[seqfan] 4-12-28-60

[K. Viswanathan Iyer]

Let the Fibonacci weighted stars T(i)'s be defined as:

1.  T(1) is an edge with one vertex as a distinguished vertex; the  
weight on the edge is taken to be F(1).
2.  For n>1, T(n) is formed by taking a copy of T(n-1) and attaching  
an edge to its distinguished vertex; the weight on the new edge is  
taken to be F(n).

The problem is to compute in T(n), the sum D(n) of the weighted  
distances over all pairs of vertices.  It follows that  D(2)=4 and  
D(n) = D(n-1) + F(n+1) +nF(n) -1. This gives D(n) = n(F(n+2) - 1). Am  
I right? Is the sequence defined by the D(n)'s interesting?

Vichu



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