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Search: id:A001267
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| A001267 |
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One-half the number of permutations of length n with exactly 3 rising or falling successions.
(Formerly M4550 N1934)
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+0
8
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| 0, 0, 0, 0, 1, 8, 60, 444, 3599, 32484, 325322, 3582600, 43029621, 559774736, 7841128936, 117668021988, 1883347579515, 32026067455084, 576605574327174, 10957672400252944, 219190037987444577, 4603645435776504120, 101292568208941883236, 2329975164242735146316
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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(1/2) times number of permutations of 12...n such that exactly 3 of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
J. Riordan, A recurrence for permutations without rising or falling successions. Ann. Math. Statist. 36 (1965), 708-710.
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FORMULA
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Coefficient of t^3 in S[n](t) defined in A002464, divided by 2.
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CROSSREFS
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Cf. A002464, A000130, A086852. Equals A086854/2. A diagonal of A010028.
Sequence in context: A093132 A094169 A129325 this_sequence A099156 A129331 A005990
Adjacent sequences: A001264 A001265 A001266 this_sequence A001268 A001269 A001270
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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