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A228320 The Wiener index of the graph obtained by applying Mycielski's construction to the cycle graph C(n). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A198981 A259330 A090486 * A247921 A240903 A250751

Adjacent sequences:  A228317 A228318 A228319 * A228321 A228322 A228323

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Aug 27 2013

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)