[seqfan] A014529 largest convex area made from n equilateral triangles - asymptotics?

Hugo Pfoertner yae9911 at gmail.com
Sun Jul 30 15:29:03 CEST 2017


from a fit of the available terms, A014529 <https://oeis.org/A014529>
"Largest convex area that can be tiled with n equilateral triangles whose
sides are relatively prime." seems to grow like a(n) ~=
exp(0.6135*n-0.6195). Is there anything known about a systematic
construction method?

The terms up to a(11) are from an addendum to the cited Scientific American
article. I have found an illustration
<http://www.randomwalk.de/sequences/a289944sanitized.jpeg> in the German
translation. Four more terms have been found by John W. Layman, who seems
to be no longer active in the OEIS. I have written an E-Mail asking for
more information on the extension of A014529 to his address provided at
vt.edu, but didn't receive a reply.

Do the other two articles by M.K. Azarian, which I can't find anywhere,
provide more insight?

As indicated in its discussion part, the derived new sequence
A289944 <https://oeis.org/history?seq=A289944>
needs a revision taking into account the occurrence of triangle sizes > n.

Any help would be appreciated.

Hugo Pfoertner

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