%I #21 Jan 07 2022 13:34:04
%S 96,300,708,1524,3156,6420,12948,26004,52116,104340,208788,417684,
%T 835476,1671060,3342228,6684564,13369236,26738580,53477268,106954644,
%U 213909396,427818900,855637908,1711275924,3422551956,6845104020,13690208148,27380416404,54760832916,109521665940,219043331988
%N a(n) = 102*2^n - 108 (n>=1).
%C a(n) is the first Zagreb index of the dendrimer molecule D[n] defined in the Ashrafi et al. reference.
%C The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
%C The M-polynomial of the dendrimer molecule D[n] is M(D[n]; x,y) = 6*2^n*x^2*y^2 + 6(2*2^n - 3)*x^2*y^3 + 3*(2^n - 1)*x^3*y^3.
%H Muniru A Asiru, <a href="/A304830/b304830.txt">Table of n, a(n) for n = 1..700</a>
%H A. R. Ashrafi, H. Shabani, M. V. Diudea, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match69/n1/match69n1_151-158.pdf">Balaban index of dendrimers</a>, MATCH, Commun. Math. Comput. Chem. 69, 2013, 151-158.
%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 href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 20 2018: (Start)
%F G.f.: 12*x*(8 + x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F (End)
%p seq(102*2^n-108, n = 1 .. 35);
%t Table[102*2^n-108,{n,40}] (* or *) LinearRecurrence[{3,-2},{96,300},40] (* _Harvey P. Dale_, Jan 07 2022 *)
%o (GAP) List([1..40], n->102*2^n-108); # _Muniru A Asiru_, May 19 2018
%o (PARI) Vec(12*x*(8 + x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 20 2018
%Y Cf. A304830.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 19 2018