[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?


This message was sent using IMP, the Internet Messaging Program.

This message has been scanned for viruses and
dangerous content by MailScanner, and is
believed to be clean.

More information about the SeqFan mailing list