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A277984 a(n) = 6*n*(9*n-5). 1
0, 24, 156, 396, 744, 1200, 1764, 2436, 3216, 4104, 5100, 6204, 7416, 8736, 10164, 11700, 13344, 15096, 16956, 18924, 21000, 23184, 25476, 27876, 30384, 33000, 35724, 38556, 41496, 44544, 47700, 50964, 54336, 57816, 61404, 65100, 68904, 72816, 76836, 80964, 85200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n>=1, a(n) is the first Zagreb index of the circumcoronene B[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 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.

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*(2+7*x)/(1-x)^3.

MAPLE

seq(54*n^2-30*n, n = 0 .. 40);

MATHEMATICA

CoefficientList[Series[12 x (2 + 7 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Nov 13 2016 *)

PROG

(MAGMA) [6*n*(9*n-5): n in [0..45]]; // Vincenzo Librandi, Nov 13 2016

(PARI) a(n)=6*n*(9*n-5) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A277985.

Sequence in context: A001702 A004308 A008663 * A125334 A126492 A222002

Adjacent sequences:  A277981 A277982 A277983 * A277985 A277986 A277987

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 11 2016

STATUS

approved

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Last modified March 18 19:58 EDT 2019. Contains 321293 sequences. (Running on oeis4.)