A062297 Number of distinct Abelian subgroups of the symmetric group S_n.

1, 2, 5, 21, 87, 612, 3649, 35515, 289927, 377118, 36947363, 657510251, 7736272845

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001

Keywords

• nonn
• more

Links

• L. Naughton and G. Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911 [math.GR], 2012-2013 and J. Int. Seq. 16 (2013) #13.5.8

Crossrefs

Cf. A005432, A051625.

Programs

GAP

# GAP 4.4
LoadPackage("sonata");;
for n in [2,3,4,5,6,7,8,9,10] do
    p := SymmetricGroup(n) ;;
    o := Order(p);
    s := Subgroups(p);
    f := Filtered(s, g -> IsAbelian(g));
    a := Size(f);
    Print(a," ") ;
od; # R. J. Mathar, May 24 2013

Extensions

a(9)-a(13) added by Liam Naughton