%I #22 May 16 2018 11:45:32
%S 528,1260,2724,5652,11508,23220,46644,93492,187188,374580,749364,
%T 1498932,2998068,5996340,11992884,23985972,47972148,95944500,
%U 191889204,383778612,767557428,1535115060,3070230324,6140460852,12280921908,24561844020,49123688244,98247376692,196494753588
%N a(n) = 366*2^n - 204 (n >= 1).
%C a(n) = the second Zagreb index of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf 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) = 3*2^n*x*y^2 + (27*2^n - 24)*x^2*y^2 + (33*2^n - 18)*x^2*y^3 + 6*2^n*x^3*y^3.
%D A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, No. 5-6, 2011, 1075-1080.
%H Colin Barker, <a href="/A304512/b304512.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 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.: 12*x*(44 - 27*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F (End)
%p seq(366*2^n-204, n = 1 .. 40);
%t Array[366*2^# - 204 &, 29] (* _Michael De Vlieger_, May 14 2018 *)
%o (GAP) List([1..40],n->366*2^n-204); # _Muniru A Asiru_, May 15 2018
%o (PARI) Vec(12*x*(44 - 27*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 15 2018
%Y Cf. A304509, A304510, A304511.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 14 2018