A216123 The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Ashrafi et al. reference.

657339, 15126495, 170253735, 1399219767, 9656453079, 59728974615, 342996234135, 1867389894807, 9768453728919, 49540857757335, 245123724445335, 1188721211741847, 5669374461982359, 26661906782549655, 123891350653597335, 569765357115700887, 2596763217388533399

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: A365024 A287591 A308086 * A282356 A114678 A254495

Adjacent sequences: A216120 A216121 A216122 * A216124 A216125 A216126

Keyword

nonn,easy

Author

Emeric Deutsch, Mar 25 2013

Status

approved