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Search: id:A092594
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| A092594 |
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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 231-pattern is equal to k. |
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| 1, 0, 2, 0, 2, 4, 0, 8, 8, 8, 0, 40, 40, 24, 16, 0, 240, 240, 144, 64, 32, 0, 1680, 1680, 1008, 448, 160, 64, 0, 13440, 13440, 8064, 3584, 1280, 384, 128, 0, 120960, 120960, 72576, 32256, 11520, 3456, 896, 256, 0, 1209600, 1209600, 725760, 322560, 115200, 34560
(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 and T(n,3)=n!/3 for n>=4 (A002301).
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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)=(k-1)*n!*2^(k-1)*/(k+1)! for k<n; T(n, n)=2^(n-1).
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EXAMPLE
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T(4,3)=8 because 1243, 1342, 2143, 2341, 3142, 3241, 4132 and 4231 are
the only permutations of [4] in which the length of the longest initial
segment avoiding both the 132- and the 231-pattern is equal to 3 (i.e.
the first three entries contain neither the 132- nor the 231-pattern but
all four of them contain at least one of these two patterns).
1; 0,2; 0,2,4; 0,8,8,8; 0,40,40,24,16; 0,240,240,144,64,32; 0,1680,1680,1008,448,160,64;
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CROSSREFS
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Cf. A000142, A002301.
Sequence in context: A143507 A071961 A120557 this_sequence A092741 A144182 A037036
Adjacent sequences: A092591 A092592 A092593 this_sequence A092595 A092596 A092597
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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) and Warren P. Johnson (wjohnson(AT)bates.edu), Apr 10 2004
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