login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143938 The Wiener index of a benzenoid consisting of a linear chain of n hexagons. 15
27, 109, 279, 569, 1011, 1637, 2479, 3569, 4939, 6621, 8647, 11049, 13859, 17109, 20831, 25057, 29819, 35149, 41079, 47641, 54867, 62789, 71439, 80849, 91051, 102077, 113959, 126729, 140419, 155061, 170687, 187329, 205019, 223789, 243671 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = (1/3)*(16*n^3 + 36*n^2 + 26*n + 3).

G.f.: z*(27+z+5*z^2-z^3)/(1-z)^4.

a(n) = Sum_{k=1,..,2*n+1} k*A143937(n,k).

EXAMPLE

a(1)=27 because in a hexagon we have 6 distances equal to 1, 6 distances equal to 2 and 3 distances equal to 3 (6*1+6*2+3*3=27).

MAPLE

seq((16*n^3+36*n^2+26*n+3)*1/3, n = 1 .. 35)

MATHEMATICA

Table[(1/3)*(16*n^3 + 36*n^2 + 26*n + 3), {n, 1, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {27, 109, 279, 569}, 50] (* G. C. Greubel, Dec 08 2016 *)

CROSSREFS

Cf. A143937.

Sequence in context: A193391 A193399 A193393 * A042428 A158554 A267812

Adjacent sequences:  A143935 A143936 A143937 * A143939 A143940 A143941

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Sep 06 2008

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 18:16 EST 2021. Contains 349467 sequences. (Running on oeis4.)