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A182603
Number of conjugacy classes in GL(n,8).
19
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
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]];
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