A182606 Number of conjugacy classes in GL(n,13).

1, 12, 168, 2184, 28548, 371112, 4826640, 62746152, 815728368, 10604468628, 137858461104, 1792159992168, 23298084722808, 302875101365928, 3937376380474992, 51185892946146672, 665416609115237772, 8650415918497693704, 112455406951074120024

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

G.f.: Product_{k>=1} (1-x^k)/(1-13*x^k). - Alois P. Heinz, Nov 03 2012

Maple

with(numtheory):
b:= proc(n) b(n):= add(phi(d)*13^(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]*13^(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>5: */ [1] cat [NumberOfClasses(GL(n, 13)): n in [1..5]];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-13*x^n)  );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */

Crossrefs

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182607, A182608, A182609, A182610, A182611, A182612.

Sequence in context: A360352 A268899 A366710 * A079679 A216702 A320761

Adjacent sequences: A182603 A182604 A182605 * A182607 A182608 A182609

Keyword

nonn

Author

Klaus Brockhaus, Nov 23 2010

Extensions

More terms from Alois P. Heinz, Nov 03 2012

MAGMA code edited by Vincenzo Librandi, Jan 24 2013

Status

approved