Warning, the protected name Chi has been redefined and unprotected
             There all together, 31, different equivalence classes

For the equivalence class of patterns, {{[2, 3, 1], [3, 2, 1], [2, 1, 3, 4]},

    {[3, 1, 2], [3, 2, 1], [1, 2, 4, 3]}, {[1, 2, 3], [1, 3, 2], [4, 3, 1, 2]},

    {[1, 2, 3], [2, 1, 3], [3, 4, 2, 1]}}

  the member , {[2, 3, 1], [3, 2, 1], [2, 1, 3, 4]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

    ],

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

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], {

    [0, 1, 0, 3, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1],

    [0, 2, 0, 1, 0]}, {4}], [[2, 1, 3, 3], {[0, 1, 3, 0, 0], [1, 1, 1, 0, 0],

    [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 2, 1, 0, 0]}, {3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3], {

    [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

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

    [[2, 1, 4, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 3, 5], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 3],

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

    [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}],

    [[2, 1, 5, 3, 4], %1, {1, 2, 3, 4, 5}],

    [[3, 1, 5, 4, 2], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 3, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 5, 4, 3], %1, {1, 2, 3, 4, 5}],

    [[3, 2, 5, 4, 1], %1, {1, 2, 3, 4, 5}]]

%1 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 10, 13, 16, 19, 22, 25]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                  [1, 6, 24, 59, 106, 165, 236, 319, 414, 521]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                      [1, 20, 148, 484, 1090, 2047, 3436]

For the equivalence class of patterns, {{[1, 3, 2], [3, 1, 2], [2, 3, 4, 1]},

    {[1, 3, 2], [3, 1, 2], [3, 2, 1, 4]}, {[2, 1, 3], [2, 3, 1], [1, 4, 3, 2]},

    {[2, 1, 3], [2, 3, 1], [4, 1, 2, 3]}}

  the member , {[1, 3, 2], [3, 1, 2], [2, 3, 4, 1]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 3], {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}]

    , [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 1],

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

    {1, 4}], [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 4], %6, {}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], %4, {2, 4}],

    [[2, 1, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1], %5, {1, 2}],

    [[2, 1, 3, 4], %6, {}],

    [[2, 3, 1, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {2, 4}],

    [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], %4, {3, 4}],

    [[3, 4, 2, 1], %5, {3}], [[2, 3, 1, 4], %6, {}], [[3, 2, 1, 4], %5, {1, 2}],

    [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

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

    [[4, 3, 2, 1], %5, {2, 3}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 1], %4, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 4, 5, 2], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 5, 4], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 5, 3], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %3, {4, 5}],

    [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 5, 1], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 5], %1, {1, 2, 3, 4}], [[2, 1, 4, 5, 3], %2, {1, 2, 3, 4, 5}],

    [[3, 1, 4, 5, 2], %2, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 5], %1, {1, 2, 3, 4}], [[3, 2, 4, 5, 1], %2, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 4], %3, {4, 5}],

    [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 5, 4], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 5, 4], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 1, 5, 2], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 4, 4], %3, {4, 5}], [[3, 4, 2, 5, 1], %2, {1, 2, 3, 4, 5}],

    [[2, 4, 1, 5, 3], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 4, 5], %1, {1, 2, 3, 4}]]

%1 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

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

%2 := {[0, 1, 1, 1, 1, 0]}

%3 := {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0],

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

%4 := {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0]}

%5 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}

%6 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                  [1, 6, 24, 51, 95, 160, 250, 369, 521, 710]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                       [1, 20, 148, 367, 821, 1636, 2965]

For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2], [4, 2, 1, 3]},

    {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1]}, {[3, 1, 2], [3, 2, 1], [1, 3, 4, 2]},

    {[2, 3, 1], [3, 2, 1], [3, 1, 2, 4]}}

  the member , {[1, 2, 3], [2, 1, 3], [2, 4, 3, 1]}, has a scheme of depth , 2

                                  here it is:

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

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

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

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

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                     [1, 2, 4, 7, 12, 20, 33, 54, 88, 143]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

               [1, 6, 24, 83, 272, 872, 2773, 8790, 27832, 88087]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                    [1, 20, 148, 1060, 6780, 43679, 276783]

