[seqfan] Re: non-congruent diagonals in n-gon A165726

Max Alekseyev maxale at gmail.com
Sat Sep 26 17:09:49 CEST 2009


I got the same concern and emailed the author yesterday - no reply so far.
If the author fail to explain his sequence, it can be safely removed.


On Sat, Sep 26, 2009 at 10:46 AM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
> I fail to understand the enumeration of non-congruent diagonals in
> http://research.att.com/~njas/sequences/A165726 :
> If we take the 5-gon, starting with a diagonal at some point at an edge, the
> connections to the two adjacent points are not diagonals, which leaves
> 5-3=2 other points with lines to be called diagonals (as opposed to "sides").
> These two are congruent, because they can be mapped onto each other by flipping
> the pentagon around a line which connects the starting point of the diagonal
> to the middle of the opposite side. So I get a(5)=1, not 2 as in the sequence.
> In general, I'd expect that a(n)= ceil( (n-3)/2 ) = A004526(n-2) = A110654(n-3), right?.
> Richard J. Mathar
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