Creating a circular matrix with one input

[Gribouillis]

Here are the increments between two consecutive lines (in the 9x9 case)

Output:
   1    2    3    4    5    6    7    8    9
  31   31   31   31   31   31   31   31    1
  -1   23   23   23   23   23   23    1    1
  -1   -1   15   15   15   15    1    1    1
  -1   -1   -1    7    7    1    1    1    1
  -1   -1   -1   -1   -3    1    1    1    1
  -1   -1   -1  -11  -11  -11    1    1    1
  -1   -1  -19  -19  -19  -19  -19    1    1
  -1  -27  -27  -27  -27  -27  -27  -27    1

This could be the starting point of a non recursive algorithm.