For the equivalence class of patterns, {

    {[1, 2, 3], [3, 2, 1], [2, 1, 4, 3]}, {[1, 2, 3], [3, 2, 1], [3, 4, 1, 2]}}

  the member , {[1, 2, 3], [3, 2, 1], [2, 1, 4, 3]}, has a scheme of depth , 4

                                  here it is:

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

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

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

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

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

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

    {2, 3}], [

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

    ],

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

    [[2, 3, 1],

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

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

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

    [

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

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

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

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

    [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %1, {3, 4}],

    [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 2], %1, {1}], [

    [3, 4, 1, 2], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1],

    [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 4, 1, 3], {

    [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

    [0, 1, 1, 2, 0]}, {1, 3}], [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

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

    [0, 1, 2, 0, 0], [0, 1, 1, 0, 1]}, {1, 2, 4}], [[2, 3, 1, 1], {

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

    [0, 1, 1, 1, 0], [0, 0, 1, 1, 1]}, {3, 4}],

    [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %1, {3, 4}],

    [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]]

%1 := {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1],

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

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                         [1, 2, 4, 3, 0, 0, 0, 0, 0, 0]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                        [1, 6, 18, 7, 0, 0, 0, 0, 0, 0]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                            [1, 20, 80, 21, 0, 0, 0]

For the equivalence class of patterns, {{[2, 3, 1], [3, 2, 1], [2, 1, 4, 3]},

    {[1, 2, 3], [1, 3, 2], [3, 4, 1, 2]}, {[1, 2, 3], [2, 1, 3], [3, 4, 1, 2]},

    {[3, 1, 2], [3, 2, 1], [2, 1, 4, 3]}}

  the member , {[2, 3, 1], [3, 2, 1], [2, 1, 4, 3]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

    [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 3], {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}]

    , [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2],

    {[0, 1, 0, 2, 0], [0, 1, 2, 1, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {4}],

    [[2, 1, 3, 4],

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

    [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], {

    [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

    [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {3, 4}],

    [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], {

    [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0],

    [0, 1, 1, 2, 0, 0]}, {4, 5}],

    [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}]]

%1 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                  [1, 6, 24, 59, 115, 196, 306, 449, 629, 850]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                      [1, 20, 148, 484, 1154, 2311, 4135]

For the equivalence class of patterns, {{[1, 3, 2], [2, 3, 1], [2, 1, 3, 4]},

    {[1, 3, 2], [2, 3, 1], [4, 3, 1, 2]}, {[2, 1, 3], [3, 1, 2], [1, 2, 4, 3]},

    {[2, 1, 3], [3, 1, 2], [3, 4, 2, 1]}}

  the member , {[1, 3, 2], [2, 3, 1], [2, 1, 3, 4]}, has a scheme of depth , 4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 3], {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}]

    , [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4],

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

    {1, 2, 3}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3],

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

    [0, 2, 1, 0, 0]}, {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 18, 34, 54, 78, 106, 138, 174, 214]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 80, 149, 227, 314, 410]

For the equivalence class of patterns, {{[1, 2, 3], [2, 3, 1], [1, 4, 3, 2]},

    {[2, 1, 3], [3, 2, 1], [4, 1, 2, 3]}, {[1, 2, 3], [3, 1, 2], [3, 2, 1, 4]},

    {[1, 3, 2], [3, 2, 1], [2, 3, 4, 1]}}

  the member , {[1, 2, 3], [3, 1, 2], [3, 2, 1, 4]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

    [[1, 3, 2, 2], {[0, 1, 0, 2, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1]}, {3, 4}]

    , [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 3, 2], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {2, 3}]

    , [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], %8, {}],

    [[2, 4, 3, 1], %7, {}], [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 3], {[0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 2, 1, 0, 0]}, {3, 4}]

    , [[2, 1, 3, 1], %8, {2}],

    [[2, 1, 4, 3], {[0, 2, 1, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {1, 2}]

    , [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2],

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

    [[3, 2, 4, 1], %7, {}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3],

    {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [0, 1, 1, 0, 1], [0, 2, 1, 0, 0]}, {4}],

    [[2, 3, 1, 1], %8, {3, 4}], [[3, 4, 2, 1], %7, {}],

    [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 1], %8, {3, 4}],

    [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 3],

    {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [0, 1, 1, 0, 1], [0, 2, 1, 0, 0]}, {4}],

