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Search: id:A092741
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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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| 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; listen)
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OFFSET
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1,3
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COMMENT
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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
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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
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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
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T(3,2)=2 because only 132 and 321 satisfy the requirements.
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CROSSREFS
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Cf. A000142, A002301, A000124.
Adjacent sequences: A092738 A092739 A092740 this_sequence A092742 A092743 A092744
Sequence in context: A071961 A120557 A092594 this_sequence A037036 A055947 A015910
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 12 2004
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