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A104002
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Triangle T(n,k) read by rows: number of permutations in S_n avoiding all k-length patterns that start with 1 except one fixed pattern and containing it exactly once.
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0
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1, 2, 1, 3, 4, 1, 4, 12, 6, 1, 5, 32, 27, 8, 1, 6, 80, 108, 48, 10, 1, 7, 192, 405, 256, 75, 12, 1, 8, 448, 1458, 1280, 500, 108, 14, 1, 9, 1024, 5103, 6144, 3125, 864, 147, 16, 1, 10, 2304, 17496, 28672, 18750, 6480, 1372, 192, 18, 1, 11, 5120, 59049, 131072
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| T(n+k,k+1) = total number of occurrences of any given letter in all possible n-length words on a k-letter alphabet. For example, with the 2 letter alphabet {0,1} there are 4 possible 2-length words: {00,01,10,11}. The letter 0 occurs 4 times altogether, as does the letter 1. T(4,3) = 4. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 03 2007
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LINKS
| T. Mansour, Permutations containing and avoiding certain patterns
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FORMULA
| T(n, k) = (n-k+1) * (k-1)^(n-k), k<=n.
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EXAMPLE
| 1
2,1
3,4,1
4,12,6,1
5,32,27,8,1
6,80,108,48,10,1
7,192,405,256,75,12,1
8,448,1458,1280,500,108,14,1
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CROSSREFS
| Cf. Left-edge columns include A001787, A027471, A002697, A053464, A053469, A027473, A053539, A053540, A053541, A081127, A081128.
Sequence in context: A159856 A137649 A180915 * A073135 A063804 A078753
Adjacent sequences: A103999 A104000 A104001 * A104003 A104004 A104005
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, Feb 26 2005
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