    [[4, 3, 2, 1], %7, {}], [[2, 4, 3, 1, 5], %3, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 1, 3], %5, {1, 2, 3, 4, 5}], [[3, 5, 4, 2, 1], %4, {1, 2, 3, 4}],

    [[2, 4, 3, 1, 1], %2, {4, 5}], [[2, 5, 4, 1, 3], %3, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 1, 4], %6, {1, 2, 3, 4, 5}],

    [[3, 5, 4, 1, 2], %3, {1, 2, 3, 4, 5}],

    [[2, 5, 3, 1, 4], %3, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 1, 2], %1, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 1, 5], %3, {1, 2, 3, 4, 5}],

    [[3, 2, 5, 1, 4], %3, {1, 2, 3, 4, 5}],

    [[4, 3, 5, 1, 2], %3, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 1, 2], %1, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1], %4, {1, 2, 3, 4}],

    [[3, 2, 4, 1, 1], %2, {4, 5}], [[4, 2, 5, 1, 3], %3, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 1, 4], %6, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 1, 3], %5, {1, 2, 3, 4, 5}],

    [[4, 5, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 5, 3, 2, 1], %4, {1, 2, 3, 4}],

    [[3, 4, 2, 1, 1], %2, {4, 5}], [[3, 5, 2, 1, 4], %3, {1, 2, 3, 4, 5}],

    [[3, 4, 2, 1, 5], %3, {1, 2, 3, 4, 5}],

    [[4, 5, 2, 1, 3], %3, {1, 2, 3, 4, 5}],

    [[3, 4, 2, 1, 2], %1, {1, 2, 3, 4, 5}],

    [[3, 4, 2, 1, 3], %5, {1, 2, 3, 4, 5}],

    [[3, 4, 2, 1, 4], %6, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 1, 5], %3, {1, 2, 3, 4, 5}],

    [[5, 3, 2, 1, 4], %3, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 1, 4], %6, {1, 2, 3, 4, 5}],

    [[5, 4, 2, 1, 3], %3, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 1, 3], %5, {1, 2, 3, 4, 5}], [[5, 4, 3, 2, 1], %4, {1, 2, 3, 4}],

    [[5, 4, 3, 1, 2], %3, {1, 2, 3, 4, 5}], [[4, 3, 2, 1, 1], %2, {4, 5}],

    [[4, 3, 2, 1, 2], %1, {1, 2, 3, 4, 5}],

    [[1, 4, 3, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 2, 1],

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

    [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {1, 4}], [[1, 3, 2, 1, 1], {

    [0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0],

    [0, 0, 0, 2, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}],

    [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}]]

%1 := {[0, 1, 0, 1, 1, 0]}

%2 := {[0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0],

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

%3 := {[0, 1, 1, 1, 1, 0]}

%4 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0],

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

%5 := {[0, 1, 1, 0, 1, 0]}

%6 := {[0, 1, 1, 1, 0, 0]}

%7 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}

%8 := {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 6, 8, 10, 12, 14, 16, 18]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                     [1, 6, 19, 25, 31, 37, 43, 49, 55, 61]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 93, 105, 117, 129, 141]

For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2], [3, 2, 4, 1]},

    {[1, 2, 3], [2, 1, 3], [4, 1, 3, 2]}, {[3, 1, 2], [3, 2, 1], [2, 3, 1, 4]},

    {[2, 3, 1], [3, 2, 1], [1, 4, 2, 3]}}

  the member , {[1, 2, 3], [1, 3, 2], [3, 2, 4, 1]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

    ],

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

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

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

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

    ], [[3, 2, 1, 2],

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

    {1, 2}], [[4, 3, 2, 1], {[0, 1, 1, 1, 2], [0, 1, 3, 1, 0], [0, 3, 1, 1, 0],

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

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

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

    [0, 1, 1, 1, 0], [0, 0, 2, 1, 1], [0, 0, 1, 2, 1]}, {3, 4}], [[4, 3, 1, 2],

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

    {1, 2}], [[4, 2, 1, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1],

    [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 1, 4], {

    [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

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

    [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 4, 5], %1, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 5, 4], %1, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4],

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

    [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}],

    [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}]]

%1 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                     [1, 2, 4, 7, 12, 20, 33, 54, 88, 143]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

