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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 15 2009
EXTENSIONS
Entry revised by N. J. A. Sloane, Sep 15 2014
STATUS
approved