Not sure where I'm going with this, but I'm intrigued. The next question is whether I much I can control it: if I want a specific stitch count and a specific number of eyelets on a specific row, what's the simplest way to figure out whether it can be done, and if so, how? I suspect there's an excel spreadsheet in my future.
Shown with a cast-on count of 3 stitches.