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A229606 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229606 #7 Apr 27 2021 21:30:13
%S A229606 0,0,0,1,6,1,3,39,39,3,12,202,396,202,12,40,925,3040,3040,925,40,120,
%T A229606 3924,20714,35182,20714,3924,120,336,15795,131345,362100,362100,
%U A229606 131345,15795,336,896,61182,792929,3476928,5655616,3476928,792929,61182,896
%N A229606 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.
%C A229606 Table starts
%C A229606 ...0.....0.......1.........3..........12...........40............120
%C A229606 ...0.....6......39.......202.........925.........3924..........15795
%C A229606 ...1....39.....396......3040.......20714.......131345.........792929
%C A229606 ...3...202....3040.....35182......362100......3476928.......31848813
%C A229606 ..12...925...20714....362100.....5655616.....82613904.....1153135492
%C A229606 ..40..3924..131345...3476928....82613904...1840258874....39229935270
%C A229606 .120.15795..792929..31848813..1153135492..39229935270..1279020266434
%C A229606 .336.61182.4618048.281845934.15568071652.809714005005.40413033646242
%H A229606 R. H. Hardin, <a href="/A229606/b229606.txt">Table of n, a(n) for n = 1..312</a>
%F A229606 Empirical for column k:
%F A229606 k=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.
%F A229606 k=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 5.
%F A229606 k=3: 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 A229606 k=4: [order 9] for n > 11.
%F A229606 k=5: [order 16] for n > 17.
%F A229606 k=6: [order 21] for n > 23.
%F A229606 k=7: [order 46] for n > 47.
%e A229606 Some solutions for n=3, k=4:
%e A229606   0 1 1 2     0 1 0 1     0 1 2 1     0 1 2 1     0 1 2 0
%e A229606   2 0 0 1     1 2 1 2     1 2 1 1     2 0 1 2     1 0 2 1
%e A229606   0 2 1 2     0 2 0 0     0 1 0 2     0 0 2 0     1 2 0 2
%Y A229606 Column 1 is A052482(n-2).
%K A229606 nonn,tabl
%O A229606 1,5
%A A229606 _R. H. Hardin_, Sep 26 2013