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A229601 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229601 #7 Sep 19 2018 15:14:29
%S A229601 1,39,396,3040,20714,131345,792929,4618048,26165860,145058507,
%T A229601 790042315,4239980962,22473980838,117862612005,612450538677,
%U A229601 3156938117780,16157454978232,82173962646319,415564115855215,2090880090793526
%N A229601 Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.
%H A229601 R. H. Hardin, <a href="/A229601/b229601.txt">Table of n, a(n) for n = 1..210</a>
%F A229601 Empirical: a(n) = 15*a(n-1) - 81*a(n-2) + 185*a(n-3) - 162*a(n-4) + 60*a(n-5) - 8*a(n-6) for n>7.
%F A229601 Empirical g.f.: x*(1 + 24*x - 108*x^2 + 74*x^3 + 137*x^4 - 127*x^5 + 8*x^6) / (1 - 5*x + 2*x^2)^3. - _Colin Barker_, Sep 19 2018
%e A229601 Some solutions for n=3:
%e A229601 ..0..1..0....0..1..1....0..0..1....0..1..2....0..1..1....0..1..0....0..1..2
%e A229601 ..0..2..2....0..2..0....2..1..0....1..2..1....2..0..1....1..2..2....1..0..0
%e A229601 ..1..0..1....1..0..1....1..2..2....0..1..1....0..1..2....1..0..1....2..0..2
%Y A229601 Column 3 of A229606.
%K A229601 nonn
%O A229601 1,2
%A A229601 _R. H. Hardin_, Sep 26 2013