A057006 Number of conjugacy classes of subgroups of index n in free group of rank 3.

1, 7, 41, 604, 13753, 504243, 24824785, 1598346352, 129958211233, 13030565312011, 1579721338432537, 227804599861102676, 38541084552054952009, 7560534755192908672087, 1702288146755359962223409

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

• Vaclav Kotesovec, Table of n, a(n) for n = 1..60
• J. B. Geloun and S. Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, arXiv preprint arXiv:1307.6490 [hep-th], 2013.
• Joseph Ben Geloun and Sanjaye Ramgoolam, All-orders asymptotics of tensor model observables from symmetries of restricted partitions, arXiv:2106.01470 [hep-th], 2021.
• 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.
• P. Vrana, On the algebra of local unitary invariants of pure and mixed quantum states, J. Phys A: Math. Theor. 44 (2011) 225304 doi:10.1088/1751-8113/44/22/225304, Table 2.

Crossrefs

Cf. A057004-A057013. Inverse Euler transform of A152612.

Extensions

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