A227492 The Wiener index of the nanostar dendrimer D_n.

27, 2871, 39663, 326367, 2123199, 12126591, 63900927, 319163391, 1535375871, 7186396671, 32947236351, 148643831295, 662099705343, 2918722534911, 12756670414335, 55354839662079, 238734196604415, 1024200814362111, 4373869249953279

Offset

0,1

Comments

D_n is defined pictorially as NS2[n] in the Chen et al. reference.

a(1) and a(2) have been checked by the direct computation of the Wiener index (using Maple).

Links

Table of n, a(n) for n=0..18.

S. Chen and J. Yang, Second-order and third-order connectivity indices of dendrimer nanostars, International Mathematical Forum, 6, No, 5, 2011, 223-228.

Index entries for linear recurrences with constant coefficients, signature (13,-64,148,-160,64)

Formula

a(n) = - 513 + 2^n*(2016*n + 9468) + 4^n*(4032*n - 8928).

G.f.: 9*(3 + 280*x + 452*x^2 - 1056*x^3 - 192*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2).

Maple

a := proc (n) options operator, arrow: -513+2^n*(2016*n+9468)+4^n*(4032*n-8928) end proc: seq(a(n), n = 0 .. 20);

Mathematica

LinearRecurrence[{13, -64, 148, -160, 64}, {27, 2871, 39663, 326367, 2123199}, 20] (* Harvey P. Dale, Dec 30 2017 *)

Crossrefs

Cf. A227493.

Sequence in context: A017427 A050644 A048567 * A027363 A350135 A085529

Adjacent sequences: A227489 A227490 A227491 * A227493 A227494 A227495

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 17 2013

Status

approved