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A228318 The Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n). 2
15, 33, 59, 93, 135, 185, 243, 309, 383, 465, 555, 653, 759, 873, 995, 1125, 1263, 1409, 1563, 1725, 1895, 2073, 2259, 2453, 2655, 2865, 3083, 3309, 3543, 3785, 4035, 4293, 4559, 4833, 5115, 5405, 5703, 6009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

H. P. Patil, R. Pandiya Raj, On the total graph of Mycielski graphs. central graphs and their covering numbers, Discussiones Math., Graph Theory, 33,2013, 361-371.

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

LINKS

Table of n, a(n) for n=1..38.

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

FORMULA

a(n) = 4n^2 + 6n + 5.

G.f.: x*(15-12*x+5*x^2)/(1-x)^3.

The Hosoya-Wiener polynomial is (4n+1)t + (2n^2 + n + 2)t^2.

EXAMPLE

a(1)=15; indeed K(1,1) is the 1-edge graph; the Mycielski construction yields the cycle C(5); its Wiener index is 5*1 + 5*2 = 15.

MAPLE

a := proc (n) options operator, arrow: 4*n^2+6*n+5 end proc; seq(a(n), n = 1 .. 38);

PROG

(PARI) a(n)=4*n^2+6*n+5 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A228319.

Sequence in context: A242677 A020184 A231371 * A228321 A277385 A108517

Adjacent sequences:  A228315 A228316 A228317 * A228319 A228320 A228321

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Aug 27 2013

STATUS

approved

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Last modified August 11 03:22 EDT 2020. Contains 336421 sequences. (Running on oeis4.)