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%I #7 May 31 2018 08:17:42
%S 65,901,2573,5917,12605,25981,52733,106237,213245,427261,855293,
%T 1711357,3423485,6847741,13696253,27393277,54787325,109575421,
%U 219151613,438303997,876608765,1753218301,3506437373,7012875517,14025751805,28051504381,56103009533,112206019837,224412040445,448824081661,897648164093,1795296328957
%N a(n) = 836*2^n - 771.
%C a(n) is the second Zagreb index of the nanostar dendrimer G[n], shown pictorially as NSD[n] in the Rostami et al. reference (Fig. 2).
%C The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
%C The M-polynomial of the nanostar dendrimer G[n] is M(G[n]; x, y) = (56*2^n - 48)*x^2*y^2 + (48*2^n - 44)*x^2*y^3 +(36* 2^n - 35)*x^3*y^3.
%H Colin Barker, <a href="/A305264/b305264.txt">Table of n, a(n) for n = 0..1000</a>
%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 M. Rostami, M. Shabanian, and H. Moghanian, <a href="http://www.chalcogen.ro/247_Rostami.pdf">Some topological indices for theoretical study of two types of nanostar dendrimers</a>, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 31 2018: (Start)
%F G.f.: (65 + 706*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F (End)
%p seq(836*2^n-771, n = 0..40);
%o (PARI) Vec((65 + 706*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 31 2018
%Y Cf. A305261, A305262, A305263.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 29 2018
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