[seqfan] Trying to understand the Inventory Sequence A342585

[Neil Sloane]

Dear SeqFans:
Here are some questions I wish I knew the answer to.
Let a(n) = A342585(n) be the Inventory Sequence (n>=1)

1.  What is the upper envelope of the points?
If you click the "graph" button, you see it looks very very roughly like
sqrt(n),
I computed the RECORDS transform, and the record high points are in
A348782, and their indices are in A347305. If one draws a curve through
those points, what is its equation?

2,  What is the average value after n terms?  Let S(n) = (1/n) *
Sum_{i=1..n} a(i).  The partial sums are in A348781.  How does S(n) grow?

3.   Write the sequence (A342585) as an irregular triangle. What is the
average value of the n-th row?

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com