login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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(m-1)t[(m-1)(n-1)t+m].
The Wiener index of D(m,n) is (1/2)n(m-1)[(m-1)(2n-1)+1].
For the Wiener indices of D(3,n), D(4,n), and D(5,n) see A033991, A152743, and A028994, respectively.
LINKS
B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.
Eric Weisstein's World of Mathematics, Windmill Graph.
FORMULA
a(n) = 5n(5n-2).
G.f.: -5*x*(7*x+3)/(x-1)^3. - Colin Barker, Oct 30 2012
MAPLE
seq(5*n*(-2+5*n), n = 1 .. 40);
PROG
(PARI) a(n)=5*n*(5*n-2) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 21 2010
STATUS
approved