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Search: id:A006952
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| A006952 |
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Number of conjugacy classes in GL(n,3).
(Formerly M1842)
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+0
6
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| 1, 2, 8, 24, 78, 232, 720, 2152, 6528, 19578, 58944, 176808, 531128, 1593288, 4781952, 14345792, 43043622, 129130584, 387411144, 1162232520, 3486755688, 10460266224
(list; graph; listen)
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OFFSET
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0,2
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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).
W. D. Smith, personal communication.
W. Feit and N. J. Fine, Pairs of commuting matrices over a finite field. Duke Math. Journal, 27 (1960) 91-94.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 162
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FORMULA
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The number a(n) of conjugacy classes in the group GL(n, q) is the coefficient of t^n in the infinite product: product k=1, 2, ... (1-t^k)/(1-qt^k) - Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001.
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PROGRAM
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(MAGMA) [ NumberOfClasses(GL(n, 3)) : n in [1..10] ]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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Cf. A006951, A049314, A049315, A049316.
Sequence in context: A130495 A026070 A093833 this_sequence A034741 A085449 A063727
Adjacent sequences: A006949 A006950 A006951 this_sequence A006953 A006954 A006955
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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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