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A182603 Number of conjugacy classes in GL(n,8). 18
1, 7, 63, 504, 4088, 32697, 262080, 2096577, 16776648, 134213128, 1073737224, 8589897288, 68719439943, 549755515008, 4398046212672, 35184369697407, 281474974319672, 2251799794521144, 18014398490350584, 144115187922510840, 1152921504453534648 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 * A218191 A218367 A218314

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

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Last modified November 23 19:00 EST 2017. Contains 295128 sequences.