[seqfan] Re: non-congruent diagonals in n-gon A165726
Max Alekseyev
maxale at gmail.com
Sat Sep 26 18:19:21 CEST 2009
I doubt the importance of A140106 either since it is basically a
duplicate of A004526.
I would vote for deleting both A165726 and A140106, and adding a
comment about diagonals to A004526.
Max
On Sat, Sep 26, 2009 at 11:25 AM, Alois Heinz <heinz at hs-heilbronn.de> wrote:
> 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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