Constrained A region-count formula

Determine the exact maximum number of regions formed by n constrained long-legged A shapes, including whether the experimentally suggested formula a_{\overline{\sf A}}(n) = floor(10n²/3) holds for n > 0.

Background

A constrained long-legged A is a long-legged A whose crossbar endpoints are equidistant from its tip, considered up to similarities. Two copies can intersect in at most eight points, giving the general upper bound a_{\overline{A}}(n) ≤ 4n² − 2n + 1.

Computer searches found values 1, 3, 13, 30, 53, and 83 for n from 0 through 5, suggesting the sequence floor(10n²/3) for positive n. However, the authors emphasize that numerical precision issues and very small regions make even this proposed formula uncertain.