A304388 a(n) = 144*2^n - 20 (n>=1).

268, 556, 1132, 2284, 4588, 9196, 18412, 36844, 73708, 147436, 294892, 589804, 1179628, 2359276, 4718572, 9437164, 18874348, 37748716, 75497452, 150994924, 301989868, 603979756, 1207959532, 2415919084, 4831838188, 9663676396, 19327352812, 38654705644, 77309411308

Offset: 1

Author

Emeric Deutsch, May 13 2018

Keywords

• nonn
• easy

Comments

a(n) is the second Zagreb index of the dendrimer nanostar NS1[n], defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).

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 NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n +3)x^2*y^2 + (18*2^n - 12)x^2*y^3 + 3x^3*y^4.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• M. B. Ahmadi and M. Sadeghimehr, Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.
• Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
• 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,-2).

Crossrefs

Cf. A304386, A304387, A304389.

Programs

GAP

List([1..40],n->144*2^n-20); # Muniru A Asiru, May 13 2018

Maple

seq(144*2^n-20, n = 1 .. 40);

Mathematica

LinearRecurrence[{3,-2},{268,556},30] (* Harvey P. Dale, Nov 02 2021 *)

PARI

a(n) = 144*2^n - 20; \\ Altug Alkan, May 13 2018

PARI

Vec(4*x*(67 - 62*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018

Formula

From Colin Barker, May 18 2018: (Start)

G.f.: 4*x*(67 - 62*x) / ((1 - x)*(1 - 2*x)).

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

(End)