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

Author

Emeric Deutsch, Aug 27 2013

Keywords

• nonn
• easy

References

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

Links

• 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).

Crossrefs

Cf. A228318.

Programs

Maple

a := proc (n) options operator, arrow: 6*n^2+7*n+7 end proc: seq(a(n), n = 1 .. 42);

PARI

a(n)=6*n^2+7*n+7 \\ Charles R Greathouse IV, Jun 17 2017

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)