WALKS IN THE PLANE FROM (0,0) TO (N,N)



                      ------------------------------------

          This paper is concerned with walks from (0,0) to (N,N) where

steps from some subset of,

    {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]},

    are allowed.



Given a nonempty subset E of,

    {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]},

    define the generating function

       f(N,E;t):=sum t^a(w), where w ranges over walks from (0,0)->(N,N)

          with steps taken from E, and a is the statistic which counts

   the number of times a walk visits {y<x} or visits {y=x} coming from {y<x}.



  For each E, we generate f(N,E;t) for N=, 100, .. , 102, and , 150, .. , 152

            and use this data to conjecture how moments 1 through, 6

                           behave as functions of N.

                      ------------------------------------



                                 Theorem, 1, :

                When steps from, {[0, 1], [1, 0]}, are allowed:

                     Moment, 1, behaves like, 1.00000001, n

                      Moment, 2, behaves like, 0.34, n^, 2

                       Moment, 3, behaves like, 0.0000000

                         Moment, 4, behaves like, 1.800

                       Moment, 5, behaves like, 0.000000

                         Moment, 6, behaves like, 3.86

                      ------------------------------------

                                 Theorem, 2, :

                When steps from, {[0, 1], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.38, n

                      Moment, 2, behaves like, 0.10, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 0.900

                         Moment, 5, behaves like, -0.1

                         Moment, 6, behaves like, 1.93

                      ------------------------------------

                                 Theorem, 3, :

                When steps from, {[0, 1], [2, 1]}, are allowed:

                         Moment, 1, behaves like, 0., n

                     Moment, 2, behaves like, 0.043, n^, 2

                      Moment, 3, behaves like, 0.00000000

                         Moment, 4, behaves like, 0.900

                       Moment, 5, behaves like, 0.000000

                         Moment, 6, behaves like, 1.93

                      ------------------------------------

                                 Theorem, 4, :

                When steps from, {[0, 2], [1, 0]}, are allowed:

                        Moment, 1, behaves like, 0.38, n

                      Moment, 2, behaves like, 0.10, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 0.900

                         Moment, 5, behaves like, -0.1

                         Moment, 6, behaves like, 1.93

                      ------------------------------------

                                 Theorem, 5, :

                When steps from, {[0, 2], [2, 0]}, are allowed:

                         Moment, 1, behaves like, 0., n

                     Moment, 2, behaves like, 0.043, n^, 2

                      Moment, 3, behaves like, 0.00000000

                         Moment, 4, behaves like, 0.900

                       Moment, 5, behaves like, 0.000000

                         Moment, 6, behaves like, 1.93

                      ------------------------------------

                                 Theorem, 6, :

                When steps from, {[1, 0], [1, 2]}, are allowed:

                         Moment, 1, behaves like, 0., n

                     Moment, 2, behaves like, 0.043, n^, 2

                      Moment, 3, behaves like, 0.00000000

                         Moment, 4, behaves like, 0.900

                       Moment, 5, behaves like, 0.000000

                         Moment, 6, behaves like, 1.93

                      ------------------------------------

                                 Theorem, 7, :

            When steps from, {[0, 1], [0, 2], [1, 0]}, are allowed:

                        Moment, 1, behaves like, 0.9, n

                      Moment, 2, behaves like, 0.27, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.802

                        Moment, 5, behaves like, -0.031

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                 Theorem, 8, :

            When steps from, {[0, 1], [0, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.33, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, -0.02

                          Moment, 4, behaves like, 0.9

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                 Theorem, 9, :

            When steps from, {[0, 1], [0, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.23, n

                      Moment, 2, behaves like, 0.0, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 0.90

                         Moment, 5, behaves like, -0.02

                          Moment, 6, behaves like, 2.

