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A229479
T(n,k) = number of defective 4-colorings of an n X k 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
9
0, 1, 1, 2, 6, 2, 6, 42, 42, 6, 20, 248, 420, 248, 20, 70, 1312, 3328, 3328, 1312, 70, 246, 6528, 23964, 36116, 23964, 6528, 246, 854, 31232, 163528, 360912, 360912, 163528, 31232, 854, 2920, 145408, 1077588, 3443856, 5068384, 3443856, 1077588, 145408
OFFSET
1,4
COMMENTS
Table starts
...0......1.......2.........6..........20...........70............246
...1......6......42.......248........1312.........6528..........31232
...2.....42.....420......3328.......23964.......163528........1077588
...6....248....3328.....36116......360912......3443856.......31875248
..20...1312...23964....360912.....5068384.....68447552......900320160
..70...6528..163528...3443856....68447552...1317269920....24789931648
.246..31232.1077588..31875248...900320160..24789931648...670127758336
.854.145408.6927888.288634368.11614790144.458660072320.17852292042240
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4) for n > 6.
k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 4.
k=3: a(n) = 14*a(n-1) - 65*a(n-2) + 112*a(n-3) - 64*a(n-4) for n > 5.
k=4: [order 8] for n > 9.
k=5: [order 18] for n > 19.
k=6: [order 42] for n > 43.
EXAMPLE
Some solutions for n=4, k=4:
0 1 2 3 0 1 2 1 0 0 1 2 0 1 0 2 0 1 0 2
2 3 1 1 2 3 0 2 1 3 0 1 3 0 1 3 2 3 1 0
1 0 3 2 1 2 0 3 2 1 3 2 2 3 0 1 2 0 3 1
3 2 0 1 3 1 2 1 0 2 1 3 0 2 3 2 1 2 0 3
CROSSREFS
Sequence in context: A229578 A078992 A062321 * A086356 A242435 A086359
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 24 2013
STATUS
approved