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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.
13
0, 0, 0, 1, 3, 0, 3, 43, 40, 0, 12, 245, 626, 336, 0, 40, 1171, 5077, 6732, 2304, 0, 120, 5077, 35825, 80757, 62856, 14080, 0, 336, 20691, 230383, 848937, 1125333, 539568, 79872, 0, 896, 80757, 1400413, 8186713, 17724789, 14461173, 4377888, 430080, 0
OFFSET
1,5
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1).
k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3).
k=3: a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3) for n > 4.
k=4: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 4.
k=5: [order 6] for n > 7.
k=6: [order 9] for n > 11.
k=7: [order 12] for n > 14.
Empirical for row n:
n=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.
n=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 6.
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.
n=4: [order 9] for n > 17.
n=5: [order 21] for n > 27.
n=6: [order 29] for n > 39.
n=7: [order 86] for n > 94.
EXAMPLE
Some solutions for n=3, k=4:
0 1 2 1 0 1 0 2 0 1 0 2 0 0 1 2 0 1 0 2
0 1 0 2 0 2 0 2 0 2 1 0 1 0 0 1 0 2 1 1
1 2 1 1 2 1 2 0 2 2 1 2 2 1 2 0 1 0 2 2
Table starts
.0......0........1..........3...........12............40.............120
.0......3.......43........245.........1171..........5077...........20691
.0.....40......626.......5077........35825........230383.........1400413
.0....336.....6732......80757.......848937.......8186713........75035643
.0...2304....62856....1125333.....17724789.....258006388......3583403667
.0..14080...539568...14461173....342532665....7551515197....159377253183
.0..79872..4377888..175867605...6279934941..210095323918...6749642728251
.0.430080.34105536.2054728053.110801828529.5632122625852.275739382892979
CROSSREFS
Column 2 is A002700(n+1).
Row 1 is A052482(n-2).
Sequence in context: A327673 A279657 A272722 * A033596 A063529 A136667
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 27 2013
STATUS
approved