                      ------------------------------------

                                Theorem, 10, :

            When steps from, {[0, 1], [1, 0], [1, 1]}, are allowed:

                        Moment, 1, behaves like, 0.8, n

                      Moment, 2, behaves like, 0.2, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 11, :

            When steps from, {[0, 1], [1, 0], [1, 2]}, are allowed:

                       Moment, 1, behaves like, 0.8538, n

                      Moment, 2, behaves like, 0.25, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, 0.03

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 12, :

            When steps from, {[0, 1], [1, 0], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.9, n

                      Moment, 2, behaves like, 0.27, n^, 2

                        Moment, 3, behaves like, -0.006

                         Moment, 4, behaves like, 1.802

                        Moment, 5, behaves like, -0.031

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 13, :

            When steps from, {[0, 1], [1, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.8538, n

                      Moment, 2, behaves like, 0.25, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 14, :

            When steps from, {[0, 1], [1, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.87, n

                      Moment, 2, behaves like, 0.25, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                         Moment, 6, behaves like, 3.94

                      ------------------------------------

                                Theorem, 15, :

            When steps from, {[0, 1], [1, 1], [2, 0]}, are allowed:

                       Moment, 1, behaves like, 0.666, n

                      Moment, 2, behaves like, 0.15, n^, 2

                         Moment, 3, behaves like, 0.001

                         Moment, 4, behaves like, 1.80

                         Moment, 5, behaves like, 0.01

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 16, :

            When steps from, {[0, 1], [1, 1], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.5, n

                      Moment, 2, behaves like, 0.08, n^, 2

                         Moment, 3, behaves like, 0.04

                         Moment, 4, behaves like, 1.801

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 17, :

            When steps from, {[0, 1], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.62, n

                     Moment, 2, behaves like, 0.126, n^, 2

                          Moment, 3, behaves like, -1.

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.07

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 18, :

            When steps from, {[0, 1], [1, 2], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.4357, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 19, :

            When steps from, {[0, 1], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.33, n

                     Moment, 2, behaves like, 0.073, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 0.90

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.

                      ------------------------------------

                                Theorem, 20, :

            When steps from, {[0, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.31, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 21, :

            When steps from, {[0, 1], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.21, n

                      Moment, 2, behaves like, 0.03, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 22, :

            When steps from, {[0, 2], [1, 0], [1, 1]}, are allowed:

                       Moment, 1, behaves like, 0.666, n

                      Moment, 2, behaves like, 0.15, n^, 2

                         Moment, 3, behaves like, 0.001

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, 0.008

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 23, :

            When steps from, {[0, 2], [1, 0], [1, 2]}, are allowed:

                        Moment, 1, behaves like, 0.33, n

                     Moment, 2, behaves like, 0.073, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 0.90

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.

                      ------------------------------------

                                Theorem, 24, :

            When steps from, {[0, 2], [1, 0], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.33, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, -0.02

                          Moment, 4, behaves like, 0.9

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 25, :

            When steps from, {[0, 2], [1, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.62, n

                     Moment, 2, behaves like, 0.126, n^, 2

                          Moment, 3, behaves like, -1.

                         Moment, 4, behaves like, 1.810

                         Moment, 5, behaves like, -0.07

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 26, :

            When steps from, {[0, 2], [1, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.31, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 27, :

            When steps from, {[0, 2], [1, 1], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.5, n

                      Moment, 2, behaves like, 0.08, n^, 2

                         Moment, 3, behaves like, 0.04

                         Moment, 4, behaves like, 1.801

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 28, :

            When steps from, {[0, 2], [1, 1], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.41, n

                     Moment, 2, behaves like, 0.059, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.1

                         Moment, 6, behaves like, 3.87

                      ------------------------------------

                                Theorem, 29, :

            When steps from, {[0, 2], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.2, n

                     Moment, 2, behaves like, 0.035, n^, 2

                         Moment, 3, behaves like, -0.03

                          Moment, 4, behaves like, 0.9

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 30, :

            When steps from, {[0, 2], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.36, n

                     Moment, 2, behaves like, 0.043, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                         Moment, 6, behaves like, 3.869

                      ------------------------------------

                                Theorem, 31, :

            When steps from, {[0, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.2, n

                     Moment, 2, behaves like, 0.035, n^, 2

                         Moment, 3, behaves like, -0.03

                          Moment, 4, behaves like, 0.9

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 32, :

            When steps from, {[0, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.21, n

                      Moment, 2, behaves like, 0.03, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 33, :

            When steps from, {[0, 2], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.166, n

                     Moment, 2, behaves like, 0.019, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 0.90

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.

                      ------------------------------------

                                Theorem, 34, :

            When steps from, {[1, 0], [1, 1], [1, 2]}, are allowed:

                        Moment, 1, behaves like, 0.5, n

                      Moment, 2, behaves like, 0.08, n^, 2

                         Moment, 3, behaves like, 0.04

                         Moment, 4, behaves like, 1.801

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 35, :

            When steps from, {[1, 0], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.23, n

                      Moment, 2, behaves like, 0.0, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 0.90

                         Moment, 5, behaves like, -0.02

                          Moment, 6, behaves like, 2.