               [1, 6, 24, 70, 232, 722, 2304, 7266, 23028, 72818]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                     [1, 20, 148, 813, 5479, 33781, 217538]

For the equivalence class of patterns, {{[2, 3, 1], [3, 2, 1], [1, 2, 3, 4]},

    {[1, 2, 3], [1, 3, 2], [4, 3, 2, 1]}, {[1, 2, 3], [2, 1, 3], [4, 3, 2, 1]},

    {[3, 1, 2], [3, 2, 1], [1, 2, 3, 4]}}

  the member , {[2, 3, 1], [3, 2, 1], [1, 2, 3, 4]}, has a scheme of depth , 5

                                  here it is:

[[[], {}, {}], [[1], {[2, 3], [3, 1], [0, 5], [4, 0]}, {}], [[1, 1], {

    [0, 1, 4], [0, 0, 5], [2, 3, 0], [0, 5, 0], [2, 2, 1], [0, 4, 1], [3, 0, 1],

    [3, 1, 0], [4, 0, 0], [2, 1, 2], [0, 3, 2], [2, 0, 3], [0, 2, 3]}, {1, 2}],

    [[1, 2], {[0, 1, 3], [1, 1, 0], [0, 3, 1], [0, 4, 0]}, {}],

    [[2, 1], {[1, 1, 0], [0, 3, 1], [0, 4, 0], [0, 2, 3]}, {}],

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

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

    [0, 3, 1, 0], [0, 4, 0, 0]}, {2, 3}], [[1, 2, 1], {[0, 1, 2, 1],

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

    [0, 0, 4, 0], [1, 0, 1, 0]}, {3}],

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

    [[1, 3, 2],

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

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

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

    [0, 0, 3, 1], [0, 3, 1, 0], [0, 0, 4, 0], [1, 0, 1, 0]}, {2, 3}], [

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

    [0, 1, 0, 3], [0, 1, 3, 0], [0, 3, 1, 0], [0, 4, 0, 0]}, {1}], [[2, 1, 3],

    {[0, 1, 3, 1], [1, 1, 1, 0], [0, 1, 4, 0], [0, 1, 1, 3], [0, 2, 1, 0]}, {}]

    , [[3, 1, 2],

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

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

    [0, 1, 0, 1, 1], [0, 2, 0, 1, 0]}, {2, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %7, {3, 4}],

    [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 4, 3], %5, {}],

    [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 3], %7, {2, 4}],

    [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %8, {3, 4}],

    [[1, 4, 2, 3], %5, {}], [[1, 3, 2, 4], %6, {}], [[2, 1, 3, 4], %6, {1, 2}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2], %8, {1}], [

    [2, 1, 4, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0],

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

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

    [0, 2, 1, 0, 0], [0, 1, 4, 0, 0], [0, 1, 1, 3, 0], [0, 1, 1, 2, 1],

    [0, 1, 3, 0, 1]}, {3, 4}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %8, {3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], %7, {1, 4}],

    [[3, 1, 2, 4], %6, {}], [[4, 1, 2, 3], %5, {}],

    [[1, 2, 5, 3, 4], %3, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 5, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 3, 5], %3, {1, 2, 3, 4, 5}],

    [[1, 2, 5, 4, 3], %3, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 3, 2], %4, {1, 2, 3, 4, 5}], [[1, 2, 4, 3, 3], %1, {4, 5}],

    [[1, 3, 5, 4, 2], %3, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 3], %1, {2}], [

    [1, 3, 2, 4, 4], {[0, 1, 1, 3, 0, 0], [0, 2, 1, 1, 0, 0],

    [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0],

    [0, 1, 1, 1, 0, 1]}, {4, 5}], [[1, 3, 2, 5, 4], {[0, 1, 2, 1, 1, 0],

    [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0],

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

    [[1, 4, 3, 5, 2], %3, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 5, 1], %3, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 5, 3], %3, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 4, 5], %3, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 4, 2], %4, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 3, 3], %1, {4, 5}], [[1, 4, 2, 3, 5], %3, {1, 2, 3, 4, 5}],

    [[1, 5, 2, 3, 4], %3, {1, 2, 3, 4, 5}],

    [[2, 5, 3, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 3, 2], %4, {1, 2, 3, 4, 5}],

