A305154 a(n) = 36*2^n + 9.

45, 81, 153, 297, 585, 1161, 2313, 4617, 9225, 18441, 36873, 73737, 147465, 294921, 589833, 1179657, 2359305, 4718601, 9437193, 18874377, 37748745, 75497481, 150994953, 301989897, 603979785, 1207959561, 2415919113, 4831838217, 9663676425, 19327352841, 38654705673, 77309411337, 154618822665, 309237645321

Offset

0,1

Comments

a(n) is the second Zagreb index of the dendrimer D[n], defined pictorially in Fig. 1 of the Heydari et al. reference.

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 D[n] is M(D[n]; x, y) = 3*2^n*x*y^3 + 6*x^2*y^3 + 3*(2^n - 1)*x^3*y^3 (n>=0).

Links

Table of n, a(n) for n=0..33.

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

A. Heydari and I. Gutman, On the terminal Wiener index of thorn graphs, Kragujevac J. Sci., 32, 2010, 57-64.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Vincenzo Librandi, May 28 2018: (Start)

G.f.: 9*(5 - 6*x)/((1 - 2*x)*(1 - x)).

a(n) = 3*a(n-1) - 2*a(n-2). (End)

a(n) = 9*A000051(n+2). - R. J. Mathar, Jul 22 2022

Maple

seq(36*2^n + 9, n = 0..40);

Mathematica

Table[36 2^n + 9, {n, 0, 33}] (* Vincenzo Librandi, May 28 2018 *)
LinearRecurrence[{3, -2}, {45, 81}, 40] (* Harvey P. Dale, Jan 08 2020 *)

Prog

(Magma) [36*2^n+9: n in [0..33]]; // Vincenzo Librandi, May 28 2018

Crossrefs

Cf. A305153.

Sequence in context: A102578 A026060 A138171 * A280407 A063343 A043184

Adjacent sequences: A305151 A305152 A305153 * A305155 A305156 A305157

Keyword

nonn,easy

Author

Emeric Deutsch, May 27 2018

Status

approved