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”).

A180579
The Wiener index of the Dutch windmill graph D(5,n) (n>=1).
2
15, 78, 189, 348, 555, 810, 1113, 1464, 1863, 2310, 2805, 3348, 3939, 4578, 5265, 6000, 6783, 7614, 8493, 9420, 10395, 11418, 12489, 13608, 14775, 15990, 17253, 18564, 19923, 21330, 22785, 24288, 25839, 27438, 29085, 30780, 32523, 34314
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.
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