A304375 a(n) = 27*n^2/2 + 45*n/2 - 12 (n>=1).

24, 87, 177, 294, 438, 609, 807, 1032, 1284, 1563, 1869, 2202, 2562, 2949, 3363, 3804, 4272, 4767, 5289, 5838, 6414, 7017, 7647, 8304, 8988, 9699, 10437, 11202, 11994, 12813, 13659, 14532, 15432, 16359, 17313, 18294, 19302, 20337, 21399, 22488, 23604, 24747, 25917, 27114, 28338, 29589, 30867, 32172, 33504

Offset

1,1

Comments

a(n) is the second Zagreb index of the triangular benzenoid T(n) (see the M. Ghorbani et al. references).

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 triangular benzenoid T(n) is M(T(n); x,y) = 6*x^2*y^2 + 6*(n-1)*x^2*y^3 + 3*n*(n-1)*x^3*y^3/2.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

M. Ghorbani and M. Ghazi, Computing geometric arithmetic index of some graphs, Digest J. of Nanomaterials and Biostructures, 5, No. 4, 2010, 837-841.

M. Ghorbani and M. Ghazi, Computing some topological indices of triangular benzenoid, Digest J. of Nanomaterials and Biostructures, 5, No. 4, 2010, 1107-1111.

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

Formula

From Colin Barker, May 12 2018: (Start)

G.f.: 3*x*(8 + 5*x - 4*x^2) / (1 - x)^3.

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

(End)

Maple

seq(27*n^2/2 + 45*n/2 - 12, n=1..50);

Mathematica

Table[(27n^2)/2+(45n)/2-12, {n, 50}] (* or  *) LinearRecurrence[{3, -3, 1}, {24, 87, 177}, 50] (* Harvey P. Dale, Dec 30 2023 *)

Prog

(PARI) a(n) = 27*n^2/2 + 45*n/2 - 12; \\ Altug Alkan, May 12 2018
(PARI) Vec(3*x*(8 + 5*x - 4*x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 12 2018

Crossrefs

Cf. A304374.

Sequence in context: A007201 A228874 A211328 * A044211 A044592 A211632

Adjacent sequences: A304372 A304373 A304374 * A304376 A304377 A304378

Keyword

nonn,easy

Author

Emeric Deutsch, May 12 2018

Status

approved