    [[1, 5, 2, 4, 3], %3, {1, 2, 3, 4, 5}],

    [[1, 5, 3, 4, 2], %3, {1, 2, 3, 4, 5}],

    [[3, 1, 2, 4, 1], %2, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 4], {

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

    [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {4, 5}],

    [[4, 1, 2, 5, 3], %3, {1, 2, 3, 4, 5}], [[3, 1, 2, 5, 4], {

    [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

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

    [[3, 1, 2, 4, 5], %3, {1, 2, 3, 4, 5}],

    [[4, 2, 3, 5, 1], %3, {1, 2, 3, 4, 5}],

    [[3, 1, 2, 4, 2], %4, {1, 2, 3, 4, 5}], [[3, 1, 2, 4, 3], %1, {1}],

    [[4, 1, 3, 5, 2], %3, {1, 2, 3, 4, 5}],

    [[4, 1, 2, 3, 5], %3, {1, 2, 3, 4, 5}],

    [[4, 1, 2, 3, 2], %4, {1, 2, 3, 4, 5}],

    [[5, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[5, 1, 2, 4, 3], %3, {1, 2, 3, 4, 5}],

    [[5, 1, 3, 4, 2], %3, {1, 2, 3, 4, 5}],

    [[5, 1, 2, 3, 4], %3, {1, 2, 3, 4, 5}],

    [[4, 1, 2, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 3], %1, {4, 5}],

    [[4, 1, 2, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}]]

%1 := {[0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0],

    [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1]}

%2 := {[0, 0, 1, 1, 1, 0]}

%3 := {[0, 1, 1, 1, 1, 0]}

%4 := {[0, 1, 0, 1, 1, 0]}

%5 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

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

%6 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

    [0, 1, 1, 3, 0]}

%7 := {[0, 1, 3, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1],

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

%8 := {[0, 1, 0, 1, 3], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0],

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

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                         [1, 2, 4, 7, 5, 1, 0, 0, 0, 0]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                       [1, 6, 24, 40, 15, 1, 0, 0, 0, 0]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                          [1, 20, 148, 207, 45, 1, 0]

For the equivalence class of patterns, {{[2, 3, 1], [3, 2, 1], [1, 3, 2, 4]},

    {[1, 2, 3], [1, 3, 2], [4, 2, 3, 1]}, {[3, 1, 2], [3, 2, 1], [1, 3, 2, 4]},

    {[1, 2, 3], [2, 1, 3], [4, 2, 3, 1]}}

  the member , {[2, 3, 1], [3, 2, 1], [1, 3, 2, 4]}, has a scheme of depth , 4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %2, {3, 4}],

    [[1, 2, 3, 4], %1, {1, 2}], [[1, 2, 3, 2],

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

    {1, 2, 4}], [[1, 2, 4, 3],

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

    {1, 2}], [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 3], %2, {3, 4}], [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2],

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

    {1, 2, 4}], [[2, 1, 4, 3],

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

    {1, 2}], [[2, 1, 3, 4], %1, {1, 2}],

    [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 3], %2, {1}],

    [[4, 1, 2, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0]}, {2, 3}]

    , [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 4], %1, {2, 3}],

    [[3, 1, 2, 2], {[1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {3, 4}]]

%1 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 1]}

%2 := {[0, 1, 2, 0, 1], [0, 1, 2, 1, 0], [1, 1, 1, 0, 0], [0, 2, 1, 0, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                 [1, 6, 24, 70, 152, 278, 456, 694, 1000, 1382]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                      [1, 20, 148, 813, 2636, 6319, 12645]

For the equivalence class of patterns, {

    {[2, 3, 1], [3, 1, 2], [2, 1, 4, 3]}, {[1, 3, 2], [2, 1, 3], [3, 4, 1, 2]}}

  the member , {[2, 3, 1], [3, 1, 2], [2, 1, 4, 3]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

    [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 3], {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}]

    , [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 2],

    {[0, 1, 0, 2, 0], [0, 1, 2, 1, 0], [1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {4}],

    [[2, 1, 3, 4],

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

    [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}]

    , [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}]

    , [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4],

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

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

    [[2, 1, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 5], {

    [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

    [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {3, 4}],

    [[3, 1, 4, 5, 2], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 5, 1], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 4], {

