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A227496 The Wiener index of the nanostar dendrimer defined pictorially as NS_3 in the Ashrafi et al. references. 2
58278, 386154, 2197138, 11480034, 56846210, 271400130, 1262261058, 5756835906, 25860706882, 114780464706, 504480353858, 2199370440258, 9523306249794, 40996576329282, 175599810575938, 748853449588290, 3181230972730946, 13468193224392258 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 28 15:37 EST 2023. Contains 359895 sequences. (Running on oeis4.)