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.

8580, 751148, 13742092, 145113196, 1166551916, 7991214060, 49348860396, 283593693164, 1546469947372, 8104770527212, 41179270758380, 204101468659692, 991328100589548, 4734560147021804, 22293506692030444, 103708270251417580, 477422926327128044

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 * A370972 A370970 A116326

Adjacent sequences: A221050 A221051 A221052 * A221054 A221055 A221056

Keyword

nonn,easy

Author

Emeric Deutsch, Mar 28 2013

Status

approved