%I #21 Sep 08 2022 08:46:17
%S 0,72,306,702,1260,1980,2862,3906,5112,6480,8010,9702,11556,13572,
%T 15750,18090,20592,23256,26082,29070,32220,35532,39006,42642,46440,
%U 50400,54522,58806,63252,67860,72630,77562,82656,87912,93330,98910
%N a(n) = 81*n^2 - 9*n.
%C For n > 0, a(n) is the second Zagreb index of the polycyclic aromatic hydrocarbon PAH[n]. 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. The pictorial definition of PAH[n] can be viewed in the Farahani reference.
%C The M-polynomial of the polycyclic aromatic hydrocarbon PAH[n] is M(PAH[n], x, y) = 6*n*x*y^3 + 3*n*(3*n-1)*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. R. Farahani, <a href="http://www.jchemacta.com/index.php/amc/article/view/99">Some connectivity indices of polycyclic aromatic hydrocarbons (PAHs)</a>, Advances in Materials and Corrosion, 1, 2013, 65-69.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: 18*x*(4 + 5x)/(1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Nov 13 2016
%p seq(81*n^2-9*n, n = 1..35);
%o (Magma) [81*n^2-9*n: n in [0..35]]; // _Vincenzo Librandi_, Nov 13 2016
%o (PARI) a(n)=81*n^2-9*n \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A277990.
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Nov 12 2016