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Search: id:A001268
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| A001268 |
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One-half the number of permutations of length n with exactly 4 rising or falling successions.
(Formerly M4805 N2053)
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+0
5
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| 0, 0, 0, 0, 0, 1, 11, 113, 1099, 11060, 118484, 1366134, 16970322, 226574211, 3240161105, 49453685911, 802790789101, 13815657556958, 251309386257874, 4818622686395380, 97145520138758844, 2054507019515346789, 45484006970415223287, 1052036480881734378541
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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(1/2) times number of permutations of 12...n such that exactly 4 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^4 in S[n](t) defined in A002464, divided by 2.
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CROSSREFS
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Cf. A002464, A000130, A086852. Equals A086855/2. A diagonal of A010028.
Adjacent sequences: A001265 A001266 A001267 this_sequence A001269 A001270 A001271
Sequence in context: A050758 A111463 A142483 this_sequence A065538 A104096 A087391
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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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