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

Author

N. J. A. Sloane, Sep 15 2014

Keywords

• nonn
• easy

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

• 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).

Crossrefs

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

Programs

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]];

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 *)

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

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

Extensions

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