[seqfan] Re: non-congruent diagonals in n-gon A165726
Alois Heinz
heinz at hs-heilbronn.de
Sat Sep 26 17:25:50 CEST 2009
There is another (older & correct) version of this sequence
by the same author:
http://research.att.com/~njas/sequences/A140106
Alois
Richard Mathar schrieb:
> 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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