A little recursion problem

Are you reading this on your phone? Quick, see if you can solve this problem without getting up and switching devices.

Convolving a list with itself. Given a list [x₁, x₂, ..., x_n−1, x_n], where n is unknown, construct [(x₁, x_n), (x₂, x_n−1), ..., (x_n−1, x₂), (x_n, x₁)] in n recursive calls.

If you can't do it, try installing Lua Carousel below and try again.

(Problem found in this paper (pdf).)