login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182605 Number of conjugacy classes in GL(n,11). 18
1, 10, 120, 1320, 14630, 160920, 1771440, 19485720, 214357440, 2357931730, 25937408640, 285311493720, 3138428201160, 34522710196920, 379749831637440, 4177248147997440, 45949729842155150, 505447028263532520, 5559917313256631160, 61159090445821012920 (list; graph; refs; listen; history; text; internal format)
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)/(1-11*x^k). - Alois P. Heinz, Nov 03 2012

MAPLE

with (numtheory):

b:= proc(n) b(n):= add(phi(d)*11^(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]*11^(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, 11)): n in [1..6]];

(PARI)

N=66; x='x+O('x^N);

gf=prod(n=1, N, (1-x^n)/(1-11*x^n)  );

v=Vec(gf)

/* Joerg Arndt, Jan 24 2013 */

CROSSREFS

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182606, A182607, A182608, A182609, A182610, A182611, A182612.

Sequence in context: A226767 A300522 A252874 * A024127 A005949 A027568

Adjacent sequences:  A182602 A182603 A182604 * A182606 A182607 A182608

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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 14:08 EST 2018. Contains 317239 sequences. (Running on oeis4.)