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A200674
Total eccentricity of Tower of Hanoi graph H_n^{3} (divided by 3).
0
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
COMMENTS
a(n) is 1/3 the sum of the eccentricities of the vertices. - Andrew Howroyd, Aug 08 2024
LINKS
Andreas M. Hinz and Daniele Parisse, The Average Eccentricity of Sierpinski Graphs, Graphs and Combinatorics, 2011.
Eric Weisstein's World of Mathematics, Graph Eccentricity.
Eric Weisstein's World of Mathematics, Hanoi Graph.
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
Cf. A000244 (number of vertices).
Sequence in context: A016200 A001454 A243877 * A162769 A126504 A361280
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 20 2011
EXTENSIONS
a(21)-a(22) from Vincenzo Librandi, Sep 11 2015
STATUS
approved