For walks in the (hyper-cubic) lattice of dimension, 2

            The prob. of returning to the origin walking in Z^k is:

                                       1.



        The prob. of returning to the origin walking in Z^k staying in

                        [0 <= x[1], 0 <= x[2]],  equals

                                  0.1731362519



        The prob. of returning to the origin walking in Z^k staying in

                            [x[2] <= x[1]],  equals

                                  0.2146018368



        The prob. of returning to the origin walking in Z^k staying in

                      [x[2] <= x[1], 0 <= x[2]],  equals

                                  0.0742287233



             For walks in the (hyper-cubic) lattice of dimension, 3

            The prob. of returning to the origin walking in Z^k is:

                                  0.3405373295



        The prob. of returning to the origin walking in Z^k staying in

                  [0 <= x[1], 0 <= x[2], 0 <= x[3]],  equals

                                  0.1019012546



        The prob. of returning to the origin walking in Z^k staying in

                     [x[2] <= x[1], x[3] <= x[2]],  equals

                                  0.0648447157



        The prob. of returning to the origin walking in Z^k staying in

               [x[2] <= x[1], x[3] <= x[2], 0 <= x[3]],  equals

                                  0.0295951556



             For walks in the (hyper-cubic) lattice of dimension, 4

            The prob. of returning to the origin walking in Z^k is:

                                  0.1932016733



        The prob. of returning to the origin walking in Z^k staying in

             [0 <= x[1], 0 <= x[2], 0 <= x[3], 0 <= x[4]],  equals

                                  0.0721683878



        The prob. of returning to the origin walking in Z^k staying in

              [x[2] <= x[1], x[3] <= x[2], x[4] <= x[3]],  equals

                                  0.0336123614



        The prob. of returning to the origin walking in Z^k staying in

        [x[2] <= x[1], x[3] <= x[2], x[4] <= x[3], 0 <= x[4]],  equals

                                  0.0161566460



             For walks in the (hyper-cubic) lattice of dimension, 5

            The prob. of returning to the origin walking in Z^k is:

                                  0.1351786099



        The prob. of returning to the origin walking in Z^k staying in

       [0 <= x[1], 0 <= x[2], 0 <= x[3], 0 <= x[4], 0 <= x[5]],  equals

                                  0.0559088094



        The prob. of returning to the origin walking in Z^k staying in

       [x[2] <= x[1], x[3] <= x[2], x[4] <= x[3], x[5] <= x[4]],  equals

                                  0.0208948270



        The prob. of returning to the origin walking in Z^k staying in

 [x[2] <= x[1], x[3] <= x[2], x[4] <= x[3], x[5] <= x[4], 0 <= x[5]],  equals

                                  0.0102108196



              The whole thing took, 199.226, seconds of CPU time