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%I #18 May 28 2018 05:52:56
%S 22,64,148,316,652,1324,2668,5356,10732,21484,42988,85996,172012,
%T 344044,688108,1376236,2752492,5505004,11010028,22020076,44040172,
%U 88080364,176160748,352321516,704643052,1409286124,2818572268,5637144556,11274289132,22548578284,45097156588,90194313196,180388626412,360777252844
%N a(n) = 42*2^n - 20.
%C a(n) is the number of vertices in the dendrimer nanostar G[n], defined pictorially in the Iranmanesh et al. reference (Fig. 1, where G[3] is shown) or in Alikhani et al. reference (Fig. 1, where G[3] is shown).
%H Colin Barker, <a href="/A305064/b305064.txt">Table of n, a(n) for n = 0..1000</a>
%H S. Alikhani, M. A. Iranmanesh, <a href="https://doi.org/10.1007/s11786-016-0259-z">Eccentric connectivity polynomials of an infinite family of dendrimer</a>, Digest J. Nanomaterials and Biostructures, 6 (2011) 253-257.
%H E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A. Iranmanesh and N. Dorosti, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match65/n1/match65n1_209-219.pdf">Computing the Cluj index of a type dendrimer nanostars</a>, MATCH Commun. Math. Comput. Chem. 65, 2011, 209-219.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 25 2018: (Start)
%F G.f.: 2*(11 - x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F (End)
%p seq(42*2^n-20, n = 0 .. 40);
%o (PARI) Vec(2*(11 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 25 2018
%Y Cf. A305065, A305066, A305067.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 25 2018
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