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A228319
The hyper-Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).
1
20, 45, 82, 131, 192, 265, 350, 447, 556, 677, 810, 955, 1112, 1281, 1462, 1655, 1860, 2077, 2306, 2547, 2800, 3065, 3342, 3631, 3932, 4245, 4570, 4907, 5256, 5617, 5990, 6375, 6772, 7181, 7602, 8035, 8480, 8937, 9406, 9887, 10380
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) = 6n^2 + 7n + 7.
G.f.: x*(20-15*x+7*x^2)/(1-x)^3.
The Hosoya-Wiener polynomial is (4n+1)t + (2n^2 + n + 2)t^2.
MAPLE
a := proc (n) options operator, arrow: 6*n^2+7*n+7 end proc: seq(a(n), n = 1 .. 42);
PROG
(PARI) a(n)=6*n^2+7*n+7 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A228318.
Sequence in context: A219716 A044097 A044478 * A236474 A145220 A234266
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 27 2013
STATUS
approved