A095268 Graphical Partitions - Extend?

[Frank Ruskey]

With respect to A095268.

First, I don't think these should be called "graphical partitions".
If they are partitions, then they should all add up to the same value,
which they don't.  They should be called "degree sequences".
This terminology problem seems to occur elsewhere; e.g., A004251.

If someone is keen to have some numbers quickly, then the
algorithm in http://www.cs.uvic.ca/~ruskey/Publications/AlleyCat.html
is very fast (it generates the sequences themselves, so you need to
add a counter and suppress the output).  You 
also need to modify the program to filter
out the sequences have a 0 (eliminates the isolated vertices).
Unfortunately, I have no time to
pursue this myself anytime soon.

Frank




On Thu, 
17 Aug 2006, Paul D. Hanna wrote:

> Seqfans,
>     Could someone extend sequence: A095268
> "Numbers of distinct graphical partitions corresponding to graphs on n=1,
> 2, ... nodes."
>
> With offset 0, A095268 begins:
> [0, 0, 1, 2, 7, 20, 71, 240, 871, 3148, ?]
>
> The self-convolution square-root of A095268 (with offset 0) begins:
> B = [0, 1, 1, 3, 7, 24, 75, 264, 917, ?]
>
> I wonder ... do the terms of B continue to be integer?
>
> Since a g.f. for A095268 is not known, it would be interesting
> if the trend continued for more terms.
>
> More information may be found at:
> http://mathworld.wolfram.com/GraphicalPartition.html
> http://www.mathe2.uni-bayreuth.de/axel/
>
> Thanks,
>     Paul
>

-- 
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Frank Ruskey         e-mail: (last_name)(AT)cs(DOT)uvic(DOT)ca
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