%I #19 May 29 2018 14:27:55
%S 42,72,132,252,492,972,1932,3852,7692,15372,30732,61452,122892,245772,
%T 491532,983052,1966092,3932172,7864332,15728652,31457292,62914572,
%U 125829132,251658252,503316492,1006632972,2013265932,4026531852,8053063692,16106127372,32212254732,64424509452,128849018892,257698037772
%N a(n) = 30*2^n + 12.
%C a(n) is the first Zagreb index of the dendrimer D[n], defined pictorially in Fig. 1 of the Heydari 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 D[n] is M(D[n];x,y) = 3*2^n*x*y^3 + 6*x^2*y^3 + 3*(2^n - 1)*x^3*y^3 (n>=0).
%H Colin Barker, <a href="/A305153/b305153.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 A. Heydari and I. Gutman, <a href="http://www.pmf.kg.ac.rs/kjs/volumes/kjs32/kjs32heydarigutman57.pdf">On the terminal Wiener index of thorn graphs</a>, Kragujevac J. Sci., 32, 2010, 57-64.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Colin Barker_, May 29 2018: (Start)
%F G.f.: 6*(7 - 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(30*2^n+12, n = 0..40);
%o (PARI) Vec(6*(7 - 9*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ _Colin Barker_, May 29 2018
%Y Cf. A305154.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 27 2018