

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
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OFFSET

0,1


COMMENTS

The second Zagreb index of the singledefect 3gonal 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 Mpolynomial 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 Mpolynomial 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, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
T. Doslic and M. Saheli, Augmented eccentric connectivity index of singledefect nanocones, J. of Mathematical Nanoscience, 1, No. 1, 2011, 2531.
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, 18681870.
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(n1)  3*a(n2) + a(n3) 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: A109020 A099299 A344366 * A344279 A022736 A261483
Adjacent sequences: A304501 A304502 A304503 * A304505 A304506 A304507


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 13 2018


STATUS

approved



