A057010 Number of conjugacy classes of subgroups of index 4 in free group of rank n.

1, 26, 604, 14120, 334576, 7987616, 191318464, 4588288640, 110090411776, 2641931680256, 63404394241024, 1521689370306560, 36520413978750976, 876488875160477696, 21035724442850934784, 504857317670233210880

Offset

1,2

References

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.

Links

Table of n, a(n) for n=1..16.

J. H. Kwak and J. Lee, Enumeration of connected graph coverings, J. Graph Th., 23 (1996), 105-109.

J. H. Kwak and J. Lee, Enumeration of graph coverings and surface branched coverings, Lecture Note Series 1 (2001), Com^2MaC-KOSEF, Korea. See chapter 3.

V. A. Liskovets, Reductive enumeration under mutually orthogonal group actions, Acta Applic. Math., 52 (1998), 91-120.

Formula

G.f.: x(1-12x)/((1-6x)(1-8x)(1-24x)).

a(n) = 24^(n-1)+8^(n-1)-6^(n-1).

Prog

(PARI) a(n)=if(n<0, 0, 24^(n-1)+8^(n-1)-6^(n-1))

Crossrefs

Cf. A057004-A057013.

Sequence in context: A197123 A203598 A262076 * A217636 A249863 A014913

Adjacent sequences: A057007 A057008 A057009 * A057011 A057012 A057013

Keyword

nonn

Author

N. J. A. Sloane, Sep 09 2000

Extensions

More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001

Status

approved