A228318 The Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).

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

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);

Mathematica

LinearRecurrence[{3, -3, 1}, {15, 33, 59}, 50] (* Harvey P. Dale, Jan 13 2022 *)

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