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%I #14 Sep 08 2022 08:46:21
%S 228,338,558,998,1878,3638,7158,14198,28278,56438,112758,225398,
%T 450678,901238,1802358,3604598,7209078,14418038,28835958,57671798,
%U 115343478,230686838,461373558,922746998,1845493878,3690987638,7381975158,14763950198,29527900278,59055800438,118111600758,236223201398
%N a(n) = 110*2^n + 118.
%C a(n)(n>=0) is the second Zagreb index of the dendrimer graph K[n], defined pictorially in the Ghorbani et al. reference (see Figs. 9, 10, and 11).
%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 K[n] is M(K[n]; x, y) = 2*2^n*x*y^3 + 2*(2^n + 2)*x^2*y^2 + (2^4*2^n -4)*x^2*y^3 + 14*x^3*y^3.
%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 M. Ghorbani, K. Malekjani, and A. Khaki, <a href="http://dx.doi.org/10.22052/ijmc.2012.5270">Eccentric connectivity index of some dendrimer graphs</a>, Iranian J. of Math. Chemistry, 3, Supplement 1, 2012, s7 - s18.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F G.f.: (228 - 346*x)/((1 - 2*x)*(1 - x)). - _Vincenzo Librandi_, May 25 2018
%F a(n) = 3*a(n-1) - 2* a(n-2). - _Vincenzo Librandi_, May 25 2018
%p seq(110*2^n+118, n = 0 .. 40);
%t Table[110 2^n + 118, {n, 0, 31}] (* _Vincenzo Librandi_, May 25 2018 *)
%o (Magma) [110*2^n+118: n in [0..40]]; // _Vincenzo Librandi_, May 25 2018
%Y Cf. A305060, A305061, A305062.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 24 2018
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