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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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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.
Adjacent sequences: A001264 A001265 A001266 this_sequence A001268 A001269 A001270
Sequence in context: A093132 A094169 A129325 this_sequence A099156 A129331 A005990
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KEYWORD
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nonn
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AUTHOR
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njas
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