A178752 a(n) gives the number of conjugacy classes in the permutation group generated by transposition (1 2) and double n-cycle (1 3 5 7 ... 2n-1)(2 4 6 8 ... 2n). This group is a semidirect product formed by a cyclic group acting on an elementary abelian 2-group of rank n by cyclically permuting the factors.

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

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. 203-211. - From N. J. A. Sloane, Oct 05 2012

Formula

a(n) = Sum_{k=0..n-1} ( 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, n-1}, {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