A246985 Expansion of (1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-6*x)).

1, 3, 11, 49, 251, 1393, 8051, 47449, 282251, 1686433, 10097891, 60526249, 362976251, 2177317873, 13062296531, 78368963449, 470199366251, 2821153019713, 16926788715971, 101560344351049, 609360902796251, 3656161927895953, 21936961102828211, 131621735227521049, 789730317205170251, 4738381620767930593

Offset

0,2

Comments

From Álvar Ibeas, Mar 25 2015: (Start)

Number of isomorphism classes of 3-fold coverings of a connected graph with circuit rank n [Kwak and Lee].

Number of orbits of the conjugacy action of Sym(3) on Sym(3)^n [Kwak and Lee].

(End)

Links

Table of n, a(n) for n=0..25.

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:1407.5284 [math.CO], 2014.

Index entries for linear recurrences with constant coefficients, signature (11,-36,36).

Formula

G.f.: (1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-6*x)).

a(n) = 11*a(n-1) - 36*a(n-2) + 36*a(n-3) for n>2. [Bruno Berselli, Mar 25 2015]

a(n) = 2^(n-1) + 3^(n-1) + 6^(n-1). - Álvar Ibeas, Mar 25 2015

Mathematica

Table[2^(n - 1) + 3^(n - 1) + 6^(n - 1), {n, 0, 30}] (* Bruno Berselli, Mar 25 2015 *)
LinearRecurrence[{11, -36, 36}, {1, 3, 11}, 30] (* Harvey P. Dale, Jan 17 2019 *)

Prog

(Magma) [n le 3 select 2*Factorial(n)-1 else 11*Self(n-1)-36*Self(n-2)+36*Self(n-3): n in [1..30]];
(PARI) Vec((1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-6*x)) + O(x^30)) \\ Michel Marcus, Jan 14 2016

Crossrefs

Apart from first term, same as A074528. Third row of A160449.

Sequence in context: A333514 A268414 A074528 * A326521 A340813 A004211

Adjacent sequences: A246982 A246983 A246984 * A246986 A246987 A246988

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 15 2014

Extensions

Signature corrected and Ibeas formula adapted to the offset by Bruno Berselli, Mar 25 2015

Status

approved