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., Vol. 60, 1996, pp. 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) = 9*n*(5*n-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
From Elmo R. Oliveira, Apr 03 2025: (Start)
E.g.f.: 9*exp(x)*x*(3 + 5*x).
a(n) = 9*A147874(n+1).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
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
EXTENSIONS
More terms from Elmo R. Oliveira, Apr 03 2025
Duplicated a(38) removed by Sean A. Irvine, Apr 14 2025
STATUS
approved