A228319 The hyper-Wiener index of the graph obtained by applying Mycielski's construction to the star graph K(1,n).

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

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

Links

Table of n, a(n) for n=1..41.

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

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

Formula

a(n) = 6*n^2 + 7*n + 7.

G.f.: x*(20-15*x+7*x^2)/(1-x)^3.

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

From Elmo R. Oliveira, Nov 15 2024: (Start)

E.g.f.: exp(x)*(6*x^2 + 13*x + 7) - 7.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

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

Adjacent sequences: A228316 A228317 A228318 * A228320 A228321 A228322

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 27 2013

Status

approved