Consider a walk in the square lattice where the

                    distribution of the fundamental steps is

         [[[1, 0], 1/4], [[-1, 0], 1/4], [[0, 1], 1/4], [[0, -1], 1/4]]

       Let a(n) be the probability of being at the origin after n steps.

           the probability of returning to the origin after n steps .

               The linear recurrence operator annihilating a_n:=

                                         2
                                  (n + 1)     2
                                - -------- + N
                                         2
                                  (n + 2)

               The whole thing took, 2.592, seconds of CPU time