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Search: id:A001470
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| A001470 |
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Number of degree-n permutations of order dividing 3.
(Formerly M2782 N1118)
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+0
42
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| 1, 1, 1, 3, 9, 21, 81, 351, 1233, 5769, 31041, 142011, 776601, 4874013, 27027729, 168369111, 1191911841, 7678566801, 53474964993, 418199988339, 3044269834281, 23364756531621, 199008751634001, 1605461415071823
(list; graph; listen)
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OFFSET
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0,4
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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).
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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a(n) = Sum from j=0 to Int(n/3) of n!/(j!*(n-3j)!*(3^j)) (the latter formula from Roger CUCULIERE, cuculier(AT)sophocle.imaginet.fr)
E.g.f.: exp(x+1/3*x^3).
a(n)= a(n-1)+(n-1)*(n-2)*a(n-3) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 03 2009]
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CROSSREFS
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Cf. A000085, A001472.
Sequence in context: A004667 A073947 A062811 this_sequence A118932 A053499 A146909
Adjacent sequences: A001467 A001468 A001469 this_sequence A001471 A001472 A001473
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), J. H. Conway and Simon Plouffe (simon.plouffe(AT)gmail.com)
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