[seqfan] Re: A328074 Coordination sequence depends on the generation number

[Neil Sloane]

Lars,  That is very interesting!  I am not sure how to handle this.  Let me
ask Yotam Smilansky.  I will have to do that in a separate email thread.
If anyone else wants to be included, send me an email.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Wed, Oct 16, 2019 at 7:20 AM Lars Blomberg <larsl.blomberg at comhem.se>
wrote:

> Hello Seqfans,
>
>
>
> Trying to extend this sequence I found that the coordination sequence (cs)
> varies according to which generation is used to compute it.
>
> Generation      Coordination sequence
>
> 0                           1
>
> 1                           1, 12
>
> 2                           1, 12, 16
>
> 3                           1, 12, 16, 16
>
> 4                           1, 12, 16, 16, 16
>
> 5                           1, 12, 16, 16, 40, 52, 96
>
> 6                           1, 12, 16, 16, 16, 40, 52, 96
>
> 7                           1, 12, 16, 16, 40, 52, 96, 84, 72, 92, 128, 104
>
> 8                           1, 12, 16, 16, 16, 40, 52, 96, 84, 72, 92, 128,
> 104
>
> 9                           1, 12, 16, 16, 40, 52, 96, 84, 72, 92, 128,
> 104,
> 68, 104, 112, 148, 168
>
> 10                        1, 12, 16, 16, 16, 40, 52, 96, 84, 72, 92, 128,
> 104, 68, 104, 112, 148, 168
>
> It looks from this like there are two variants of cs, but further
> computations show there to be more than that.
>
> In the center there is a square of size 3^k/5^k which is unique among all
> the squares (k is not generation number).
>
> For each generation one can make a sorted list of all square sizes and note
> the position of the center square.
>
> From this it seems that one can determine which cs variant belongs to that
> generation.
>
>
>
> What is the best way to handle this?
>
>
>
> /Lars
>
>
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>