A029725 - OEIS

%I #21 Sep 08 2022 08:44:50

%S 1,1,1,2,10,59,501,3786,48337,508402,6469142,81711572,2019160542,

%T 31945830446,749115591093,15230426073946,617313283787616,

%U 13472047923890487

%N Number of distinct subgroups of alternating group A_n, counting conjugates as distinct.

%H L. Naughton, G. Pfeiffer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Naughton/naughton2.html">Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group</a>, J. Int. Seq. 16 (2013) #13.5.8

%H Götz Pfeiffer, <a href="http://schmidt.nuigalway.ie/subgroups">Numbers of subgroups of various families of groups</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Exponential transform of A116652. - _Christian G. Bower_, Feb 23 2006

%o (Magma) n := 5; &+[ Length(s):s in SubgroupLattice(Alt(n)) ];

%Y Cf. A005432. Labeled version of A029726.

%K nonn

%O 0,4

%A _N. J. A. Sloane_.

%E a(9)-a(13) added by _Christian G. Bower_, Feb 23 2006 based on Goetz Pfeiffer's web page.

%E a(14)-a(17) from _Vaclav Kotesovec_, Jul 21 2022