There are , 5, different equivalence classes

For the equivalence class of patterns, {{[3, 2, 1], [1, 2, 3], [1, 3, 2]},

    {[3, 2, 1], [1, 2, 3], [2, 1, 3]}, {[3, 2, 1], [1, 2, 3], [2, 3, 1]},

    {[3, 2, 1], [1, 2, 3], [3, 1, 2]}}

   the member , {[3, 2, 1], [1, 2, 3], [1, 3, 2]}, has a scheme of depth , 2

                                  here it is:

{[[], {}, {}], [[1], {[0, 2], [3, 0]}, {}],

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

    [[1, 2], {[0, 1, 0], [0, 0, 1], [3, 0, 0]}, {1}]}

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

    0, 0, 0, 0, 0]

                             the sequence is finite

For the equivalence class of patterns,

    {{[3, 2, 1], [1, 3, 2], [2, 1, 3]}, {[1, 2, 3], [2, 3, 1], [3, 1, 2]}}

   the member , {[3, 2, 1], [1, 3, 2], [2, 1, 3]}, has a scheme of depth , 2

                                  here it is:

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

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

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,

    22, 23, 24, 25, 26, 27, 28, 29, 30]

                      the sequence seems to be polynomial

                                     -1 + n

For the equivalence class of patterns, {{[3, 2, 1], [1, 3, 2], [2, 3, 1]},

    {[3, 2, 1], [1, 3, 2], [3, 1, 2]}, {[3, 2, 1], [2, 1, 3], [2, 3, 1]},

    {[3, 2, 1], [2, 1, 3], [3, 1, 2]}, {[1, 2, 3], [1, 3, 2], [2, 3, 1]},

    {[1, 2, 3], [1, 3, 2], [3, 1, 2]}, {[1, 2, 3], [2, 1, 3], [2, 3, 1]},

    {[1, 2, 3], [2, 1, 3], [3, 1, 2]}}

   the member , {[3, 2, 1], [1, 3, 2], [2, 3, 1]}, has a scheme of depth , 2

                                  here it is:

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

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

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,

    22, 23, 24, 25, 26, 27, 28, 29, 30]

                      the sequence seems to be polynomial

                                     -1 + n

For the equivalence class of patterns,

    {{[3, 2, 1], [2, 3, 1], [3, 1, 2]}, {[1, 2, 3], [1, 3, 2], [2, 1, 3]}}

   the member , {[3, 2, 1], [2, 3, 1], [3, 1, 2]}, has a scheme of depth , 2

                                  here it is:

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

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

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,

    4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811,

    514229, 832040, 1346269]

                  This enumerating sequence seems to have the

                                                        1
                   rational generating function, - -----------
                                                             2
                                                   -1 + x + x

For the equivalence class of patterns, {{[1, 3, 2], [2, 1, 3], [2, 3, 1]},

    {[1, 3, 2], [2, 1, 3], [3, 1, 2]}, {[1, 3, 2], [2, 3, 1], [3, 1, 2]},

    {[2, 1, 3], [2, 3, 1], [3, 1, 2]}}

   the member , {[1, 3, 2], [2, 1, 3], [2, 3, 1]}, has a scheme of depth , 2

                                  here it is:

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

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

                 Using  the scheme, the first, , 31, terms are

[1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,

    22, 23, 24, 25, 26, 27, 28, 29, 30]

                      the sequence seems to be polynomial

                                     -1 + n

                         Out of a total of , 5, cases

                      5, were successful and , 0, failed

                               Success Rate: , 1.

                             Here are the failures

                                       {}

                                       {}

                     It took, 2.408, seconds of CPU time .