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A227496 The Wiener index of the nanostar dendrimer defined pictorially as NS_3[n] 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

0,1

COMMENTS

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

REFERENCES

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

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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 := proc (n) options operator, arrow: -446+2^n*(5338-208*n)+4^n*(1300+10816*n) end proc: seq(a(n), n = 1 .. 20);

MATHEMATICA

CoefficientList[Series[2 (29139 - 185730 x + 453464 x^2 - 497024 x^3 + 198144 x^4) / ((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 40}], x] (* 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 May 18 23:56 EDT 2021. Contains 344009 sequences. (Running on oeis4.)