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A228318
The Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 27 2013
STATUS
approved