A200674 Eccentricity of Tower of Hanoi graph H_n^{3} (divided by 3).

0, 1, 9, 61, 385, 2365, 14353, 86605, 521089, 3130909, 18798577, 112830829, 677103073, 4062972733, 24378899281, 146276584333, 877669071937, 5266043129437, 31596344870065, 189578327500717, 1137470739845281, 6824826763594621, 40948967555136529

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Andreas M. Hinz and Daniele Parisse, The Average Eccentricity of Sierpinski Graphs, Graphs and Combinatorics, 2011.

Index entries for linear recurrences with constant coefficients, signature (10,-27,18).

Formula

y(0)=0; y(n+1) = 6*y(n) + 2*3^n + 3 - 2*0^n. a(n)=y(n)/3.

a(n) = -2*3^(n-2) +14*6^n/45-1/5, n>0. - R. J. Mathar, Dec 13 2011

G.f.: x*(1+x)*(2*x-1) / ( (x-1)*(6*x-1)*(3*x-1) ). - R. J. Mathar, Dec 13 2011

Mathematica

Join[{0}, LinearRecurrence[{10, -27, 18}, {1, 9, 61}, 25]] (* Vincenzo Librandi, Sep 11 2015 *)

Prog

(PARI) Vec(x*(1+x)*(2*x-1) / ( (x-1)*(6*x-1)*(3*x-1) ) + O(x^40)) \\ Michel Marcus, Sep 11 2015
(Magma) [0] cat [-2*3^(n-2) +14*6^n/45-1/5: n in [1..25]]; // Vincenzo Librandi, Sep 11 2015

Crossrefs

Sequence in context: A016200 A001454 A243877 * A162769 A126504 A361280

Adjacent sequences: A200671 A200672 A200673 * A200675 A200676 A200677

Keyword

nonn

Author

N. J. A. Sloane, Nov 20 2011

Extensions

a(21)-a(22) from Vincenzo Librandi, Sep 11 2015

Status

approved