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%I #7 Sep 21 2018 06:20:46
%S 1,60,598,2347,6809,17404,41872,97565,223075,503650,1126490,2500555,
%T 5515189,12096536,26401012,57368137,124167191,267790942,575680798,
%U 1233926231,2637709321,5624580148,11966370008,25404922357,53829723019
%N Number of defective 4-colorings of an n X 3 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order.
%H R. H. Hardin, <a href="/A229750/b229750.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) - 33*a(n-2) + 63*a(n-3) - 66*a(n-4) + 36*a(n-5) - 8*a(n-6) for n>8.
%F Conjectures from _Colin Barker_, Sep 21 2018: (Start)
%F G.f.: x*(1 + 51*x + 91*x^2 - 1118*x^3 + 1706*x^4 - 176*x^5 - 612*x^6 - 64*x^7) / ((1 - x)^3*(1 - 2*x)^3).
%F a(n) = (2*(1732+117*2^n) + (-4084+279*2^n)*n + (484+9*2^n)*n^2) / 8 for n>2.
%F (End)
%e Some solutions for n=4:
%e ..0..1..2....0..1..1....0..1..0....0..1..1....0..1..2....0..1..2....0..1..2
%e ..3..3..0....2..3..2....2..1..2....2..3..0....3..3..0....3..2..3....2..3..0
%e ..0..2..1....1..1..0....3..0..3....1..2..1....1..2..0....0..2..1....0..1..3
%e ..3..1..3....0..3..2....1..2..3....3..0..3....0..3..1....1..3..0....1..2..0
%Y Column 3 of A229755.
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 28 2013
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