[seqfan] 2D extension to A327474

[nitai.s at campus.technion.ac.il]

Hello all, I sure hope I'm doing this right!

I want to submit a new sequence which is a two-dimensional extension of the existing sequence https://oeis.org/A327474 "Number of distinct means of subsets of {1..n}, where {} has mean 0", or equivalently, https://oeis.org/A135342 "Number of distinct means of nonempty subsets of {1,...,n}".

My proposed 2D extension would be: given an n-by-n grid of points, with each point either filled or empty, a(n) is the total number of possible locations for the "center of mass" (or mean) of the filled points on the grid. It is also possible to do m-by-n grids, giving a triangle sequence (assuming n<=m to avoid duplicated terms), but I'm sticking with n-by-n for now.

I have written a Python script to calculate a(n), and I have it up to a(9) - it slows down sharply after that. I would really like it if someone could check if my math and code are correct - what's the best way to do that? Do I just share the Python code here?

Would it be appropriate to submit two sequences that differ by 1, like the above sequences? Note that they were submitted 11 years apart.

All the best,
Nitai Sasson