[seqfan] Re: A187781 - Number of noncongruent polygonal regions in a regular n-gon with all diagonals drawn

[Chris Scussel]

Brad,

While I was pretty confident of my results numerically, I was concerned
that there was some aspect of this that I had misunderstood. In addition
to verifying my result for a(12), you've also reassured me that I'm on the
right track. Once again, thanks!

Contributing to OEIS is new for me, but I've been studying the (abundant)
documentation and appears to be doable.

I was concerned about potential numerical problems, and was very
surprised to be able to get to n=60 with no hint of trouble. I stopped
(for now) at n=60 because each run took eight hours! A separate
program confirmed the congruences to 50 decimals.

For a(18) there are three accidentally congruent pairs, as well as triple.
I'm hoping that once the new values get into OEIS some clever person
will find a relationship between n and the accidental congruences.
It seems to depend on the factors of n, but it's not clear to me how.

I find it helpful and satisfying to look at figures such as you've generated.

Chris

---- Original Message ----
From: "brad klee via SeqFan" <seqfan at list.seqfan.eu>
Sent: 6/11/2023 1:14:04 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Cc: "brad klee" <bradklee at proton.me>
Subject: [seqfan] Re: A187781 - Number of noncongruent polygonal regions in a regular n-gon with all diagonals drawn

> I will attempt to enact the above changes to OEIS.

If you know what to do, I don't want to help too much. 
You may be right either sequence needing clarification
what "congruent" means in context.  

I updated the community post with cleaned code, and a 
more direct bugs analysis. It's still not perfect, but 
seems to do okay up to a 20-gon:

https://community.wolfram.com/groups/-/m/t/2934769

The code also prints Hue-colored diagrams, where we can
see the accidental congruence. It looked like the 18-gon
had numerous coincidences, but I'm still a bit skeptical 
if that is reproducible or my mistake. 

The algorithm has a way to handle change of precision, 
but I haven't looked closely enough at statistics to 
make use of precision tuning. 

--Brad
     



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