A277990 a(n) = 54*n^2 + 6*n.

0, 60, 228, 504, 888, 1380, 1980, 2688, 3504, 4428, 5460, 6600, 7848, 9204, 10668, 12240, 13920, 15708, 17604, 19608, 21720, 23940, 26268, 28704, 31248, 33900, 36660, 39528, 42504, 45588, 48780, 52080, 55488, 59004, 62628, 66360, 70200, 74148, 78204, 82368, 86640

Offset: 0

Author

Emeric Deutsch, Nov 12 2016

Keywords

• nonn
• easy

Comments

For n > 0, a(n) is the first Zagreb index of the polycyclic aromatic hydrocarbon PAH[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 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.

Also sequence found by reading the line from 0, in the direction 0, 60, ..., in the square spiral whose vertices are the generalized 29-gonal numbers (A303815). - Omar E. Pol, Nov 12 2016

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.
• I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A277991, A303815.

Programs

Magma

[54*n^2+6*n: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016

Maple

seq(54*n^2+6*n, n = 1..45);

Mathematica

Table[54n^2+6n,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,60,228},50] (* Harvey P. Dale, Jan 28 2020 *)

PARI

a(n)=54*n^2+6*n \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: 12*x*(5 + 4*x)/(1 - x)^3.

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