A277985 a(n) = 3*(9*n - 1)*(3*n - 2).

6, 24, 204, 546, 1050, 1716, 2544, 3534, 4686, 6000, 7476, 9114, 10914, 12876, 15000, 17286, 19734, 22344, 25116, 28050, 31146, 34404, 37824, 41406, 45150, 49056, 53124, 57354, 61746, 66300, 71016, 75894, 80934, 86136, 91500, 97026, 102714, 108564, 114576, 120750, 127086

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

Table of n, a(n) for n=0..40.

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

Cf. A277984.

Sequence in context: A018981 A052594 A320944 * A091097 A231317 A223105

Adjacent sequences: A277982 A277983 A277984 * A277986 A277987 A277988

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 11 2016

Status

approved