    [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0],

    [0, 1, 1, 2, 0, 0]}, {4, 5}],

    [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 5, 4], %1, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 4],

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

    [0, 1, 1, 2, 0, 0]}, {4, 5}],

    [[3, 2, 1, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 5, 4], %1, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 5, 1], %1, {1, 2, 3, 4, 5}], [[3, 2, 1, 4, 5], {

    [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

    [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 2, 3, 4}],

    [[4, 3, 1, 5, 2], %1, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 4, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 5, 3], %1, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3],

    {[0, 2, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0]}, {4, 5}],

    [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 4],

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

    [0, 1, 1, 0, 2, 0], [1, 1, 1, 0, 1, 0]}, {1, 4}],

    [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}]]

%1 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 19, 36, 57, 82, 111, 144, 181, 222]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 93, 175, 266, 366, 475]

For the equivalence class of patterns, {{[1, 3, 2], [2, 1, 3], [2, 3, 4, 1]},

    {[1, 3, 2], [2, 1, 3], [4, 1, 2, 3]}, {[2, 3, 1], [3, 1, 2], [1, 4, 3, 2]},

    {[2, 3, 1], [3, 1, 2], [3, 2, 1, 4]}}

  the member , {[1, 3, 2], [2, 1, 3], [2, 3, 4, 1]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 3], {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}]

    , [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 4],

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

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

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

    [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 1, 4], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 1, 3], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 2, 1], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 4, 1, 2], %2, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1], {

    [0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0],

    [0, 0, 0, 2, 1, 0], [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}],

    [[1, 3, 4, 5, 2], %1, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 5, 4], %1, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 5, 3], %1, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], {

    [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0],

    [0, 1, 1, 2, 0, 0]}, {4, 5}],

    [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 1], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5],

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

    [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 2, 3, 4}]]

%1 := {[0, 1, 1, 1, 1, 0]}

%2 := {[0, 0, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                     [1, 2, 4, 7, 12, 20, 33, 54, 88, 143]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

               [1, 6, 19, 63, 198, 631, 1993, 6314, 19971, 63207]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                     [1, 20, 93, 710, 4166, 27511, 171549]

For the equivalence class of patterns, {{[1, 3, 2], [2, 3, 1], [3, 1, 2, 4]},

    {[1, 3, 2], [2, 3, 1], [4, 2, 1, 3]}, {[2, 1, 3], [3, 1, 2], [1, 3, 4, 2]},

    {[2, 1, 3], [3, 1, 2], [2, 4, 3, 1]}}

  the member , {[1, 3, 2], [2, 3, 1], [4, 2, 1, 3]}, has a scheme of depth , 4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %1, {3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 4], %2, {1, 2, 3}],

    [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %1, {3, 4}],

    [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 4], %2, {1, 2, 3}], [[3, 1, 2, 4], %2, {1, 2, 3}], [

    [3, 1, 2, 1],

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

    {1, 2, 4}], [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 2], {[1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {3, 4}],

    [[4, 1, 2, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0]}, {1}],

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

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

    {3, 4}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 4], %2, {1, 2, 3}], [[3, 2, 1, 2],

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

    {1, 2, 4}], [[3, 2, 1, 3], %1, {1}],

    [[4, 3, 2, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 2, 0], [1, 2, 1, 1, 0]}, {2}],

    [[4, 3, 1, 2], {[0, 2, 1, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {2}]]

%1 := {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}

%2 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 18, 34, 54, 78, 106, 138, 174, 214]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 80, 149, 227, 314, 410]

For the equivalence class of patterns, {

    {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4]}, {[2, 3, 1], [3, 1, 2], [4, 3, 2, 1]}}

  the member , {[1, 3, 2], [2, 1, 3], [1, 2, 3, 4]}, has a scheme of depth , 5

                                  here it is:

[[[], {}, {}], [[1], {[0, 3]}, {}], [[2, 1], {[0, 1, 1], [0, 4, 0]}, {1}],

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

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

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

    [[2, 3, 1], {[0, 4, 1, 0], [0, 1, 1, 1], [0, 1, 2, 0]}, {2}], [

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0]}, {2, 3}]

    , [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3],

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

    {3, 4}], [[1, 2, 3, 1],

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

    [[1, 2, 3, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 4, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[1, 2, 3, 1, 1],

