Degree Sequences (was Graphical Partitions)

[Gordon Royle]

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