[seqfan] 4-12-28-60
K. Viswanathan Iyer
kvi at nitt.edu
Wed Jun 23 08:24:44 CEST 2010
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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