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

    [0, 0, 0, 2, 1, 0], [0, 1, 0, 1, 1, 0]}, {4, 5}], [[2, 3, 4, 2, 1], {

    [0, 1, 1, 1, 1, 0], [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0],

    [0, 1, 0, 1, 1, 1]}, {1, 2, 3, 4}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                     [1, 2, 4, 7, 13, 24, 44, 81, 149, 274]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

              [1, 6, 19, 69, 244, 865, 3069, 10882, 38595, 136873]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                     [1, 20, 93, 752, 4733, 33133, 221358]

For the equivalence class of patterns, {{[1, 2, 3], [1, 3, 2], [3, 2, 1, 4]},

    {[1, 2, 3], [2, 1, 3], [1, 4, 3, 2]}, {[2, 3, 1], [3, 2, 1], [4, 1, 2, 3]},

    {[3, 1, 2], [3, 2, 1], [2, 3, 4, 1]}}

  the member , {[1, 2, 3], [1, 3, 2], [3, 2, 1, 4]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

    ],

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

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

    [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3],

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

    {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1],

    {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0]}, {4}],

    [[3, 2, 4, 1],

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

    [[4, 3, 5, 1, 2], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0],

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

    [3, 2, 4, 1, 2], {[0, 1, 1, 1, 1, 0], [0, 2, 0, 1, 1, 0],

    [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {1, 2, 3, 5}],

    [[3, 2, 4, 1, 5], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 5, 1, 4], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[4, 2, 5, 1, 3], {[0, 1, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[4, 3, 5, 2, 1],

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

    [3, 2, 4, 1, 1], {[0, 0, 3, 1, 1, 0], [0, 0, 1, 1, 2, 0],

    [0, 1, 1, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                     [1, 2, 4, 7, 13, 24, 44, 81, 149, 274]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

             [1, 6, 24, 83, 325, 1220, 4592, 17369, 65505, 247234]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                    [1, 20, 148, 1060, 8491, 64482, 496313]

For the equivalence class of patterns, {{[2, 3, 1], [3, 2, 1], [1, 2, 4, 3]},

    {[1, 2, 3], [1, 3, 2], [3, 4, 2, 1]}, {[1, 2, 3], [2, 1, 3], [4, 3, 1, 2]},

    {[3, 1, 2], [3, 2, 1], [2, 1, 3, 4]}}

  the member , {[2, 3, 1], [3, 2, 1], [1, 2, 4, 3]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

    [[2, 1, 3], {[1, 1, 1, 0], [0, 2, 1, 0]}, {}], [[1, 2, 3, 3], %8, {3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 2],

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

    {2, 4}], [[1, 2, 3, 4], %7, {}],

    [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 2], {[1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {3, 4}],

    [[1, 3, 2, 3], %8, {2, 4}], [[1, 3, 2, 4], %7, {}], [[1, 4, 2, 3], %6, {}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

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

    [[2, 1, 3, 4], %7, {1, 2}],

    [[2, 1, 3, 3], {[1, 1, 1, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}],

    [[2, 1, 4, 3], %6, {1, 2}], [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 2], {[1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {3, 4}],

    [[3, 1, 2, 3], %8, {1, 4}], [[3, 1, 2, 4], %7, {}], [[4, 1, 2, 3], %6, {}],

    [[1, 3, 4, 5, 2], %4, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 5, 4], %4, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 5, 3], %4, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 4], %2, {4, 5}],

    [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 5, 1], %4, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 2], %5, {1, 2, 3, 4, 5}], [[1, 2, 3, 4, 5], %1, {1, 2, 3, 4}],

    [[1, 3, 2, 4, 4], %2, {4, 5}], [[1, 3, 2, 5, 4], %4, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 4, 3, 5, 2], %4, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 5, 1], %4, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 5, 3], %4, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 4, 2], %5, {1, 2, 3, 4, 5}], [[1, 3, 2, 4, 5], %1, {2, 3, 4}],

    [[1, 4, 2, 3, 5], %1, {1, 2, 3, 4}], [[1, 4, 2, 3, 4], %2, {2}], [

    [1, 4, 2, 3, 3],

    {[0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0]}, {4, 5}],

    [[2, 5, 3, 4, 1], %4, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 3, 1], %3, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 3, 2], %5, {1, 2, 3, 4, 5}],

