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A221053 The hyper-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. 2
8580, 751148, 13742092, 145113196, 1166551916, 7991214060, 49348860396, 283593693164, 1546469947372, 8104770527212, 41179270758380, 204101468659692, 991328100589548, 4734560147021804, 22293506692030444, 103708270251417580, 477422926327128044 (list; graph; refs; listen; history; text; internal format)
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 hyper-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 (19,-150,636,-1560,2208,-1664,512).

FORMULA

a(n) = 204780 - 1311272*2^n + 1106480*4^n + 360*2^n*n^2 + 129600*4^n*n^2 + 7852*2^n*n - 633600*4^n*n.

G.f.: 4*x*(1536*x^6-1645696*x^5-1592416*x^4+2192808*x^3-189320*x^2 -147032*x -2145) / ((x-1)*(2*x-1)^3*(4*x-1)^3). - Colin Barker, Apr 01 2013

MAPLE

a := proc(n) 204780-1311272*2^n+1106480*4^n+360*2^n*n^2+129600*4^n*n^2 +7852*2^n*n-633600*4^n*n end proc: seq(a(n), n = 1 .. 17);

PROG

(PARI) Vec(4*x*(1536*x^6-1645696*x^5-1592416*x^4+2192808*x^3-189320*x^2 -147032*x-2145)/((x-1)*(2*x-1)^3*(4*x-1)^3) + O(x^20)) \\ Colin Barker, Jun 04 2016

CROSSREFS

Cf. A221052.

Sequence in context: A287119 A156846 A324711 * A116326 A031809 A252471

Adjacent sequences:  A221050 A221051 A221052 * A221054 A221055 A221056

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Mar 28 2013

STATUS

approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)