A218963 Total number of maximal cyclic subgroups of the alternating group, counting conjugates as distinct.

1, 1, 1, 1, 7, 31, 121, 806, 5706, 40902, 345444, 3627834, 44916840, 473882124, 5607925896, 73429902300, 1169960275680, 18289685306640, 315392669158416, 5046227338720884, 98328156602878800, 1862418125263338720, 36536960773307025360, 777453614193997039320

Offset: 0

Author

Liam Naughton, Nov 23 2012

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Liam Naughton and Goetz Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911 [math.GR], 2012-2013.
• Liam Naughton, CountingSubgroups.g
• Liam Naughton and Goetz Pfeiffer, Tomlib, The GAP table of marks library

Crossrefs

Cf. A051636, A218932, A218949, A218958.

Programs

PARI

\\ See A218958 for PARI script file.
a(n)=MaximalCyclicSubgroupCount(n, v->sum(i=1, #v, v[i]-1)%2==0); \\ Andrew Howroyd, Jul 17 2018

Extensions

a(3)-a(13) corrected by Liam Naughton, Jul 17 2018

Terms a(14) and beyond from Andrew Howroyd, Jul 17 2018