A305061 a(n) = 20*2^n + 14.

34, 54, 94, 174, 334, 654, 1294, 2574, 5134, 10254, 20494, 40974, 81934, 163854, 327694, 655374, 1310734, 2621454, 5242894, 10485774, 20971534, 41943054, 83886094, 167772174, 335544334, 671088654, 1342177294, 2684354574, 5368709134, 10737418254, 21474836494, 42949672974, 85899345934, 171798691854

Offset

0,1

Comments

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

Links

Colin Barker, Table of n, a(n) for n = 0..1000

M. Ghorbani, K. Malekjani, and A. Khaki, Eccentric connectivity index of some dendrimer graphs, Iranian J. of Math. Chemistry, 3, Supplement 1 (2012), 7-18.

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

Formula

From Colin Barker, May 25 2018: (Start)

G.f.: 2*(17 - 24*x) / ((1 - x)*(1 - 2*x)).

a(n) = 3*a(n-1) - 2*a(n-2) for n>1.

(End)

Maple

seq(20*2^n+14, n = 0 .. 40);

Mathematica

20*2^Range[0, 40]+14 (* or *) LinearRecurrence[{3, -2}, {34, 54}, 40] (* Harvey P. Dale, Sep 16 2021 *)

Prog

(PARI) Vec(2*(17 - 24*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 25 2018

Crossrefs

Cf. A305060, A305062, A305063.

Sequence in context: A217768 A217704 A274380 * A051969 A241520 A067243

Adjacent sequences: A305058 A305059 A305060 * A305062 A305063 A305064

Keyword

nonn,easy

Author

Emeric Deutsch, May 24 2018

Status

approved