A143938 The Wiener index of a benzenoid consisting of a linear chain of n hexagons.

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

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