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

Author

N. J. A. Sloane, Sep 09 2000

Keywords

• nonn

References

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

Links

• 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.

Crossrefs

Cf. A057004-A057013.

Programs

PARI

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

Formula

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

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

Extensions

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