[seqfan] Re: Sequence re partitions of n-gon needs more terms

[David Newman]

Perhaps I haven't understood the problem.
Is it the case that the entire description of the sequence is "re partitions
of n-gon?"

If so my initial interpretation was to draw edges between vertices of an
regular n-gon and call the result a partition.  Two partitions could be
thought of as identical if they can be made to coincide by rotation or
flipping.  Then, for a 1-gon there is just one partition, because no new
edge can be drawn.  Similarly, for a 2-gon or triangle there is just one
partition.  For a square we can add one diagonal or two, giving three
possible partitions.  But for a pentagon I find 8 partitions, not 7.

 Here's how I count them.  Label the vertices of the pentagon with the
numbers 1 through 5.  I indicate an edge by the set of its endpoints, and a
partition by the set of its edges.  Here then are the "partitions" of the
pentagon with zero, one, two, or three additional edges by my definition.
You can get the partitions with 4 or 5 additional edges by taking these
partitions and deleting the edges that are there and adding the edges that
are not there.

{ {  } } ,
{ { 1 , 3 } } ,
{ { 1 , 3 } , { 1 , 4 } },
{ { 1 , 3 } , { 2 , 4 } },
{ { 1 , 3 } , { 2 , 4 } , { 3 , 5 } },
{ { 1 , 3 } , { 2 , 5 } , { 3 , 5 } }

So I guess this is not what the author of this sequence meant.
On Thu, Feb 17, 2011 at 9:31 PM, N. J. A. Sloane <njas at research.att.com>wrote:

>
> Dear SeqFans, A181148 is one of the oldest sequences waiting in
> the stack to be approved. The trouble is, it starts 1,1,1,3,7, and
> we really need one or two more terms to distinguish it from the neighboring
> sequences. Can someone help?
> Neil
>
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