A305267 a(n) = 68*2^n + 358.

426, 494, 630, 902, 1446, 2534, 4710, 9062, 17766, 35174, 69990, 139622, 278886, 557414, 1114470, 2228582, 4456806, 8913254, 17826150, 35651942, 71303526, 142606694, 285213030, 570425702, 1140851046, 2281701734, 4563403110, 9126805862, 18253611366, 36507222374, 73014444390, 146028888422

Offset

0,1

Comments

For n>=1, a(n) is the first Zagreb index of the first type of dendrimer nanostar G[n], shown pictorially in the Iranmanesh et al. reference (Fig. 1).

The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.

The M-polynomial of the dendrimer nanostar G[n] is M(G[n]; x, y) = (4*2^n + 23)*x^2*y^2 + (8*2^n + 34)*x^2*y^3 +(2*2^n +16)*x^3*y^3.

Links

Table of n, a(n) for n=0..31.

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

A. Iranmanesh, N. A. Gholami, Computing the Szeged index of two type dendrimer nanostars, Croatica Chemica Acta, 81, No. 2, 2008, 299-303.

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

Formula

G.f.: 2*(213-392*x)/((1-x)*(1-2*x)). - Vincenzo Librandi, May 30 2018

Maple

seq(68*2^n+358, n = 0..40);

Mathematica

Table[68 2^n + 358, {n, 0, 35}] (* Vincenzo Librandi, May 30 2018 *)
LinearRecurrence[{3, -2}, {426, 494}, 40] (* Harvey P. Dale, Mar 22 2019 *)

Prog

(Magma) [68*2^n + 358: n in [0..35]]; // Vincenzo Librandi, May 30 2018

Crossrefs

Cf. A305265, A305266, A305268.

Sequence in context: A207226 A207013 A048922 * A045094 A252411 A236605

Adjacent sequences: A305264 A305265 A305266 * A305268 A305269 A305270

Keyword

nonn,easy

Author

Emeric Deutsch, May 29 2018

Status

approved