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A216123 The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Ashrafi et al. reference. 1
657339, 15126495, 170253735, 1399219767, 9656453079, 59728974615, 342996234135, 1867389894807, 9768453728919, 49540857757335, 245123724445335, 1188721211741847, 5669374461982359, 26661906782549655, 123891350653597335, 569765357115700887, 2596763217388533399 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..17.

A. R. Ashrafi and M. Mirzagar, PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers, Indian J. of Chemistry, 47A, 2008, 538-541.

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.

J. Yang, F. Xia, and S. Chen, Second-order and third-order connectivity indices of an infinite family of dendrimer nanostars, Int. J. Contemp. Math. Sciences, 6, 2011, No. 5, 215-220.

Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).

FORMULA

a(n) = -685719 - 2949654*2^n + 2264412*4^n  + 495780*n*2^n - 1584720*n*4^n - 136500*n^2*2^n + 608400*n^2*4^n.

G.f.: -3*x*(81408*x^6 +1294464*x^5 +4778592*x^4 +5101816*x^3 -6182940*x^2 +879018*x +219113) / ((x -1)*(2*x -1)^3*(4*x -1)^3). - Colin Barker, Apr 01 2013

MAPLE

a := proc (n) options operator, arrow: 685719-2949654*2^n+2264412*4^n-1584720*4^n*n+495780*2^n*n-136500*2^n*n^2+608400*4^n*n^2 end proc: seq(a(n), n = 1 .. 17);

CROSSREFS

Cf. A216122.

Sequence in context: A205941 A287591 A308086 * A282356 A114678 A254495

Adjacent sequences:  A216120 A216121 A216122 * A216124 A216125 A216126

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Mar 25 2013

STATUS

approved

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Last modified November 27 06:49 EST 2021. Contains 349365 sequences. (Running on oeis4.)