

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
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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



FORMULA

a(n) = 3n(8n3).
The Wiener polynomial of the graph D(5,n) is nt(t+1)[2(n1)t^2+2(n1)t+5].


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*n3), n = 1 .. 40);


MATHEMATICA

Table[3n(8n3), {n, 40}] (* or *) LinearRecurrence[{3, 3, 1}, {15, 78, 189}, 40] (* Harvey P. Dale, May 01 2023 *)


PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



