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A006952
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Number of conjugacy classes in GL(n,3).
(Formerly M1842)
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15
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| W. Feit and N. J. Fine, Pairs of commuting matrices over a finite field. Duke Math. Journal, 27 (1960) 91-94.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
W. D. Smith, personal communication.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 162
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FORMULA
| 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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PROG
| (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
| Cf. A006951, A049314, A049315, A049316.
Sequence in context: A130495 A026070 A093833 * A034741 A063727 A085449
Adjacent sequences: A006949 A006950 A006951 * A006953 A006954 A006955
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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