                      ------------------------------------

                                Theorem, 36, :

            When steps from, {[1, 0], [1, 2], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.4357, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 37, :

            When steps from, {[1, 0], [1, 2], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.21, n

                      Moment, 2, behaves like, 0.03, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 38, :

            When steps from, {[1, 1], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.41, n

                     Moment, 2, behaves like, 0.059, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.1

                         Moment, 6, behaves like, 3.87

                      ------------------------------------

                                Theorem, 39, :

            When steps from, {[1, 1], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.37, n

                      Moment, 2, behaves like, 0.05, n^, 2

                          Moment, 3, behaves like, 0.1

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.3

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 40, :

            When steps from, {[1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.36, n

                     Moment, 2, behaves like, 0.043, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                         Moment, 6, behaves like, 3.869

                      ------------------------------------

                                Theorem, 41, :

            When steps from, {[1, 2], [2, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.166, n

                     Moment, 2, behaves like, 0.019, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 0.90

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.

                      ------------------------------------

                                Theorem, 42, :

            When steps from, {[1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.30, n

                     Moment, 2, behaves like, 0.032, n^, 2

                         Moment, 3, behaves like, 0.04

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 43, :

        When steps from, {[0, 1], [0, 2], [1, 0], [1, 1]}, are allowed:

                       Moment, 1, behaves like, 0.811, n

                      Moment, 2, behaves like, 0.22, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 44, :

        When steps from, {[0, 1], [0, 2], [1, 0], [1, 2]}, are allowed:

                        Moment, 1, behaves like, 0.84, n

                      Moment, 2, behaves like, 0.2, n^, 2

                         Moment, 3, behaves like, 0.00

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 45, :

        When steps from, {[0, 1], [0, 2], [1, 0], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.80, n

                      Moment, 2, behaves like, 0.21, n^, 2

                        Moment, 3, behaves like, -0.012

                         Moment, 4, behaves like, 1.805

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 46, :

        When steps from, {[0, 1], [0, 2], [1, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.80, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, 0.00

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 47, :

        When steps from, {[0, 1], [0, 2], [1, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.838, n

                      Moment, 2, behaves like, 0.2, n^, 2

                         Moment, 3, behaves like, 0.00

                        Moment, 4, behaves like, 1.8072

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 48, :

        When steps from, {[0, 1], [0, 2], [1, 1], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.6, n

                      Moment, 2, behaves like, 0.1, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 49, :

        When steps from, {[0, 1], [0, 2], [1, 1], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.46, n

                      Moment, 2, behaves like, 0.1, n^, 2

                         Moment, 3, behaves like, 0.03

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 50, :

        When steps from, {[0, 1], [0, 2], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.60, n

                      Moment, 2, behaves like, 0.12, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 51, :

        When steps from, {[0, 1], [0, 2], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.42, n

                      Moment, 2, behaves like, 0.06, n^, 2

                        Moment, 3, behaves like, -0.005

                          Moment, 4, behaves like, 1.8

                       Moment, 5, behaves like, -0.01549

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 52, :

        When steps from, {[0, 1], [0, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.30, n

                     Moment, 2, behaves like, 0.058, n^, 2

                         Moment, 3, behaves like, -0.02

                         Moment, 4, behaves like, 0.91

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 53, :

        When steps from, {[0, 1], [0, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.30, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 0.91

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 54, :

        When steps from, {[0, 1], [0, 2], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.202, n

                      Moment, 2, behaves like, 0.03, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 55, :

        When steps from, {[0, 1], [1, 0], [1, 1], [1, 2]}, are allowed:

                        Moment, 1, behaves like, 0.78, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.02

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 56, :

        When steps from, {[0, 1], [1, 0], [1, 1], [2, 0]}, are allowed:

                       Moment, 1, behaves like, 0.811, n

                      Moment, 2, behaves like, 0.22, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 57, :

        When steps from, {[0, 1], [1, 0], [1, 1], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.78, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.02

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 58, :

        When steps from, {[0, 1], [1, 0], [1, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.79, n

