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) = 3n(8n-3).
a(n) = A180867(4,n).
The Wiener polynomial of the graph D(5,n) is nt(t+1)[2(n-1)t^2+2(n-1)t+5].
G.f.: -3*x*(11*x+5)/(x-1)^3. - Colin Barker, Oct 31 2012
EXAMPLE
a(1)=15 because in D(5,1)=C_5 we have 5 distances equal to 1 and 5 distances equal to 2.
MAPLE
seq(3*n*(8*n-3), n = 1 .. 40);
MATHEMATICA
Table[3n(8n-3), {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {15, 78, 189}, 40] (* Harvey P. Dale, May 01 2023 *)
PROG
(PARI) a(n)=3*n*(8*n-3) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Sep 30 2010
STATUS
approved