A Quilter's Puzzle Leads to a New Sequence for Minimum L-Seams
Rabbit Hole: Minimum L-seams

While preparing a post on Mrs. Perkins's Quilt, Sophia Wood got sidetracked by a practical question: for an optimal n×n quilt, how many L-shaped seams are needed? She computed the sequence a(n) for n=1 to 17, finding values like a(13)=2 and a(16)=2, and shares her data, open questions, and references.
For any optimal Mrs. Perkins' Quilt of side n, what is the minimum number of L-seams required?