|
%I #29 Sep 08 2022 08:46:09
%S 1,3,11,49,251,1393,8051,47449,282251,1686433,10097891,60526249,
%T 362976251,2177317873,13062296531,78368963449,470199366251,
%U 2821153019713,16926788715971,101560344351049,609360902796251,3656161927895953,21936961102828211,131621735227521049,789730317205170251,4738381620767930593
%N Expansion of (1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-6*x)).
%C From _Álvar Ibeas_, Mar 25 2015: (Start)
%C Number of isomorphism classes of 3-fold coverings of a connected graph with circuit rank n [Kwak and Lee].
%C Number of orbits of the conjugacy action of Sym(3) on Sym(3)^n [Kwak and Lee].
%C (End)
%H J. H. Kwak and J. Lee, <a href="http://dx.doi.org/10.4153/CJM-1990-039-3">Isomorphism classes of graph bundles</a>. Can. J. Math., 42(4), 1990, pp. 747-761.
%H A. Prasad, <a href="http://arxiv.org/abs/1407.5284">Equivalence classes of nodes in trees and rational generating functions</a>, arXiv:1407.5284 [math.CO], 2014.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-36,36).
%F G.f.: (1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-6*x)).
%F a(n) = 11*a(n-1) - 36*a(n-2) + 36*a(n-3) for n>2. [_Bruno Berselli_, Mar 25 2015]
%F a(n) = 2^(n-1) + 3^(n-1) + 6^(n-1). - _Álvar Ibeas_, Mar 25 2015
%t Table[2^(n - 1) + 3^(n - 1) + 6^(n - 1), {n, 0, 30}] (* _Bruno Berselli_, Mar 25 2015 *)
%t LinearRecurrence[{11,-36,36},{1,3,11},30] (* _Harvey P. Dale_, Jan 17 2019 *)
%o (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]];
%o (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
%Y Apart from first term, same as A074528. Third row of A160449.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Sep 15 2014
%E Signature corrected and Ibeas formula adapted to the offset by _Bruno Berselli_, Mar 25 2015
|
