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A229694 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229694 #9 Apr 28 2021 01:25:30
%S A229694 0,0,0,1,3,0,3,43,40,0,12,245,626,336,0,40,1171,5077,6732,2304,0,120,
%T A229694 5077,35825,80757,62856,14080,0,336,20691,230383,848937,1125333,
%U A229694 539568,79872,0,896,80757,1400413,8186713,17724789,14461173,4377888,430080,0
%N A229694 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%H A229694 R. H. Hardin, <a href="/A229694/b229694.txt">Table of n, a(n) for n = 1..286</a>
%F A229694 Empirical for column k:
%F A229694 k=1: a(n) = a(n-1).
%F A229694 k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3).
%F A229694 k=3: a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3) for n > 4.
%F A229694 k=4: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 4.
%F A229694 k=5: [order 6] for n > 7.
%F A229694 k=6: [order 9] for n > 11.
%F A229694 k=7: [order 12] for n > 14.
%F A229694 Empirical for row n:
%F A229694 n=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.
%F A229694 n=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 6.
%F A229694 n=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 > 10.
%F A229694 n=4: [order 9] for n > 17.
%F A229694 n=5: [order 21] for n > 27.
%F A229694 n=6: [order 29] for n > 39.
%F A229694 n=7: [order 86] for n > 94.
%e A229694 Some solutions for n=3, k=4:
%e A229694   0 1 2 1     0 1 0 2     0 1 0 2     0 0 1 2     0 1 0 2
%e A229694   0 1 0 2     0 2 0 2     0 2 1 0     1 0 0 1     0 2 1 1
%e A229694   1 2 1 1     2 1 2 0     2 2 1 2     2 1 2 0     1 0 2 2
%e A229694 Table starts
%e A229694 .0......0........1..........3...........12............40.............120
%e A229694 .0......3.......43........245.........1171..........5077...........20691
%e A229694 .0.....40......626.......5077........35825........230383.........1400413
%e A229694 .0....336.....6732......80757.......848937.......8186713........75035643
%e A229694 .0...2304....62856....1125333.....17724789.....258006388......3583403667
%e A229694 .0..14080...539568...14461173....342532665....7551515197....159377253183
%e A229694 .0..79872..4377888..175867605...6279934941..210095323918...6749642728251
%e A229694 .0.430080.34105536.2054728053.110801828529.5632122625852.275739382892979
%Y A229694 Column 2 is A002700(n+1).
%Y A229694 Row 1 is A052482(n-2).
%K A229694 nonn,tabl
%O A229694 1,5
%A A229694 _R. H. Hardin_, Sep 27 2013