A160450 Expansion of (1-34*x+276*x^2-584*x^3)/((1-3*x)*(1-4*x)*(1-8*x)*(1-24*x)).

1, 5, 43, 681, 14491, 336465, 7997683, 191374041, 4588603531, 110092229025, 2641942301923, 63404456863401, 1521689741669371, 36520416189619185, 876488888356983763, 21035724521756752761, 504857318142580028011, 12116575072428716250945, 290797797234516859979203, 6979147097598917713826121

Offset: 0

Author

N. J. A. Sloane, Nov 15 2009

Keywords

• nonn
• easy

Comments

Number of isomorphism classes of 4-fold coverings of a connected graph with Betti number n. [Kwak and Lee]

Number of orbits of the conjugacy action of Sym(4) on Sym(4)^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..500
• 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 (39,-428,1728,-2304).

Crossrefs

Fourth row of A160449.

Programs

Mathematica

Table[3^(n - 1) + 2*4^(n - 1) + 8^(n - 1) + 24^(n - 1), {n, 0, 19}] (* Michael De Vlieger, Mar 24 2015 *)
LinearRecurrence[{39,-428,1728,-2304},{1,5,43,681},20] (* Harvey P. Dale, Feb 06 2017 *)

PARI

Vec((1-34*x+276*x^2-584*x^3)/((1-3*x)*(1-4*x)*(1-8*x)*(1-24*x)) + O(x^30)) \\ Michel Marcus, Jan 14 2016

Formula

G.f.: (1-34*x+276*x^2-584*x^3)/((1-3*x)*(1-4*x)*(1-8*x)*(1-24*x)).

a(n) = 3^(n-1) + 2*4^(n-1) + 8^(n-1) + 24^(n-1). - Álvar Ibeas, Mar 24 2015

Extensions

Entry revised by N. J. A. Sloane, Sep 15 2014