OFFSET
1,2
COMMENTS
Previous name: "Regular coverings having dihedral voltage groups: see Kwak-Lee reference in A160870 for precise definition."
From Álvar Ibeas, Oct 30 2015: (Start)
Also, number of isomorphism classes of connected (C_4 x C_2)-fold coverings of a connected graph with circuit rank n.
Also, number of lattices L in Z^n such that the quotient group Z^n / L is C_4 x C_2.
Also, number of subgroups of (C_4)^n isomorphic to C_4 x C_2.
(End)
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..1000
J. H. Kwak, J.-H. Chun, and J. Lee, Enumeration of regular graph coverings having finite abelian covering transformation groups, SIAM J. Discrete Math. 11(2), 1998, pp. 273-285.
Index entries for linear recurrences with constant coefficients, signature (14,-56,64).
FORMULA
a(n) = 2^(n-2) * (2^n - 1) * (2^(n-1) - 1) = 8^(n-1) - 6*4^(n-2) + 2^(n-2) [Kwak, Chun, and Lee]. - Álvar Ibeas, Oct 30 2015
From Colin Barker, Oct 30 2015: (Start)
a(n) = 2^(-3+n) * (2-3*2^n+4^n).
a(n) = 14*a(n-1)-56*a(n-2)+64*a(n-3) for n>3.
G.f.: -3*x^2/((2*x-1)*(4*x-1)*(8*x-1)). (End)
MATHEMATICA
Table[2^(-3+n)*(2-3*2^n+4^n), {n, 1, 30}] (* or *) LinearRecurrence[{14, -56, 64}, {0, 3, 42}, 30] (* G. C. Greubel, Apr 30 2018 *)
PROG
(PARI) a(n) = 2^(-3+n) * (2-3*2^n+4^n) \\ Colin Barker, Oct 30 2015
(PARI) concat(0, Vec(-3*x^2/((2*x-1)*(4*x-1)*(8*x-1)) + O(x^30))) \\ Colin Barker, Oct 30 2015
(Magma) [2^(-3+n)*(2-3*2^n+4^n): n in [1..30]]; // G. C. Greubel, Apr 30 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 15 2009
EXTENSIONS
Name clarified by Álvar Ibeas, Oct 30 2015
STATUS
approved