OFFSET
0,1
COMMENTS
For n>=1, a(n) is the second Zagreb index of the circumcoronene B[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 definition of the circumcoronene can be viewed in the Gutman et al. and in the Farahani et al. references.
The M-polynomial of the circumcoronene B[n] is M(B[n],x,y) = 6*x^2*y^2 + 12*(n-1)*x^2*y^3 + 3*(3*n-2)*(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, M. R. Rajesh Kanna, M. K. Jamil, and M. Imran, Computing the M-polynomial of benzenoid molecular graphs, Sci. Int. (Lahore), 28(4), 2016, 3251-3255.
I. Gutman, S. J. Cyvin, and V. Ivanov-Petrovic, Topological properties of circumcoronenes, Z. Naturforsch., 53a, 1998, 699-703.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: 6*(1+x+25*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Nov 13 2016
MAPLE
seq(81*n^2-63*n+6, n = 0 .. 40);
MATHEMATICA
CoefficientList[Series[6 (1 + x + 25 x^2) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Nov 13 2016 *)
PROG
(Magma) [3*(9*n-1)*(3*n-2): n in [0..45]]; // Vincenzo Librandi, Nov 13 2016
(PARI) a(n)=3*(9*n-1)*(3*n-2) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 11 2016
STATUS
approved