A305261 a(n) = 120*2^n - 108.

12, 132, 372, 852, 1812, 3732, 7572, 15252, 30612, 61332, 122772, 245652, 491412, 982932, 1965972, 3932052, 7864212, 15728532, 31457172, 62914452, 125829012, 251658132, 503316372, 1006632852, 2013265812, 4026531732, 8053063572, 16106127252, 32212254612, 64424509332, 128849018772, 257698037652

Offset

0,1

Comments

a(n) is the number of vertices in the nanostar dendrimer G[n], shown pictorially as NSD[n] in the Rostami et al. reference (Fig. 2).

Links

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

M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.

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

Formula

From Colin Barker, May 31 2018: (Start)

G.f.: 12*(1 + 8*x) / ((1 - x)*(1 - 2*x)).

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

(End)

Maple

seq(120*2^n-108, n = 0 .. 40);

Prog

(PARI) Vec(12*(1 + 8*x) / ((1 - x)*(1 - 2*x) + O(x^40))) \\ Colin Barker, May 31 2018
(Magma) [120*2^n - 108 : n in [0..30]]; // Wesley Ivan Hurt, Apr 23 2021

Crossrefs

Cf. A305262, A305263, A305264.

Sequence in context: A097783 A260018 A078218 * A048643 A111085 A002721

Adjacent sequences: A305258 A305259 A305260 * A305262 A305263 A305264

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved