

A178752


a(n) gives the number of conjugacy classes in the permutation group generated by transposition (1 2) and double ncycle (1 3 5 7 ... 2n1)(2 4 6 8 ... 2n). This group is a semidirect product formed by a cyclic group acting on an elementary abelian 2group of rank n by cyclically permuting the factors.


1



2, 5, 8, 13, 16, 28, 32, 56, 80, 136, 208, 400, 656, 1232, 2240, 4192, 7744, 14728, 27632, 52664, 99968, 190984, 364768, 699760, 1342256, 2582120, 4971248, 9588880, 18512848, 35795104, 69273728, 134224064, 260301632, 505301920, 981707008
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OFFSET

1,1


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000
J. A. Siehler, The Finite Lamplighter Groups: A Guided Tour, College Mathematics Journal, Vol. 43, No. 3 (May 2012), pp. 203211.  From N. J. A. Sloane, Oct 05 2012


FORMULA

a(n) = Sum_{k=0..n1} ( 1/gcd(n,k) 2^s phi(gcd(n,k)/s), s in divisors(gcd(n,k)) ).


MATHEMATICA

a[n_]:= Sum[(1/GCD[n, k])2^s EulerPhi[GCD[n, k]/s], {k, 0, n1}, {s, Divisors[GCD[n, k]]}];


CROSSREFS

Sequence in context: A004711 A291922 A000789 * A225255 A076145 A332774
Adjacent sequences: A178749 A178750 A178751 * A178753 A178754 A178755


KEYWORD

easy,nonn


AUTHOR

Jacob A. Siehler, Jun 09 2010


EXTENSIONS

More terms from Robert G. Wilson v, Jun 10 2010


STATUS

approved



