

A180577


The Wiener index of the windmill graph D(6,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs).


4



15, 80, 195, 360, 575, 840, 1155, 1520, 1935, 2400, 2915, 3480, 4095, 4760, 5475, 6240, 7055, 7920, 8835, 9800, 10815, 11880, 12995, 14160, 15375, 16640, 17955, 19320, 20735, 22200, 23715, 25280, 26895, 28560, 30275, 32040, 33855, 35720
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OFFSET

1,1


COMMENTS

The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
The Wiener polynomial of D(m,n) is (1/2)n(m1)t[(m1)(n1)t+m].
The Wiener index of D(m,n) is (1/2)n(m1)[(m1)(2n1)+1].
For the Wiener indices of D(3,n), D(4,n), and D(5,n) see A033991, A152743, and A028994, respectively.


LINKS

Table of n, a(n) for n=1..38.
B. E. Sagan, YN. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959969.
Eric Weisstein's World of Mathematics, Windmill Graph.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 5n(5n2).
G.f.: 5*x*(7*x+3)/(x1)^3.  Colin Barker, Oct 30 2012


MAPLE

seq(5*n*(2+5*n), n = 1 .. 40);


PROG

(PARI) a(n)=5*n*(5*n2) \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A028994, A033991, A152743.
Sequence in context: A269657 A189922 A085808 * A033594 A059377 A123865
Adjacent sequences: A180574 A180575 A180576 * A180578 A180579 A180580


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Sep 21 2010


STATUS

approved



