The maximal number of regions into which lines divide a plane are

which, for , 2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124), the same maximal number of regions into which a circle, square, etc. can be divided by lines.

More things to try:

Weisstein, Eric W. "Plane Division by Lines." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlaneDivisionbyLines.html