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A342239
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Table read by upward antidiagonals: T(n,k) is the number of strings of length k over an n-letter alphabet that are bifix free; n >= 1, k >= 1.
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2
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1, 2, 0, 3, 2, 0, 4, 6, 4, 0, 5, 12, 18, 6, 0, 6, 20, 48, 48, 12, 0, 7, 30, 100, 180, 144, 20, 0, 8, 42, 180, 480, 720, 414, 40, 0, 9, 56, 294, 1050, 2400, 2832, 1242, 74, 0, 10, 72, 448, 2016, 6300, 11900, 11328, 3678, 148, 0, 11, 90, 648, 3528, 14112, 37620, 59500, 45132, 11034, 284, 0
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n,0) = n.
T(n,2k) = n*T(n,2k-1) - T(n,k).
T(n,2k+1) = n*T(n,2k).
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EXAMPLE
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Table begins:
n\k | 1 2 3 4 5 6 7 8 9
----+------------------------------------------------------
1 | 1 0 0 0 0 0 0 0 0
2 | 2 2 4 6 12 20 40 74 148
3 | 3 6 18 48 144 414 1242 3678 11034
4 | 4 12 48 180 720 2832 11328 45132 180528
5 | 5 20 100 480 2400 11900 59500 297020 1485100
6 | 6 30 180 1050 6300 37620 225720 1353270 8119620
7 | 7 42 294 2016 14112 98490 689430 4823994 33767958
8 | 8 56 448 3528 28224 225344 1802752 14418488 115347904
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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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