A277991 a(n) = 81*n^2 - 9*n.

0, 72, 306, 702, 1260, 1980, 2862, 3906, 5112, 6480, 8010, 9702, 11556, 13572, 15750, 18090, 20592, 23256, 26082, 29070, 32220, 35532, 39006, 42642, 46440, 50400, 54522, 58806, 63252, 67860, 72630, 77562, 82656, 87912, 93330, 98910

Offset: 0

Author

Emeric Deutsch, Nov 12 2016

Keywords

• nonn
• easy

Comments

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.

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.

Links

• E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
• M. R. Farahani, Some connectivity indices of polycyclic aromatic hydrocarbons (PAHs), Advances in Materials and Corrosion, 1, 2013, 65-69.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A277990.

Programs

Magma

[81*n^2-9*n: n in [0..35]]; // Vincenzo Librandi, Nov 13 2016

Maple

seq(81*n^2-9*n, n = 1..35);

PARI

a(n)=81*n^2-9*n \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: 18*x*(4 + 5x)/(1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Nov 13 2016