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%I #16 May 16 2018 11:19:04
%S 88,232,520,1096,2248,4552,9160,18376,36808,73672,147400,294856,
%T 589768,1179592,2359240,4718536,9437128,18874312,37748680,75497416,
%U 150994888,301989832,603979720,1207959496,2415919048,4831838152,9663676360,19327352776,38654705608,77309411272,154618822600,309237645256,618475290568
%N a(n) = 72*2^n -56 (n>=1).
%C a(n) is the second Zagreb index of the nanostar dendrimer NS2[n] from the Madanshekaf et al. reference.
%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 NS2[n] is M(NS2[n]; x,y) = 2*2^n *x*y^2 + (8*2^n - 5)*x^2*y^2 + (6*2^n - 6)*x^2*y^3.
%H Colin Barker, <a href="/A304519/b304519.txt">Table of n, a(n) for n = 1..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 A. Madanshekaf and M. Moradi, <a href="http://dx.doi.org/10.22052/ijmc.2014.5541">The first geometric-arithmetic index of some nanostar dendrimers</a>, Iranian J. Math. Chemistry, 5, Supplement 1, 2014, s1-s6.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 15 2018: (Start)
%F G.f.: 8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F (End)
%p seq(72*2^n-56, n = 1 .. 40);
%o (GAP) List([1..40],n->72*2^n-56); # _Muniru A Asiru_, May 15 2018
%o (PARI) Vec(8*x*(11 - 4*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 15 2018
%Y Cf. A304517, A304518.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 15 2018
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