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%I #14 May 18 2018 11:02:51
%S -4,168,512,1200,2576,5328,10832,21840,43856,87888,175952,352080,
%T 704336,1408848,2817872,5635920,11272016,22544208,45088592,90177360,
%U 180354896,360709968,721420112,1442840400,2885680976,5771362128,11542724432,23085449040,46170898256,92341796688,184683593552
%N a(n) = 172*2^n - 176.
%C a(n) is the first Zagreb index of the Wang's helicene-based nanostar DNS[n]. 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. The pictorial definition of DNS[n] can be viewed in the H. Shabani A. R. et al. reference (it is denoted DNS_{2}[n]).
%C The M-polynomial of the Wang's helicene-based dendrimer DNS[n] is M(DNS[n],x,y) = (2*2^n - 1)*x*y^3 + (6*2^n -4)*x^2*y^2 + (10*2^n - 12)*x^2*y^3 + (15*2^n - 16)*x^3*y^3.
%D H. Shabani, A. R. Ashrafi, and I. Gutman, Geometric-arithmetic index: an algebraic approach, Studia UBB, Chemia, 55, No. 4, 107-112, 2010.
%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 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 G.f.: 4*(-1 + 45*x)/((1 - x)*(1 - 2*x).
%F a(n) = 3*a(n-1) - 2*a(n-2).
%p seq(172*2^n-176, n = 0 .. 35);
%Y Cf. A278125.
%K sign,easy
%O 0,1
%A _Emeric Deutsch_, Nov 13 2016
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