A221052 The Wiener index of the nanostar dendrimer NSC_5C_6[n], defined pictorially in the A. R. Ashrafi et al. reference and in the M. Rostami et al. reference.

2071, 73675, 796915, 5807107, 35057827, 190384867, 967962979, 4709311075, 22210776163, 102384824419, 463801636963, 2072447248483, 9159135201379, 40114693752931, 174372925524067, 753151386437731, 3235250457266275, 13831593842428003

Offset

1,1

Comments

a(2) has been checked by the direct computation of the Wiener index (using Maple).

The given references do not consider the Wiener index.

Links

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

A. R. Ashrafi and P. Nikzad, Szeged index of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 1, 2009, 155-157.

M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.

Index entries for linear recurrences with constant coefficients, signature (13,-64,148,-160,64).

Formula

a(n) = -14237 + 46170*2^n - 32004*4^n +12960*n*4^n +72*n*2^n.

G.f.: x*(4544*x^4+144096*x^3+28316*x^2-46752*x-2071) / ((x-1)*(2*x-1)^2*(4*x-1)^2). - Colin Barker, Mar 31 2013

Maple

a := proc(n) -14237+46170*2^n-32004*4^n+12960*4^n*n+72*2^n*n end proc: seq(a(n), n = 1 .. 18);

Prog

(PARI) Vec(x*(4544*x^4+144096*x^3+28316*x^2-46752*x-2071)/((x-1)*(2*x-1)^2*(4*x-1)^2) + O(x^20)) \\ Colin Barker, Jun 04 2016

Crossrefs

Cf. A221053.

Sequence in context: A249288 A200829 A035871 * A062913 A096927 A076425

Adjacent sequences: A221049 A221050 A221051 * A221053 A221054 A221055

Keyword

nonn,easy

Author

Emeric Deutsch, Mar 28 2013

Status

approved