OFFSET
1,1
COMMENTS
The Dutch windmill graph D(m,n) (also called friendship graph) is the graph obtained by taking n copies of the cycle graph C_m with a vertex in common (i.e., a bouquet of n C_m graphs).
The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
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, Dutch Windmill Graph.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A180867(6,n).
a(n) = 9n(5n-2).
The Wiener polynomial of the graph D(6,n) is (1/2)nt(t^2+2t+2)((n-1)t^3+2(n-1)t^2+2(n-1)t+6).
G.f.: -9*x*(7*x+3)/(x-1)^3. - Colin Barker, Oct 31 2012
EXAMPLE
a(1)=27 because in D(6,1)=C_6 we have 6 distances equal to 1, 6 distances equal to 2, and 3 di stances equal to 3.
MAPLE
seq(9*n*(5*n-2), n = 1 .. 40);
PROG
(PARI) a(n)=9*n*(5*n-2) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 30 2010
STATUS
approved