login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A224435 The Wiener index of the polyphenylene dendrimer G[n] defined pictorially in the N. E. Arif et al. reference. 2
1248, 136272, 1590360, 11608536, 69325368, 371933112, 1870634040, 9019095096, 42224645688, 193479671352, 872186750520, 3881641715256, 17097660401208, 74673784423992, 323824724575800, 1395810233321016, 5985270160655928, 25549161151039032, 108628885484045880 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 22 08:21 EDT 2022. Contains 353933 sequences. (Running on oeis4.)