Search: id:A000702
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%I A000702 M2307 N0910
%S A000702 1,3,4,5,7,9,14,18,24,31,43,55,72,94,123,156,200,254,324,408,513,
%T A000702 641,804,997,1236,1526,1883,2308,2829,3451,4209,5109,6194,7485,9038,10871
%N A000702 a(n) = number of conjugacy classes in the alternating group A_n.
%D A000702 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000702 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000702 Girse, Robert D.; The number of conjugacy classes of the alternating 
               group. Nordisk Tidskr. Informationsbehandling (BIT) 20 (1980), no. 
               4, 515-517.
%D A000702 M. Osima, On the irreducible representations of the symmetric group, 
               Canad. J. Math., 4 (1952), 381-384.
%H A000702 T. D. Noe, <a href="b000702.txt">Table of n, a(n) for n=2..1000</a>
%H A000702 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlternatingGroup.html">Link to a section of The World of Mathematics.</
               a>
%F A000702 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]
%F A000702 a(n) = 2p(n) + 3*Sum_{r>=1} (-1)^r*p(n-2r^2). [Girse]
%F A000702 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]
%o A000702 (MAGMA) [ NumberOfClasses(Alt(n)) : n in [2..10] ]; [A useful example 
               of MAGMA code, but it is better to use the formulae]
%Y A000702 Cf. A073584.
%Y A000702 Sequence in context: A067530 A082922 A036971 this_sequence A067526 A101760 
               A165713
%Y A000702 Adjacent sequences: A000699 A000700 A000701 this_sequence A000703 A000704 
               A000705
%K A000702 nonn,nice,easy
%O A000702 2,2
%A A000702 N. J. A. Sloane (njas(AT)research.att.com).

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