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Search: id:A000702
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| A000702 |
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a(n) = number of conjugacy classes in the alternating group A_n.
(Formerly M2307 N0910)
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+0
7
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| 1, 3, 4, 5, 7, 9, 14, 18, 24, 31, 43, 55, 72, 94, 123, 156, 200, 254, 324, 408, 513, 641, 804, 997, 1236, 1526, 1883, 2308, 2829, 3451, 4209, 5109, 6194, 7485, 9038, 10871
(list; graph; listen)
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OFFSET
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2,2
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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).
Girse, Robert D.; The number of conjugacy classes of the alternating group. Nordisk Tidskr. Informationsbehandling (BIT) 20 (1980), no. 4, 515-517.
M. Osima, On the irreducible representations of the symmetric group, Canad. J. Math., 4 (1952), 381-384.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = (p(n) + 3Q(n))/2 where p(n) denotes the number of unrestricted partitions of n (A000041) and Q(n) the number of partitions of n into distinct odd parts (A000700) [Denes-Erdos-Turan]
a(n) = 2p(n) + 3*Sum_{r>=1} (-1)^r*p(n-2r^2). [Girse]
Sum_{r>=0} (-1)^r*a(n-(3r^2 +- r)/2) = 3(-1)^t if n = 2t^2 or 0 otherwise, where p(u) and a(u) are taken as 0 unless u is a nonnegative integer and t = 1,2,3,... [Girse]
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PROGRAM
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(MAGMA) [ NumberOfClasses(Alt(n)) : n in [2..10] ]; [A useful example of MAGMA code, but it is better to use the formulae]
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CROSSREFS
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Cf. A073584.
Sequence in context: A067530 A082922 A036971 this_sequence A067526 A101760 A165713
Adjacent sequences: A000699 A000700 A000701 this_sequence A000703 A000704 A000705
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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