Degree Sequences (was Graphical Partitions)

[franktaw at netscape.net]

This seems to be a fairly good match for 4 - 5/(2n), which suggests
that it does converge.  Ratios approaching 4 from below are
typical of central binomial coefficients (and hence Catalan numbers).

No, how I don't see how that ties in to this sequence.

Franklin T. Adams-Watters

-----Original Message-----
From: gordon at csse.uwa.edu.au

Dear seqfansters 
 
The sequence http://www.research.att.com/~njas/sequences/A095268 that 
was discussed recently gives the number of different degree sequences 
from all the n-vertex graphs with no isolated vertices. 
 
[BTW, I think the offset should be "2" not "1"] 
 
One thing that I noticed while extending this was the behaviour of the 
ratio a(n+1)/a(n) which is as follows: 
 
2 
3.5 
2.857 
3.550 
3.380 
3.629 
3.614 
3.702 
3.718 
3.756 
3.773 
3.794 
3.808 
3.822 
3.833 
3.843 
3.851 
3.859 
 
Question: does a(n+1)/a(n) tend to a limit? If so, is it 4? If so, 
why... anyone have even a heuristic argument as to why there should be 
4 times as many degree sequences on n+1 vertices as there are on n? 
 
Cheers 
 
Gordon 


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