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%I #23 Jun 01 2018 03:46:14
%S 24,126,330,738,1554,3186,6450,12978,26034,52146,104370,208818,417714,
%T 835506,1671090,3342258,6684594,13369266,26738610,53477298,106954674,
%U 213909426,427818930,855637938,1711275954,3422551986,6845104050,13690208178,27380416434,54760832946,109521665970,219043332018
%N a(n) = 102*2^n - 78.
%C a(n) is the first Zagreb index of the all-aromatic dendrimer G[n], shown pictorially as DNS1[n] in the Shabani et al. reference (Fig. 1).
%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 G[n] is M(G[n]; x, y) = 6*2^n*x^2*y^2 + 12*(2^n - 1)*x^2*y^3 +3* (2^n - 1)*x^3*y^3.
%H Muniru A Asiru, <a href="/A305159/b305159.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 H. Shabani, A. R. Ashrafi, and I. Gutman, <a href="http://studia.ubbcluj.ro/arhiva/abstract_en.php?editie=CHEMIA&nr=4&an=2010&id_art=8624">Geometric-arithmetic index: an algebraic approach</a>, Studia UBB, Chemia, 55, No. 4, 107-112, 2010.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 30 2018: (Start)
%F G.f.: 6*(4 + 9*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F (End)
%p seq(102*2^n-78, n = 0..40);
%o (GAP) List([0..40], n->102*2^n-78); # _Muniru A Asiru_, May 30 2018
%o (PARI) Vec(6*(4 + 9*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 30 2018
%Y Cf. A305158, A305160.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 29 2018
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