A152612 Number of isomorphism classes of n-fold coverings of a connected graph with Betti number 3.

1, 8, 49, 681, 14721, 524137, 25471105, 1628116890, 131789656610, 13174980291658, 1593894406662866, 229496526010111571, 38782290669508033003, 7600987633299112125995, 1710169549495739472301076, 437793904386312274903991653, 126520458075485848061740557461

Offset: 1

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• nonn

Comments

Number of orbits of the conjugacy action of Sym(n) on Sym(n)^3 [Kwak and Lee, 2001]. - Álvar Ibeas, Mar 24 2015

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.

Links

• Álvar Ibeas, Table of n, a(n) for n = 1..60
• Joseph Ben Geloun and Sanjaye Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, Annales de l'Institut Henri Poincaré D, Vol. 1, No. 1 (2014), pp. 77-138; arXiv preprint, arXiv:1307.6490 [hep-th], 2013.
• Jin Ho Kwak and Jaeun Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.

Crossrefs

Euler transform of A057006.

Fourth column of A160449.

Programs

Mathematica

A057006 = Import["https://oeis.org/A057006/b057006.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
a = etr[A057006[[#]]&];
Array[a, 15] (* Jean-François Alcover, Aug 29 2019 *)

Sage

[sum(p.aut()**2 for p in Partitions(n)) for n in range(1,8)] # Álvar Ibeas, Mar 24 2015

Extensions

a(6) and a(7) from Geloun and Ramgoolan (2013) added by N. J. A. Sloane, Nov 21 2013

Name clarified and more terms added by Álvar Ibeas, Mar 24 2015