683400,28361247430082330,357801016917216768,4496495606303951624
%N Number of defective 3-colorings of a 6 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
%C Row 6 of A229534.
%H R. H. Hardin, <a href="/A229539/b229539.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 12*a(n-1) + 182*a(n-2) - 1820*a(n-3) - 15113*a(n-4) + 101664*a(n-5) + 646022*a(n-6) - 3003324*a(n-7) -1 5725808*a(n-8) + 55305760*a(n-9) + 234926070*a(n-10) - 698528578*a(n-11) - 2270736611*a(n-12) + 6320752450*a(n-13) + 14600825558*a(n-14) - 41434331996*a(n-15) - 62768577651*a(n-16) + 196263429930*a(n-17) + 176943063476*a(n-18) - 669462409316*a(n-19) - 305019512324*a(n-20) + 1647405492614*a(n-21) + 230358934675*a(n-22) - 2942270801898*a(n-23) + 243588718325*a(n-24) + 3841770422896*a(n-25) - 923967990222*a(n-26) - 3689384232910*a(n-27) + 1300617284437*a(n-28) + 2614259101122*a(n-29) - 1127033659748*a(n-30) - 1366254718948*a(n-31) + 660843537364*a(n-32) + 524090586634*a(n-33) - 269727615782*a(n-34) - 146010681184*a(n-35) + 76928224259*a(n-36) + 28983533038*a(n-37) - 15160113967*a(n-38) - 3964319226*a(n-39) + 2009807783*a(n-40) + 352152984*a(n-41) -1 70267256*a(n-42) - 18138336*a(n-43) + 8296524*a(n-44) + 408240*a(n-45) - 176400*a(n-46) for n > 48.
%e Some solutions for n=3:
%e 0 1 0 0 1 0 0 1 0 0 1 0 0 1 2 0 1 0 0 1 2
%e 0 1 0 0 1 2 0 1 2 0 2 0 0 1 0 0 1 2 0 1 2
%e 2 2 0 0 2 0 2 0 2 0 2 0 1 2 0 2 1 0 0 1 0
%e 0 1 0 0 1 0 2 1 2 2 1 0 0 2 1 2 1 2 0 1 2
%e 0 1 2 0 1 0 0 1 2 0 1 2 0 2 1 1 0 2 0 1 2
%e 0 1 0 2 1 0 2 1 2 0 1 0 1 2 0 1 0 2 2 0 2
%Y Cf. A229534.
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 25 2013
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