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A305261
a(n) = 120*2^n - 108.
4
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
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.
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);
MATHEMATICA
Table[120*2^n-108, {n, 0, 40}] (* or *) LinearRecurrence[{3, -2}, {12, 132}, 40] (* Harvey P. Dale, Sep 26 2024 *)
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 29 2018
STATUS
approved