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A092741
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Triangle read by rows: T(n,k) is the number of permutations p of [n] in which the length of the longest initial segment avoiding both the 132- and the 321-pattern is equal to k.
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0
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1, 0, 2, 0, 2, 4, 0, 8, 9, 7, 0, 40, 45, 24, 11, 0, 240, 270, 144, 50, 16, 0, 1680, 1890, 1008, 350, 90, 22, 0, 13440, 15120, 8064, 2800, 720, 147, 29, 0, 120960, 136080, 72576, 25200, 6480, 1323, 224, 37, 0, 1209600, 1360800, 725760, 252000, 64800, 13230
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are the factorial numbers (A000142). T(n,2)=n!/3 for n>=3 (A002301). T(n,3)=3n!/8 for n>=4. Diagonal yields A000124.
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REFERENCES
| E. Deutsch and W. P. Johnson, Create your own permutation statistic, Math. Mag., 77, 130-134, 2004.
R. Simion and F. W. Schmidt, Restricted permutations, European J. Combin., 6, 383-406, 1985.
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FORMULA
| T(n, k)=n!k/[2(k-2)!(k+1)] for k<n; T(n, n)=n(n-1)/2.
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EXAMPLE
| T(3,2)=2 because only 132 and 321 satisfy the requirements.
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CROSSREFS
| Cf. A000142, A002301, A000124.
Sequence in context: A172040 A120557 A092594 * A144182 A037036 A055947
Adjacent sequences: A092738 A092739 A092740 * A092742 A092743 A092744
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 12 2004
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