[seqfan] Re: A347521 Number of polyominoes with n cells formed by coordinates that are not coprime

[Tom Duff]

Dunno. I see all 5 tetrominoes in the black squares of the diagram he gives
at https://oeis.org/A347521/a347521.pdf
(Btw, I recomputed the diagram to be sure that his wasn't busted somehow.)
Some of them I just see as sub-polyominoes of larger polyominoes (without
looking very carefully).
Maybe he means to divide the diagram into maximal polyominoes and maybe
there are some that can't occur maximally.
How would you do that? The diagram is infinite, so you can't proceed by
inspection.
Proving that a particular polyomino can't occur at any position and in any
orientation with all coordinates coprime, and none of the
orthogonally adjacent cells coprime seems like it would be a Diophantine
(Euclidean?) nightmare. Or I'm just not sufficiently clever. (It's happened
before...)

In any case, A347521 is not sufficiently descriptive.

On Wed, Sep 14, 2022 at 5:28 AM John Mason <masonmilan33 at gmail.com> wrote:

> Hi sequence fans
> I have looked at this sequence but I don't know how it works.
> Could anyone maybe give an explanation of, e.g., a(4)=1, say by
> illustrating why 4 of the 5 tetrominoes are excluded and just 1 is
> included?
> I would contact the author but his wiki page says no email address is
> available.
> Thanks
> john
>
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