Cyclic or Sandwich Striped or Semi-Striped
Even-Odd Order Magic Square Generator

Cyclic: each layer is 4 rotated (pinwheel) equal-sum magic rectangles wrapping the next layer down. Sandwich: each layer is two 2×n rectangles (top/bottom, full width) plus two (n−4)×2 rectangles (left/right). Either way, the base is fully split whenever it lands on order 4 (two 2×4 rectangles) or order 6 (a sequential 2×6 band of 12 consecutive numbers plus three 2×4 strips); bases of order 3 or 5 have no known split yet and stay plain. Works for any order n ≥ 3 except n=2 (impossible under any construction). Speed note: Cyclic stays fast at every order (well under 5 seconds even at n=108). Sandwich's matching step gets noticeably slower as n grows — a few seconds up to about order 50, but potentially a minute or more beyond order 80. For very large orders, Cyclic is the quicker choice.