|
%I #16 Sep 08 2022 08:46:17
%S 132,420,996,2148,4452,9060,18276,36708,73572,147300,294756,589668,
%T 1179492,2359140,4718436,9437028,18874212,37748580,75497316,150994788,
%U 301989732,603979620,1207959396,2415918948,4831838052,9663676260,19327352676,38654705508
%N a(n) = 288*2^n - 156.
%C a(n) is the first Zagreb index of the phenylazomethine dendrimer G[n], defined pictorially in the Golriz et al. reference (Fig. 1). The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, 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 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 I. Gutman and K. C. Das, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match50/match50_83-92.pdf">The first Zagreb index 30 years after</a>, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F O.g.f.: 12*(11 + 2*x)/((1 - x)*(1 - 2*x)).
%F E.g.f.: 12*(-13 + 24*exp(x))*exp(x).
%F a(n) = 3*a(n-1) - 2*a(n-2).
%p seq(288*2^n-156, n = 0..35);
%t Table[288 2^n - 156, {n, 0, 30}] (* _Bruno Berselli_, Nov 15 2016 *)
%o (Magma) [288*2^n-156: n in [0..40]]; // _Vincenzo Librandi_, Nov 15 2016
%Y Cf. A278129.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Nov 14 2016
%E Edited by _Bruno Berselli_, Nov 15 2016
|
