The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006952 Number of conjugacy classes in GL(n,3). (Formerly M1842) 25
 1, 2, 8, 24, 78, 232, 720, 2152, 6528, 19578, 58944, 176808, 531128, 1593288, 4781952, 14345792, 43043622, 129130584, 387411144, 1162232520, 3486755688, 10460266224, 31380972784, 94142915640, 282429275616, 847287817866, 2541865038832, 7625595108432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). W. D. Smith, personal communication. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..700 W. Feit and N. J. Fine, Pairs of commuting matrices over a finite field, Duke Math. Journal, 27 (1960) 91-94. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 162 I. G. Macdonald, Numbers of conjugacy classes in some finite classical groups, Bulletin of the Australian Mathematical Society, vol.23, no.01, pp.23-48, (February-1981). FORMULA G.f. prod(n>=1, (1-x^n)/(1-3*x^n)  ). [Joerg Arndt, Jan 02 2013] The number a(n) of conjugacy classes in the group GL(n, q) is the coefficient of t^n in prod(k>=1, (1-t^k)/(1-q*t^k) ). - Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001. a(n) ~ 3^n - (1+sqrt(3) + (-1)^n*(1-sqrt(3))) * 3^(n/2) / 4. - Vaclav Kotesovec, May 06 2018 G.f.: exp(Sum_{k>=1} ( Sum_{d|k} d*(3^(k/d) - 1) ) * x^k/k). - Ilya Gutkovskiy, Sep 27 2018 MAPLE with(numtheory): b:= n-> add(phi(d)*3^(n/d), d=divisors(n))/n-1: a:= proc(n) option remember; `if`(n=0, 1,        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)     end: seq(a(n), n=0..30);  # Alois P. Heinz, Nov 03 2012 MATHEMATICA b[n_] := Sum[EulerPhi[d]*3^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] =  If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *) PROG (MAGMA) /* The program does not work for n>12: */ [1] cat [NumberOfClasses(GL(n, 3)) : n in [1..12]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006; edited by Vincenzo Librandi, Jan 23 2013 (PARI) N=66; x='x+O('x^N); gf=prod(n=1, N, (1-x^n)/(1-3*x^n)  ); v=Vec(gf) /* Joerg Arndt, Jan 02 2013 */ CROSSREFS Cf. A006951, A049314, A049315, A049316, A304082. Sequence in context: A026070 A093833 A228404 * A327550 A034741 A063727 Adjacent sequences:  A006949 A006950 A006951 * A006953 A006954 A006955 KEYWORD nonn AUTHOR EXTENSIONS More terms from Alois P. Heinz, Nov 03 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 24 13:52 EST 2020. Contains 331194 sequences. (Running on oeis4.)