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
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
Programs
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Mathematica
a[n_]:= Sum[(1/GCD[n,k])2^s EulerPhi[GCD[n,k]/s], {k, 0, n-1}, {s, Divisors[GCD[n,k]]}];
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)) ).
Extensions
More terms from Robert G. Wilson v, Jun 10 2010