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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..38.

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.

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

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

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

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Last modified August 7 10:57 EDT 2020. Contains 336275 sequences. (Running on oeis4.)