                      Moment, 2, behaves like, 0.22, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 59, :

        When steps from, {[0, 1], [1, 0], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.80, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.00

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, 0.00

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 60, :

        When steps from, {[0, 1], [1, 0], [1, 2], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.767, n

                      Moment, 2, behaves like, 0.20, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 61, :

        When steps from, {[0, 1], [1, 0], [1, 2], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.79, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 62, :

        When steps from, {[0, 1], [1, 0], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.84, n

                      Moment, 2, behaves like, 0.2, n^, 2

                         Moment, 3, behaves like, 0.00

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.01

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 63, :

        When steps from, {[0, 1], [1, 0], [2, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.838, n

                      Moment, 2, behaves like, 0.2, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.807

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 64, :

        When steps from, {[0, 1], [1, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.79, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 65, :

        When steps from, {[0, 1], [1, 1], [1, 2], [2, 0]}, are allowed:

                       Moment, 1, behaves like, 0.6013, n

                      Moment, 2, behaves like, 0.12, n^, 2

                         Moment, 3, behaves like, 0.001

                          Moment, 4, behaves like, 2.

                         Moment, 5, behaves like, 0.014

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 66, :

        When steps from, {[0, 1], [1, 1], [1, 2], [2, 1]}, are allowed:

                         Moment, 1, behaves like, 0., n

                      Moment, 2, behaves like, 0.07, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.805

                          Moment, 5, behaves like, 0.2

                         Moment, 6, behaves like, 3.90

                      ------------------------------------

                                Theorem, 67, :

        When steps from, {[0, 1], [1, 1], [2, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.621, n

                      Moment, 2, behaves like, 0.13, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 68, :

        When steps from, {[0, 1], [1, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.61, n

                      Moment, 2, behaves like, 0.13, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 69, :

        When steps from, {[0, 1], [1, 1], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.44, n

                     Moment, 2, behaves like, 0.071, n^, 2

                          Moment, 3, behaves like, 0.

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 70, :

        When steps from, {[0, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                      Moment, 2, behaves like, 0.11, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.04

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 71, :

        When steps from, {[0, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.6, n

                      Moment, 2, behaves like, 0.11, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 72, :

        When steps from, {[0, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.39, n

                      Moment, 2, behaves like, 0.05, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 73, :

        When steps from, {[0, 1], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.297, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 74, :

        When steps from, {[0, 2], [1, 0], [1, 1], [1, 2]}, are allowed:

                       Moment, 1, behaves like, 0.621, n

                      Moment, 2, behaves like, 0.13, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 75, :

        When steps from, {[0, 2], [1, 0], [1, 1], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.6, n

                      Moment, 2, behaves like, 0.1, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 76, :

        When steps from, {[0, 2], [1, 0], [1, 1], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.6013, n

                      Moment, 2, behaves like, 0.12, n^, 2

                         Moment, 3, behaves like, 0.001

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, 0.014

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 77, :

        When steps from, {[0, 2], [1, 0], [1, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.61, n

                      Moment, 2, behaves like, 0.13, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 2.

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 78, :

        When steps from, {[0, 2], [1, 0], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.30, n

                     Moment, 2, behaves like, 0.058, n^, 2

                         Moment, 3, behaves like, -0.02

                         Moment, 4, behaves like, 0.91

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 79, :

        When steps from, {[0, 2], [1, 0], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                      Moment, 2, behaves like, 0.11, n^, 2

                         Moment, 3, behaves like, -0.01

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.04

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 80, :

        When steps from, {[0, 2], [1, 0], [1, 2], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.297, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 81, :

        When steps from, {[0, 2], [1, 0], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.60, n

                      Moment, 2, behaves like, 0.12, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 82, :

        When steps from, {[0, 2], [1, 0], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.30, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 0.91

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 83, :

        When steps from, {[0, 2], [1, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.6, n

                      Moment, 2, behaves like, 0.11, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 84, :

        When steps from, {[0, 2], [1, 1], [1, 2], [2, 0]}, are allowed:

                       Moment, 1, behaves like, 0.471, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, -0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 85, :

        When steps from, {[0, 2], [1, 1], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.39, n

                     Moment, 2, behaves like, 0.054, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.803

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 86, :

        When steps from, {[0, 2], [1, 1], [2, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.471, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, -0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 87, :

        When steps from, {[0, 2], [1, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.44, n

                     Moment, 2, behaves like, 0.071, n^, 2

                          Moment, 3, behaves like, 0.

