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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-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]]; 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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