login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304504 a(n) = 3*(3*n+1)*(9*n+8)/2. 2
12, 102, 273, 525, 858, 1272, 1767, 2343, 3000, 3738, 4557, 5457, 6438, 7500, 8643, 9867, 11172, 12558, 14025, 15573, 17202, 18912, 20703, 22575, 24528, 26562, 28677, 30873, 33150, 35508, 37947, 40467, 43068, 45750, 48513, 51357, 54282, 57288, 60375, 63543, 66792 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The second Zagreb index of the single-defect 3-gonal nanocone CNC(3,n) (see definition in the Doslic et al. reference, p. 27).

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 M-polynomial of CNC(3,n) is M(CNC(3,n); x,y) = 3*x^2*y^2 + 6*n*x^2*y^3 + 3*n*(3*n+1)*x^3*y^3/2.

More generally, the M-polynomial of CNC(k,n) is M(CNC(k,n); x,y) = k*x^2*y^2 + 2*k*n*x^2*y^3 + k*n*(3*n + 1)*x^3*y^3/2.

8*a(n) + 25 is a square. - Bruno Berselli, May 14 2018

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

T. Doslic and M. Saheli, Augmented eccentric connectivity index of single-defect nanocones, J. of Mathematical Nanoscience, 1, No. 1, 2011, 25-31.

A. Khaksar, M. Ghorbani, and H. R. Maimani, On atom bond connectivity and GA indices of nanocones, Optoelectronics and Advanced Materials - Rapid Communications, 4, No. 11, 2010, 1868-1870.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

From Colin Barker, May 14 2018: (Start)

G.f.: 3*(4 + 22*x + x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)

MAPLE

seq((1/2)*(3*(9*n+8))*(3*n+1), n = 0 .. 40);

PROG

(PARI) Vec(3*(4 + 22*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 14 2018

CROSSREFS

Cf. A304503.

Sequence in context: A008547 A109020 A099299 * A022736 A261483 A082151

Adjacent sequences:  A304501 A304502 A304503 * A304505 A304506 A304507

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 13 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)