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 88, :

        When steps from, {[0, 2], [1, 1], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.37, n

                       Moment, 2, behaves like, 0., n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 89, :

        When steps from, {[0, 2], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.4, n

                     Moment, 2, behaves like, 0.061, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.2

                         Moment, 6, behaves like, 3.89

                      ------------------------------------

                                Theorem, 90, :

        When steps from, {[0, 2], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.21, n

                     Moment, 2, behaves like, 0.029, n^, 2

                         Moment, 3, behaves like, -0.02

                         Moment, 4, behaves like, 0.91

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 91, :

        When steps from, {[0, 2], [1, 2], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.328, n

                     Moment, 2, behaves like, 0.037, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.803

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 92, :

        When steps from, {[0, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.21, n

                     Moment, 2, behaves like, 0.029, n^, 2

                         Moment, 3, behaves like, -0.02

                         Moment, 4, behaves like, 0.91

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 93, :

        When steps from, {[1, 0], [1, 1], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.46, n

                      Moment, 2, behaves like, 0.1, n^, 2

                         Moment, 3, behaves like, 0.03

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 94, :

        When steps from, {[1, 0], [1, 1], [1, 2], [2, 1]}, are allowed:

                         Moment, 1, behaves like, 0., n

                      Moment, 2, behaves like, 0.07, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.805

                          Moment, 5, behaves like, 0.2

                         Moment, 6, behaves like, 3.90

                      ------------------------------------

                                Theorem, 95, :

        When steps from, {[1, 0], [1, 1], [1, 2], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.44, n

                     Moment, 2, behaves like, 0.071, n^, 2

                          Moment, 3, behaves like, 0.

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 96, :

        When steps from, {[1, 0], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.42, n

                      Moment, 2, behaves like, 0.06, n^, 2

                        Moment, 3, behaves like, -0.005

                          Moment, 4, behaves like, 1.8

                       Moment, 5, behaves like, -0.01549

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 97, :

        When steps from, {[1, 0], [1, 2], [2, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.202, n

                      Moment, 2, behaves like, 0.03, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 98, :

        When steps from, {[1, 0], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.39, n

                      Moment, 2, behaves like, 0.05, n^, 2

                         Moment, 3, behaves like, 0.02

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 99, :

        When steps from, {[1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.39, n

                     Moment, 2, behaves like, 0.054, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.803

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 100, :

        When steps from, {[1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.37, n

                       Moment, 2, behaves like, 0., n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 101, :

        When steps from, {[1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.3, n

                     Moment, 2, behaves like, 0.044, n^, 2

                          Moment, 3, behaves like, 0.1

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 102, :

        When steps from, {[1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.328, n

                     Moment, 2, behaves like, 0.037, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.803

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 103, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2]}, are allowed:

                       Moment, 1, behaves like, 0.776, n

                      Moment, 2, behaves like, 0.20, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 104, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                        Moment, 3, behaves like, -0.0042

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.01

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 105, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 106, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.78, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                         Moment, 6, behaves like, 3.92

                      ------------------------------------

                                Theorem, 107, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.76, n

                      Moment, 2, behaves like, 0.19, n^, 2

                        Moment, 3, behaves like, -0.015

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.05

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 108, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.76, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.00

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 109, :

    When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.793, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 110, :

    When steps from, {[0, 1], [0, 2], [1, 0], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.76, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, -0.01

                          Moment, 4, behaves like, 2.

                         Moment, 5, behaves like, -0.05

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 111, :

    When steps from, {[0, 1], [0, 2], [1, 0], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.77, n

                      Moment, 2, behaves like, 0.20, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.04

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 112, :

    When steps from, {[0, 1], [0, 2], [1, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.76, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 113, :

    When steps from, {[0, 1], [0, 2], [1, 1], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                     Moment, 2, behaves like, 0.113, n^, 2

                        Moment, 3, behaves like, -0.010

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 114, :

    When steps from, {[0, 1], [0, 2], [1, 1], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.44, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, 0.03

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 115, :

    When steps from, {[0, 1], [0, 2], [1, 1], [2, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.580, n

                      Moment, 2, behaves like, 0.11, n^, 2

                        Moment, 3, behaves like, -0.008

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 116, :

    When steps from, {[0, 1], [0, 2], [1, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                      Moment, 2, behaves like, 0.11, n^, 2

                        Moment, 3, behaves like, -0.0096

                          Moment, 4, behaves like, 2.

