Possibly helpful, possibly not: I just realized that since f = 2d - 1 + e and we're looking for 2d(n-1), we're also technically looking for (f+1-e)(n-1).
I know, but I'm talking more specifically about visual symmetry, rather than the links between (x+n) squares based on the finite set of non-(x+n)^2=f values. The way VQC said it made it sound like it was far more specific about symmetry than in PMA's picture. If it was obvious and directly related to what we're currently paying attention to, we'd have it by now.
>It would be helpful if someone else could verify these formulas.
If you're talking about the formulae here >>5631 then sorry I didn't reply to this earlier considering I did do a reasonable amount of work on the concept (I guess I mustn't have been paying enough attention last week). It doesn't correlate with what I found in these tests >>5581 here. I found valid values of everything within a particular (x+n) set for every value of n iterating from 1 upwards by 1 each time up to some kind of maximum n value, whereas you have that n is +/- 2 (unless you're referring to something else or I'm reading it wrong). Here's another example in pic related, but I have more detail in the terminal screencaps in my original post. And here's the code I used to generate those outputs (I was lazy and manually changed the if statement's value each time): https://pastebin.com/0gF6rgiR