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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..35.

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 ( 1/gcd(n,k) 2^s phi(gcd(n,k)/s), k=0..n-1, 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: A053614 A004711 A000789 * A225255 A076145 A256829

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

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Last modified December 4 17:40 EST 2016. Contains 278755 sequences.