                        Moment, 5, behaves like, -0.032

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 117, :

    When steps from, {[0, 1], [0, 2], [1, 1], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.43, n

                      Moment, 2, behaves like, 0.07, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 118, :

    When steps from, {[0, 1], [0, 2], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                      Moment, 2, behaves like, 0.10, n^, 2

                         Moment, 3, behaves like, -0.02

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 119, :

    When steps from, {[0, 1], [0, 2], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                     Moment, 2, behaves like, 0.103, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 120, :

    When steps from, {[0, 1], [0, 2], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.39, n

                      Moment, 2, behaves like, 0.05, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 121, :

    When steps from, {[0, 1], [0, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.28, n

                     Moment, 2, behaves like, 0.052, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 122, :

    When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 0]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 123, :

    When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.73, n

                      Moment, 2, behaves like, 0.18, n^, 2

                         Moment, 3, behaves like, 0.02

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 124, :

    When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 125, :

    When steps from, {[0, 1], [1, 0], [1, 1], [2, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.776, n

                      Moment, 2, behaves like, 0.20, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 126, :

    When steps from, {[0, 1], [1, 0], [1, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.78, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.

                         Moment, 6, behaves like, 3.91

                      ------------------------------------

                                Theorem, 127, :

    When steps from, {[0, 1], [1, 0], [1, 1], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 128, :

    When steps from, {[0, 1], [1, 0], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.76, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.000

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, 0.015

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 129, :

    When steps from, {[0, 1], [1, 0], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.76, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 130, :

    When steps from, {[0, 1], [1, 0], [1, 2], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.728, n

                      Moment, 2, behaves like, 0.18, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 131, :

    When steps from, {[0, 1], [1, 0], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.793, n

                      Moment, 2, behaves like, 0.21, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 132, :

    When steps from, {[0, 1], [1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.57, n

                      Moment, 2, behaves like, 0.11, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 133, :

    When steps from, {[0, 1], [1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.57, n

                      Moment, 2, behaves like, 0.11, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 134, :

    When steps from, {[0, 1], [1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.42, n

                     Moment, 2, behaves like, 0.064, n^, 2

                          Moment, 3, behaves like, 0.

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 135, :

    When steps from, {[0, 1], [1, 1], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                      Moment, 2, behaves like, 0.12, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 136, :

    When steps from, {[0, 1], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.54, n

                      Moment, 2, behaves like, 0.10, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                         Moment, 6, behaves like, 3.948

                      ------------------------------------

                                Theorem, 137, :

    When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 0]}, are allowed:

                       Moment, 1, behaves like, 0.580, n

                      Moment, 2, behaves like, 0.11, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 138, :

    When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.57, n

                      Moment, 2, behaves like, 0.11, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                         Moment, 6, behaves like, 3.90

                      ------------------------------------

                                Theorem, 139, :

    When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                      Moment, 2, behaves like, 0.12, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 140, :

    When steps from, {[0, 2], [1, 0], [1, 1], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                     Moment, 2, behaves like, 0.113, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 141, :

    When steps from, {[0, 2], [1, 0], [1, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.58, n

                      Moment, 2, behaves like, 0.11, n^, 2

                        Moment, 3, behaves like, -0.010

                          Moment, 4, behaves like, 1.8

                        Moment, 5, behaves like, -0.0323

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 142, :

    When steps from, {[0, 2], [1, 0], [1, 1], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.57, n

                      Moment, 2, behaves like, 0.11, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 143, :

    When steps from, {[0, 2], [1, 0], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                      Moment, 2, behaves like, 0.10, n^, 2

                         Moment, 3, behaves like, -0.02

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 144, :

    When steps from, {[0, 2], [1, 0], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.28, n

                     Moment, 2, behaves like, 0.052, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 0.91

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 2.0

                      ------------------------------------

                                Theorem, 145, :

    When steps from, {[0, 2], [1, 0], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.54, n

                      Moment, 2, behaves like, 0.10, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 146, :

    When steps from, {[0, 2], [1, 0], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                     Moment, 2, behaves like, 0.103, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 147, :

    When steps from, {[0, 2], [1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.449, n

