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A229460
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T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and vertically with exactly one mistake and colors introduced in row-major 0..2 order.
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8
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0, 1, 1, 2, 4, 2, 6, 20, 20, 6, 16, 84, 140, 84, 16, 40, 324, 863, 863, 324, 40, 96, 1188, 4962, 7940, 4962, 1188, 96, 224, 4212, 27313, 68790, 68790, 27313, 4212, 224, 512, 14580, 145932, 573342, 903332, 573342, 145932, 14580, 512, 1152, 49572, 763031
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OFFSET
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1,4
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COMMENTS
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Table starts
...0.....1......2........6.........16..........40............96.............224
...1.....4.....20.......84........324........1188..........4212...........14580
...2....20....140......863.......4962.......27313........145932..........763031
...6....84....863.....7940......68790......573342.......4651079........36985536
..16...324...4962....68790.....903332....11451686.....141595454......1718447506
..40..1188..27313...573342...11451686...221410052....4182294415.....77626332302
..96..4212.145932..4651079..141595454..4182294415..120864516084...3435347473308
.224.14580.763031.36985536.1718447506.77626332302.3435347473308.149656305350148
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1) - 4*a(n-2) for n > 4.
k=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 3.
k=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).
k=4: [order 6] for n > 7.
k=5: [order 10].
k=6: [order 14] for n > 15.
k=7: [order 26].
k=8: [order 38] for n > 39.
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EXAMPLE
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Some solutions for n=3, k=4:
0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 2
2 1 2 1 2 1 2 0 2 2 1 0 1 0 2 1 1 0 2 0
0 2 1 2 1 2 1 2 0 1 2 1 2 0 1 0 1 2 0 2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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