A182612 Number of conjugacy classes in GL(n,27).

1, 26, 728, 19656, 531414, 14348152, 387419760, 10460332792, 282429516096, 7625596933890, 205891131543552, 5559060551656248, 150094635282119528, 4052555152616676888, 109418989131110078784, 2954312706539971597184, 79766443076861647780830

Offset: 0

Author

Klaus Brockhaus, Nov 23 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182610, A182611.

Programs

Magma

/* The program does not work for n>4: */ [1] cat [ NumberOfClasses(GL(n, 27)) : n in [1..4] ];

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*27^(n/d), d=divisors(n))/n-1 end:
a:= proc(n) a(n):= `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..20);  # Alois P. Heinz, Nov 03 2012

Mathematica

b[n_] := Sum[EulerPhi[d]*27^(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, 20}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)

PARI

N=66; x='x+O('x^N);
gf=prod(n=1,N, (1-x^n)/(1-27*x^n)  );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */

Formula

G.f.: Product_{k>=1} (1-x^k)/(1-27*x^k). - Alois P. Heinz, Nov 03 2012

Extensions

More terms from Alois P. Heinz, Nov 03 2012

MAGMA code edited by Vincenzo Librandi, Jan 24 2013