                     Moment, 2, behaves like, 0.067, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 148, :

    When steps from, {[0, 2], [1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.442, n

                      Moment, 2, behaves like, 0.07, n^, 2

                        Moment, 3, behaves like, -0.012

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.05

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 149, :

    When steps from, {[0, 2], [1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.36, n

                      Moment, 2, behaves like, 0.05, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 150, :

    When steps from, {[0, 2], [1, 1], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.442, n

                      Moment, 2, behaves like, 0.07, n^, 2

                        Moment, 3, behaves like, -0.012

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.05

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 151, :

    When steps from, {[0, 2], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.41, n

                      Moment, 2, behaves like, 0.05, n^, 2

                         Moment, 3, behaves like, -0.03

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.11

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 152, :

    When steps from, {[1, 0], [1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.44, n

                      Moment, 2, behaves like, 0.07, n^, 2

                         Moment, 3, behaves like, 0.03

                         Moment, 4, behaves like, 1.80

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 153, :

    When steps from, {[1, 0], [1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.43, n

                      Moment, 2, behaves like, 0.07, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 154, :

    When steps from, {[1, 0], [1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.42, n

                     Moment, 2, behaves like, 0.064, n^, 2

                          Moment, 3, behaves like, 0.

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 155, :

    When steps from, {[1, 0], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.39, n

                      Moment, 2, behaves like, 0.05, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 156, :

    When steps from, {[1, 1], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.36, n

                      Moment, 2, behaves like, 0.05, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 157, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0]}, are allowed:

                       Moment, 1, behaves like, 0.726, n

                      Moment, 2, behaves like, 0.18, n^, 2

                        Moment, 3, behaves like, -0.003

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 158, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.73, n

                      Moment, 2, behaves like, 0.18, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 159, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 160, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 0], [2, 1]}, are allowed:

                       Moment, 1, behaves like, 0.726, n

                      Moment, 2, behaves like, 0.18, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 161, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.74, n

                      Moment, 2, behaves like, 0.18, n^, 2

                        Moment, 3, behaves like, -0.002

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, 0.00

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 162, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.730, n

                     Moment, 2, behaves like, 0.181, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 163, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.7, n

                      Moment, 2, behaves like, 0.17, n^, 2

                        Moment, 3, behaves like, -0.010

                          Moment, 4, behaves like, 1.8

                         Moment, 5, behaves like, -0.03

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 164, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.74, n

                      Moment, 2, behaves like, 0.18, n^, 2

                        Moment, 3, behaves like, -0.009

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.03

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 165, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.729, n

                      Moment, 2, behaves like, 0.18, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 166, :

When steps from, {[0, 1], [0, 2], [1, 0], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.74, n

                      Moment, 2, behaves like, 0.18, n^, 2

                        Moment, 3, behaves like, -0.009

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.03

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 167, :

When steps from, {[0, 1], [0, 2], [1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                     Moment, 2, behaves like, 0.103, n^, 2

                         Moment, 3, behaves like, -0.01

                        Moment, 4, behaves like, 1.8063

                        Moment, 5, behaves like, -0.041

                         Moment, 6, behaves like, 3.89

                      ------------------------------------

                                Theorem, 168, :

When steps from, {[0, 1], [0, 2], [1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.561, n

                      Moment, 2, behaves like, 0.10, n^, 2

                       Moment, 3, behaves like, -0.00911

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.03

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 169, :

When steps from, {[0, 1], [0, 2], [1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.4, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, 0.04

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 170, :

When steps from, {[0, 1], [0, 2], [1, 1], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                     Moment, 2, behaves like, 0.104, n^, 2

                        Moment, 3, behaves like, -0.007

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 171, :

When steps from, {[0, 1], [0, 2], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.54, n

                      Moment, 2, behaves like, 0.09, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                       Moment, 5, behaves like, -0.08632

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 172, :

When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.73, n

                      Moment, 2, behaves like, 0.18, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 173, :

When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.730, n

                     Moment, 2, behaves like, 0.181, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 174, :

When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.71, n

                      Moment, 2, behaves like, 0.17, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 175, :

When steps from, {[0, 1], [1, 0], [1, 1], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.75, n

                      Moment, 2, behaves like, 0.19, n^, 2

                         Moment, 3, behaves like, 0.01

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 176, :

