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A229672
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T(n,k) = number of defective 4-colorings of an n X k 0..3 array connected horizontally, antidiagonally and vertically with exactly two mistakes, and colors introduced in row-major 0..3 order.
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9
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0, 0, 0, 1, 4, 1, 3, 61, 61, 3, 12, 652, 1555, 652, 12, 50, 5048, 19805, 19805, 5048, 50, 210, 33152, 194575, 328160, 194575, 33152, 210, 861, 197248, 1673561, 4331928, 4331928, 1673561, 197248, 861, 3416, 1098752, 13271403, 50919512, 78681904
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OFFSET
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1,5
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 12*a(n-1) - 57*a(n-2) + 136*a(n-3) - 171*a(n-4) + 108*a(n-5) - 27*a(n-6) for n > 9.
k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n > 6.
k=3: [order 6] for n > 7.
k=4: [order 12] for n > 14.
k=5: [order 27] for n > 29.
k=6: [order 63] for n > 65.
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EXAMPLE
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Some solutions for n=3, k=4:
0 1 0 1 0 1 2 3 0 1 2 0 0 1 0 2 0 1 2 0
2 1 2 2 2 0 1 2 2 3 1 3 2 3 3 0 3 0 2 3
3 0 1 3 3 3 1 3 0 1 3 0 1 2 0 2 1 0 1 0
Table starts
...0.......0........1..........3...........12.............50.............210
...0.......4.......61........652.........5048..........33152..........197248
...1......61.....1555......19805.......194575........1673561........13271403
...3.....652....19805.....328160......4331928.......50919512.......557478448
..12....5048...194575....4331928.....78681904.....1289285440.....19833096240
..50...33152..1673561...50919512...1289285440....29775277216....649844491552
.210..197248.13271403..557478448..19833096240...649844491552..20240623720512
.861.1098752.99602405.5814322288.292113020848.13636997291008.608439629860544
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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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