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

0,2

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).

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

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 *)

Prog

(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

Crossrefs

Fourth row of A160449.

Sequence in context: A307362 A280776 A255895 * A114604 A085098 A271679

Adjacent sequences: A160447 A160448 A160449 * A160451 A160452 A160453

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 15 2009

Extensions

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

Status

approved