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%I #24 Sep 09 2021 11:28:52
%S 450,1086,2358,4902,9990,20166,40518,81222,162630,325446,651078,
%T 1302342,2604870,5209926,10420038,20840262,41680710,83361606,
%U 166723398,333446982,666894150,1333788486,2667577158,5335154502,10670309190,21340618566,42681237318,85362474822,170724949830,341449899846,682899799878
%N a(n) = 318*2^n - 186 (n>=1).
%C a(n) = the first Zagreb index of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf 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 nanostar 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="/A304511/b304511.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.: 6*x*(75 - 44*x) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F (End)
%p seq(318*2^n-186, n = 1 .. 40);
%t Array[318*2^# - 186 &, 31] (* _Michael De Vlieger_, May 14 2018 *)
%t LinearRecurrence[{3,-2},{450,1086},40] (* _Harvey P. Dale_, Sep 09 2021 *)
%o (GAP) List([1..40],n->318*2^n-186); # _Muniru A Asiru_, May 15 2018
%o (PARI) Vec(6*x*(75 - 44*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 15 2018
%Y Cf. A304509, A304510, A304512.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, May 14 2018
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