|
%I #29 Sep 08 2022 08:45:55
%S 1,8,80,720,6552,58960,531360,4782160,43045920,387413208,3486777120,
%T 31380993360,282429470960,2541865231440,22876791858720,
%U 205891126722080,1853020183479912,16677181651254480,150094635248646000,1350851717237225040,12157665458621220720
%N Number of conjugacy classes in GL(n,9).
%H Alois P. Heinz, <a href="/A182604/b182604.txt">Table of n, a(n) for n = 0..350</a>
%F G.f.: Product_{k>=1} (1-x^k)/(1-9*x^k). - _Alois P. Heinz_, Nov 03 2012
%p with(numtheory):
%p b:= proc(n) b(n):= add(phi(d)*9^(n/d), d=divisors(n))/n-1 end:
%p a:= proc(n) a(n):= `if`(n=0, 1,
%p add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p end:
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Nov 03 2012
%t b[n_] := Sum[EulerPhi[d]*9^(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_ *)
%o (Magma) /* The program does not work for n>6: */ [1] cat [NumberOfClasses(GL(n, 9)): n in [1..6]];
%o (PARI)
%o N=66; x='x+O('x^N);
%o gf=prod(n=1,N, (1-x^n)/(1-9*x^n) );
%o v=Vec(gf)
%o /* _Joerg Arndt_, Jan 24 2013 */
%Y Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182605, A182606, A182607, A182608, A182609, A182610, A182611, A182612.
%K nonn
%O 0,2
%A _Klaus Brockhaus_, Nov 23 2010
%E More terms from _Alois P. Heinz_, Nov 03 2012
%E MAGMA code edited by _Vincenzo Librandi_, Jan 24 2013
|
