A227496 The Wiener index of the nanostar dendrimer defined pictorially as NS_3 in the Ashrafi et al. references.

58278, 386154, 2197138, 11480034, 56846210, 271400130, 1262261058, 5756835906, 25860706882, 114780464706, 504480353858, 2199370440258, 9523306249794, 40996576329282, 175599810575938, 748853449588290, 3181230972730946, 13468193224392258

Offset

1,1

Comments

a(1) has been checked by the direct computation of the Wiener index (using Maple).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1001 [Offset shifted to 1 by Georg Fischer, Aug 19 2021]

A. R. Ashrafi and P. Nikzad, Connectivity index of the family of dendrimer nanostars, Digest J. Nanomaterials and Biostructures, 4, 2009, 269-273.

A. R. Ashrafi and P. Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. Nanomaterials and Biostructures, 4, 2009, 383-388.

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

Formula

a(n) = -446 + 2^n*(5338 - 208*n) + 4^n*(1300 + 10816*n).

G.f.: 2*x*(29139 - 185730*x + 453464*x^2 - 497024*x^3 + 198144*x^4) / ((1-x)*(1-2*x)^2*(1-4*x)^2).

Maple

a := n -> -446+2^n*(5338-208*n)+4^n*(1300+10816*n): seq(a(n), n = 1..18);

Mathematica

gf := -(58278 x + 4 x^2 (-92865 + 4 x (56683 + 16 x (-3883 + 1548 x)))) / ((-1 + x) (1 - 6 x + 8 x^2)^2); ser := Series[gf, {x, 0, 18}];
Table[Coefficient[ser, x, n], {n, 1, 18}] (* Vincenzo Librandi, Jul 20 2013 *)

Prog

(Magma) [-446 + 2^n*(5338 - 208*n) + 4^n*(1300 + 10816*n): n in [1..20]]; // Vincenzo Librandi, Jul 20 2013

Crossrefs

Cf. A227497.

Sequence in context: A184372 A237402 A210106 * A295448 A220987 A273318

Adjacent sequences: A227493 A227494 A227495 * A227497 A227498 A227499

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 19 2013

Status

approved