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A057004 Array T(n,k) = number of conjugacy classes of subgroups of index k in free group of rank n, read by antidiagonals. 11
1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 41, 26, 1, 1, 31, 235, 604, 97, 1, 1, 63, 1361, 14120, 13753, 624, 1, 1, 127, 7987, 334576, 1712845, 504243, 4163, 1, 1, 255, 47321, 7987616, 207009649, 371515454, 24824785, 34470, 1, 1, 511, 281995, 191318464 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
REFERENCES
J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), pp. 76, 112.
LINKS
M. Hofmeister, A Note on Counting Connected Graph Covering Projections, SIAM J. Discrete Math., 11 (1998), 286-292. See page 291 Table 4.3.
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.
EXAMPLE
Array T(n,k) begins:
1 1 1 1 1 1 1 ...
1 3 7 26 97 624 4163 ...
1 7 41 604 13753 504243 ...
1 15 235 14120 1712845 ...
CROSSREFS
Rows, columns, main diagonal give A057005-A057013, A160871.
Sequence in context: A022166 A141689 A058669 * A059328 A174387 A176791
KEYWORD
nonn,tabl,nice
AUTHOR
N. J. A. Sloane, Sep 09 2000
EXTENSIONS
More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001
STATUS
approved

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Last modified May 20 04:44 EDT 2024. Contains 372703 sequences. (Running on oeis4.)