OFFSET
0,2
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).
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
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 *)
PROG
(Magma) [54*n^2+6*n: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016
(PARI) a(n)=54*n^2+6*n \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 12 2016
STATUS
approved