A224435 The Wiener index of the polyphenylene dendrimer G[n] defined pictorially in the N. E. Arif et al. reference.

1248, 136272, 1590360, 11608536, 69325368, 371933112, 1870634040, 9019095096, 42224645688, 193479671352, 872186750520, 3881641715256, 17097660401208, 74673784423992, 323824724575800, 1395810233321016, 5985270160655928, 25549161151039032, 108628885484045880

Offset

0,1

Comments

a(0) has been checked by the direct computation of the Wiener index (using Maple).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

N. E. Arif, Roslan Hasni and Saeid Alikhani, Fourth order and fourth sum connectivity indices of polyphenylene dendrimers, J. Applied Science, 12 (21), 2012, 2279-2282.

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

Formula

a(n) = -31176 + 136464*2^n + 93600*n*4^n - 31860*n*2^n - 104040*4^n.

G.f.: 24*(52 + 5002*x - 4221*x^2 - 22060*x^3 + 9536*x^4)/((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2).

a(n) = 13*a(n-1) - 64*a(n-2) + 148*a(n-3) - 160*a(n-4) + 64*a(n-5) for n>4.

Maple

a := proc (n) options operator, arrow: -31176+136464*2^n+93600*4^n*n-31860*2^n*n-104040*4^n end proc: seq(a(n), n = 0 .. 18);

Prog

(PARI) Vec(24*(52 + 5002*x - 4221*x^2 - 22060*x^3 + 9536*x^4) / ((1 - x)*(1 - 2*x)^2*(1 - 4*x)^2) + O(x^50)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A224436.

Sequence in context: A233167 A266037 A233179 * A233261 A233201 A233244

Adjacent sequences: A224432 A224433 A224434 * A224436 A224437 A224438

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 06 2013

Status

approved