A228320 The Wiener index of the graph obtained by applying Mycielski's construction to the cycle graph C(n).

203, 280, 369, 470, 583, 708, 845, 994, 1155, 1328, 1513, 1710, 1919, 2140, 2373, 2618, 2875, 3144, 3425, 3718, 4023, 4340, 4669, 5010, 5363, 5728, 6105, 6494, 6895, 7308, 7733, 8170, 8619, 9080, 9553, 10038, 10535, 11044, 11565

Offset

7,1

References

D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.

Links

Table of n, a(n) for n=7..45.

R. Balakrishnan, S. F. Raj, The Wiener number of powers of the Mycielskian, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).

M. Eliasi, G.Raeisi, B. Taeri, Wiener index of some graph operations, Discrete Appl. Math., 160, 2012, 1333-1344 (see Example 2.5).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 6n^2 - 13n.

G.f.: x^7*(203 - 329*x + 138*x^2)/(1 - x)^3.

The Hosoya-Wiener polynomial is conjectured to be 4nt +(1/2)n(n+9)t^2 + n(n-4)t^3 + (1/2)n(n-7)t^4.

Maple

a := proc (n) options operator, arrow: 6*n^2-13*n end proc: seq(a(n), n = 7 .. 45);

Mathematica

DeleteCases[CoefficientList[Series[x^7*(203 - 329 x + 138 x^2)/(1 - x)^3, {x, 0, 45}], x], 0] (* or *)
Array[6 #^2 - 13 # &, 39, 7] (* Michael De Vlieger, May 27 2018 *)

Prog

(PARI) a(n)=6*n^2-13*n \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A259330 A090486 A348664 * A346899 A247921 A346883

Adjacent sequences: A228317 A228318 A228319 * A228321 A228322 A228323

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 27 2013

Status

approved