A160454 Number of isomorphism classes of 5-fold coverings of a connected graph with Betti number n.

1, 7, 161, 14721, 1730861, 207388305, 24883501301, 2985987361161, 358318118583341, 42998170050574305, 5159780357316368741, 619173642303122852601, 74300837069552376921821, 8916100448264989434407505, 1069932053790827570370392981

Offset: 0

Author

N. J. A. Sloane, Nov 15 2009

Keywords

• nonn
• easy

Comments

Number of orbits of the conjugacy action of Sym(5) on Sym(5)^n [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 = 0..450
• M. W. Hero and J. F. Willenbring, Stable Hilbert series as related to the measurement of quantum entanglement, Discrete Math., 309 (2010), 6508-6514.
• J. H. Kwak and J. Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.
• A. Prasad, Equivalence classes of nodes in trees and rational generating functions, arXiv preprint arXiv:1407.5284 [math.CO], 2014.
• Index entries for linear recurrences with constant coefficients, signature (155,-4670,59440,-374304,1152000,-1382400).

Crossrefs

Fifth row of A160449.

Programs

Mathematica

LinearRecurrence[{155,-4670,59440,-374304,1152000,-1382400},{1,7,161,14721,1730861,207388305},20] (* Harvey P. Dale, Apr 08 2016 *)

PARI

Vec(-(249792*x^5-159200*x^4+36984*x^3-3746*x^2+148*x-1) / ((4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)*(12*x-1)*(120*x-1)) + O(x^100)) \\ Colin Barker, Mar 24 2015

Formula

a(n+1) = 4^n + 5^n + 2 * 6^n + 8^n + 12^n + 120^n. - Álvar Ibeas, Mar 24 2015

G.f.: -(249792*x^5-159200*x^4+36984*x^3-3746*x^2+148*x-1) / ((4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)*(12*x-1)*(120*x-1)). - Colin Barker, Mar 24 2015

Extensions

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