A182603 Number of conjugacy classes in GL(n,8).

1, 7, 63, 504, 4088, 32697, 262080, 2096577, 16776648, 134213128, 1073737224, 8589897288, 68719439943, 549755515008, 4398046212672, 35184369697407, 281474974319672, 2251799794521144, 18014398490350584, 144115187922510840, 1152921504453534648

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: prod((1-x^k)/(1-8*x^k),k=1..infinity).

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*8^(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..30);  # Alois P. Heinz, Nov 03 2012

Mathematica

b[n_] := Sum[EulerPhi[d]*8^(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>6: */ [1] cat [NumberOfClasses(GL(n, 8)): n in [1..6]];

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182604 - A182612.

Sequence in context: A166153 A123009 A219058 * A320073 A218191 A218367

Adjacent sequences: A182600 A182601 A182602 * A182604 A182605 A182606

Keyword

nonn

Author

Klaus Brockhaus, Nov 23 2010

Extensions

Extended by D. S. McNeil, Dec 06 2010

MAGMA code edited by Vincenzo Librandi, Jan 23 2013

Status

approved