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A182612
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Number of conjugacy classes in GL(n,27).
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18
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1, 26, 728, 19656, 531414, 14348152, 387419760, 10460332792, 282429516096, 7625596933890, 205891131543552, 5559060551656248, 150094635282119528, 4052555152616676888, 109418989131110078784, 2954312706539971597184, 79766443076861647780830
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..250
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FORMULA
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G.f.: Product_{k>=1} (1-x^k)/(1-27*x^k). - Alois P. Heinz, Nov 03 2012
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MAPLE
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with(numtheory):
b:= proc(n) b(n):= add(phi(d)*27^(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..20); # Alois P. Heinz, Nov 03 2012
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MATHEMATICA
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b[n_] := Sum[EulerPhi[d]*27^(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, 20}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)
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PROG
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(Magma) /* The program does not work for n>4: */ [1] cat [ NumberOfClasses(GL(n, 27)) : n in [1..4] ];
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-27*x^n) );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */
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CROSSREFS
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Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182610, A182611.
Sequence in context: A158643 A181227 A094738 * A143900 A282790 A180792
Adjacent sequences: A182609 A182610 A182611 * A182613 A182614 A182615
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus, Nov 23 2010
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EXTENSIONS
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More terms from Alois P. Heinz, Nov 03 2012
MAGMA code edited by Vincenzo Librandi, Jan 24 2013
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STATUS
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approved
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