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A305060

a(n) = 18*2^n + 10.

28, 46, 82, 154, 298, 586, 1162, 2314, 4618, 9226, 18442, 36874, 73738, 147466, 294922, 589834, 1179658, 2359306, 4718602, 9437194, 18874378, 37748746, 75497482, 150994954, 301989898, 603979786, 1207959562, 2415919114, 4831838218, 9663676426, 19327352842, 38654705674, 77309411338, 154618822666, 309237645322

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OFFSET

0,1

COMMENTS

a(n) (n>=0) is the number of vertices of the dendrimer graph K[n], defined pictorially in the Ghorbani et al. reference (see Figs. 9, 10, and 11).

LINKS

Table of n, a(n) for n=0..34.

M. Ghorbani, K. Malekjani, and A. Khaki, Eccentric connectivity index of some dendrimer graphs, Iranian J. of Math. Chemistry, 3, Supplement 1, 2012, s7-s18.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

From Bruno Berselli, May 25 2018: (Start)

O.g.f.: 2*(14 - 19*x)/((1 - x)*(1 - 2*x)).

E.g.f.: 2*(5 + 9*exp(x))*exp(x).

a(n) = 3*a(n-1) - 2*a(n-2) = 2*a(n-1) - 10. (End)

MAPLE

seq(18*2^n+10, n = 0 .. 40);

MATHEMATICA

Table[18 2^n + 10, {n, 0, 40}] (* Bruno Berselli, May 25 2018 *)

LinearRecurrence[{3, -2}, {28, 46}, 40] (* Harvey P. Dale, Feb 11 2024 *)

CROSSREFS