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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 20 2011
EXTENSIONS
a(21)-a(22) from Vincenzo Librandi, Sep 11 2015
STATUS
approved