# [seqfan] Re: Rings of regular polygons

Luca Petrone luca.petrone at libero.it
Mon Mar 27 09:18:47 CEST 2017

```That is (2 n)/(-2 - 2 a + n) must be a positive integer for a = 1 to n/2.
The sequence is the same as A023645, except for N = 6, for which A023645 is 2
Best Regards,
Luca Petrone

>----Messaggio originale----
>Da: "Luca Petrone" <luca.petrone at libero.it>
>Data: 27/03/2017 7.52
>A: "Sequence Fanatics Discussion list"<seqfan at list.seqfan.eu>
>Ogg: [seqfan] Re: Rings of regular polygons
>
>
>The number of configurations for rings of n-gons are the number of integer
>solution in k (number of rings) of the equation (a - 1) (1 + 2/n) + 4/n +
2/k
>== a, with a (number of sides of the n-gon inside the ring) varying from 1
to
>n/2.
>
>Regards,
>
>Luca Petrone
>
>>----Messaggio originale----
>>Da: "Andrew Weimholt" <andrew.weimholt at gmail.com>
>>Data: 26/03/2017 23.59
>>A: "Sequence Fanatics Discussion list"<seqfan at list.seqfan.eu>
>>Ogg: [seqfan] Re: Rings of regular polygons
>>
>>On Sun, Mar 26, 2017 at 2:15 PM, Peter Munn <techsubs at pearceneptune.co.uk>
>>wrote:
>>
>>>
>>> If you defined it as including all those where neighbouring polygons
>>> shared an edge, that is including 6 triangles around a point etc., I think
>>> the sequence might be A023645, the number of divisors of n less than n/2.
>>> So, I think your a(13) term should be 1.
>>>
>>> Peter
>>>
>>>
>>I agree. 26 13-gons DO form a ring.
>>Something is wrong with the 13-gons in the his PDF (uneven edge lengths
>>perhaps).
>>
>>
>>Andrew
>>
>>--
>>Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>

```