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%I #15 Sep 08 2022 08:46:17
%S 160,508,1204,2596,5380,10948,22084,44356,88900,177988,356164,712516,
%T 1425220,2850628,5701444,11403076,22806340,45612868,91225924,
%U 182452036,364904260,729808708,1459617604,2919235396,5838470980,11676942148,23353884484
%N a(n) = 348*2^n - 188.
%C a(n) is the second Zagreb index of the phenylazomethine dendrimer G[n], defined pictorially in the Golriz et al. reference (Fig. 1). 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 the dendrimer G[n] is M(G[n],x,y) = (24*2^n - 8)*x^2*y^2 + (24*2^n - 16)*x^2*y^3 + (12*2^n -12)*x^3*y^3 +4*x^3*y^4.
%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. Golriz, M. R. Darafsheh, and M. H. Khalifeh, <a href="http://chalcogen.ro/1545_Golriz.pdf">The Wiener, Szeged and PI-indices of a phenylazomethine dendrimer</a>, Digest J. Nanomaterials and Biostructures, 6, No. 4, 2011, 1545-1549.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F O.g.f.: 4*(40 + 7*x)/((1 - x)*(1 - 2*x)).
%F E.g.f.: 4*(-47 + 87*exp(x))*exp(x).
%F a(n) = 3*a(n-1) - 2*a(n-2).
%p seq(348*2^n-188, n = 0..35);
%t Table[348 2^n - 188, {n, 0, 30}] (* _Bruno Berselli_, Nov 15 2016 *)
%t LinearRecurrence[{3,-2},{160,508},30] (* _Harvey P. Dale_, Jul 22 2021 *)
%o (Magma) [348*2^n-188: n in [0..40]]; // _Vincenzo Librandi_, Nov 15 2016
%Y Cf. A278128.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Nov 15 2016
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