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

Richard Mathar mathar at strw.leidenuniv.nl
Sat Sep 26 16:46:20 CEST 2009

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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