When steps from, {[0, 1], [1, 0], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.729, n

                      Moment, 2, behaves like, 0.18, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 177, :

When steps from, {[0, 1], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.549, n

                      Moment, 2, behaves like, 0.10, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 178, :

When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                     Moment, 2, behaves like, 0.103, n^, 2

                         Moment, 3, behaves like, -0.01

                         Moment, 4, behaves like, 1.806

                        Moment, 5, behaves like, -0.0405

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 179, :

When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.56, n

                     Moment, 2, behaves like, 0.104, n^, 2

                        Moment, 3, behaves like, -0.007

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 180, :

When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.549, n

                      Moment, 2, behaves like, 0.10, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 181, :

When steps from, {[0, 2], [1, 0], [1, 1], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.561, n

                      Moment, 2, behaves like, 0.10, n^, 2

                       Moment, 3, behaves like, -0.00911

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.03

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 182, :

When steps from, {[0, 2], [1, 0], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.54, n

                      Moment, 2, behaves like, 0.09, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                        Moment, 5, behaves like, -0.086

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 183, :

When steps from, {[0, 2], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                       Moment, 1, behaves like, 0.429, n

                      Moment, 2, behaves like, 0.06, n^, 2

                          Moment, 3, behaves like, 0.0

                          Moment, 4, behaves like, 1.8

                        Moment, 5, behaves like, -0.048

                         Moment, 6, behaves like, 3.88

                      ------------------------------------

                                Theorem, 184, :

When steps from, {[1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]}, are allowed:

                        Moment, 1, behaves like, 0.4, n

                      Moment, 2, behaves like, 0.06, n^, 2

                         Moment, 3, behaves like, 0.04

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.2

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 185, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1]},

    are allowed:

                       Moment, 1, behaves like, 0.703, n

                      Moment, 2, behaves like, 0.2, n^, 2

                          Moment, 3, behaves like, 0.0

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 186, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 2]},

    are allowed:

                        Moment, 1, behaves like, 0.71, n

                      Moment, 2, behaves like, 0.17, n^, 2

                        Moment, 3, behaves like, -0.001

                          Moment, 4, behaves like, 1.8

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 187, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 1], [2, 2]},

    are allowed:

                       Moment, 1, behaves like, 0.708, n

                      Moment, 2, behaves like, 0.17, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 188, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 1], [2, 0], [2, 1], [2, 2]},

    are allowed:

                        Moment, 1, behaves like, 0.71, n

                      Moment, 2, behaves like, 0.17, n^, 2

                        Moment, 3, behaves like, -0.001

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.0

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 189, :

When steps from, {[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1], [2, 2]},

    are allowed:

                        Moment, 1, behaves like, 0.71, n

                      Moment, 2, behaves like, 0.17, n^, 2

                        Moment, 3, behaves like, -0.008

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.02

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 190, :

When steps from, {[0, 1], [0, 2], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]},

    are allowed:

                       Moment, 1, behaves like, 0.540, n

                      Moment, 2, behaves like, 0.10, n^, 2

                        Moment, 3, behaves like, -0.0070

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.02

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 191, :

When steps from, {[0, 1], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]},

    are allowed:

                       Moment, 1, behaves like, 0.708, n

                      Moment, 2, behaves like, 0.17, n^, 2

                         Moment, 3, behaves like, 0.01

                         Moment, 4, behaves like, 1.81

                          Moment, 5, behaves like, 0.1

                          Moment, 6, behaves like, 3.9

                      ------------------------------------

                                Theorem, 192, :

When steps from, {[0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]},

    are allowed:

                       Moment, 1, behaves like, 0.540, n

                      Moment, 2, behaves like, 0.10, n^, 2

                        Moment, 3, behaves like, -0.0070

                         Moment, 4, behaves like, 1.81

                         Moment, 5, behaves like, -0.02

                          Moment, 6, behaves like, 4.

                      ------------------------------------

                                Theorem, 193, :

When steps from,

    {[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]},

    are allowed:

                        Moment, 1, behaves like, 0.69, n

                      Moment, 2, behaves like, 0.16, n^, 2

                         Moment, 3, behaves like, 0.00

                         Moment, 4, behaves like, 1.810

                          Moment, 5, behaves like, 0.

                         Moment, 6, behaves like, 3.93

                      ------------------------------------

                               Computation time:

                                   928777.70