The maximal number of regions into which n lines divide a plane are N(n) = 1/2(n^2 + n + 2) which, for n = 1, 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 n lines.
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