A304619 a(n) = 324*n^2 - 804*n + 468 (n>=2).

156, 972, 2436, 4548, 7308, 10716, 14772, 19476, 24828, 30828, 37476, 44772, 52716, 61308, 70548, 80436, 90972, 102156, 113988, 126468, 139596, 153372, 167796, 182868, 198588, 214956, 231972, 249636, 267948, 286908, 306516, 326772, 347676, 369228, 391428, 414276, 437772, 461916, 486708

Offset

2,1

Comments

For n>=3, a(n) is the second Zagreb index of the hexagonal network HX(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 M-polynomial of the hexagonal network HX(n) is M(HX(n); x,y) = 12*x^3*y^4 + 6*x^3*y^6 + 6*(n-3)*x^4*y^4 + 12*(n-2)*x^4*y^6 + (9*n^2-33*n+30)*x^6*y^6.

9*a(n) + 277 is a square. - Bruno Berselli, May 18 2018

Links

Colin Barker, Table of n, a(n) for n = 2..1000

S. Hayat and M. Imran, Computation of topological indices of certain networks, Applied Mathematics and Computation, 240, 2014, 213-228/

M. N. Husin and R. Hasni, More results on computation of topological indices of certain networks, Int. J. Networking and Virtual Organisations, 17, No. 1, 2017, 46-63.

B. Rajan , A. William, C. Grigorius, and S. Stephen, On certain topological indices of silicate, honeycomb and hexagonal networks, J. Comp. & Math. Sci., 3, No. 5, 2012, 530-535.

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

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

Formula

From Colin Barker, May 18 2018: (Start)

G.f.: 12*x^2*(13 + 42*x - x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

Maple

seq(468-804*n+324*n^2, n = 2..40);

Prog

(GAP) List([2..40], n->324*n^2-804*n+468); # Muniru A Asiru, May 18 2018
(PARI) a(n) = 324*n^2 - 804*n + 468; \\ Altug Alkan, May 18 2018
(PARI) Vec(12*x^2*(13 + 42*x - x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 18 2018

Crossrefs

Cf. A304618.

Sequence in context: A038476 A158550 A156994 * A204718 A232718 A204957

Adjacent sequences: A304616 A304617 A304618 * A304620 A304621 A304622

Keyword

nonn,easy

Author

Emeric Deutsch, May 17 2018

Status

approved