    [[1, 5, 2, 4, 3], %4, {1, 2, 3, 4, 5}],

    [[1, 5, 3, 4, 2], %4, {1, 2, 3, 4, 5}], [[1, 5, 2, 3, 4], {

    [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

    [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 4, 5], %1, {1, 4}],

    [[3, 1, 2, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[4, 1, 2, 5, 3], %4, {1, 2, 3, 4, 5}],

    [[4, 2, 3, 5, 1], %4, {1, 2, 3, 4, 5}],

    [[3, 1, 2, 4, 2], %5, {1, 2, 3, 4, 5}],

    [[4, 1, 3, 5, 2], %4, {1, 2, 3, 4, 5}],

    [[3, 1, 2, 5, 4], %4, {1, 2, 3, 4, 5}],

    [[3, 1, 2, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 1, 2, 4, 4], %2, {4, 5}], [[4, 1, 2, 3, 2], %5, {1, 2, 3, 4, 5}],

    [[5, 2, 3, 4, 1], %4, {1, 2, 3, 4, 5}],

    [[5, 1, 2, 4, 3], %4, {1, 2, 3, 4, 5}],

    [[5, 1, 3, 4, 2], %4, {1, 2, 3, 4, 5}],

    [[4, 1, 2, 3, 1], %3, {1, 2, 3, 4, 5}], [[4, 1, 2, 3, 4], %2, {1}], [

    [5, 1, 2, 3, 4], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0],

    [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0]}, {1, 2, 3, 4}], [[4, 1, 2, 3, 3],

    {[0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0], [1, 1, 1, 0, 1, 0]}, {4, 5}],

    [[4, 1, 2, 3, 5], %1, {1, 2, 3, 4}]]

%1 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

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

%2 := {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [1, 1, 1, 1, 0, 0],

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

%3 := {[0, 0, 1, 1, 1, 0]}

%4 := {[0, 1, 1, 1, 1, 0]}

%5 := {[0, 1, 0, 1, 1, 0]}

%6 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0]}

%7 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}

%8 := {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 10, 13, 16, 19, 22, 25]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                    [1, 6, 24, 40, 53, 66, 79, 92, 105, 118]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 148, 207, 250, 293, 336]

For the equivalence class of patterns, {{[1, 2, 3], [2, 3, 1], [4, 1, 3, 2]},

    {[1, 2, 3], [3, 1, 2], [3, 2, 4, 1]}, {[1, 3, 2], [3, 2, 1], [2, 3, 1, 4]},

    {[2, 1, 3], [3, 2, 1], [1, 4, 2, 3]}}

  the member , {[1, 2, 3], [2, 3, 1], [4, 1, 3, 2]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

    [[3, 2, 1],

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

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

    [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2],

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

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

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

    {3, 4}], [[1, 3, 2, 1], {[0, 0, 3, 1, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0],

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

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 4, 3],

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

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3],

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

    {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0],

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

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

    [0, 0, 1, 2, 1]}, {3, 4}], [[3, 2, 1, 2], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0],

    [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0]}, {1, 2}], [[3, 2, 1, 4],

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

    {2, 3}], [[4, 3, 1, 2], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1],

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

    [0, 1, 3, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1],

    [0, 2, 1, 0, 0]}, {}], [[4, 2, 1, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0],

    [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {}], [[4, 3, 2, 1], {

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

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

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

    [[4, 2, 1, 3, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[5, 3, 1, 4, 2], %3, {1, 2, 3, 4, 5}],

    [[5, 2, 1, 4, 3], %3, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 3, 1], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[5, 2, 1, 3, 4], %3, {1, 2, 3, 4, 5}],

    [[5, 3, 2, 4, 1], %3, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 3, 2], %1, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 3, 5], %3, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], {

    [0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0],

    [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}], [

    [4, 3, 2, 1, 3], {[0, 1, 2, 0, 1, 0], [0, 2, 1, 0, 1, 0],

    [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0],

    [0, 1, 1, 0, 1, 1]}, {2}], [[5, 4, 3, 1, 2], %2, {1, 2, 3}],

    [[5, 4, 3, 2, 1], {}, {3}], [[4, 3, 2, 1, 2], {[0, 1, 1, 1, 1, 0],

    [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0], [0, 1, 0, 2, 1, 0],

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

    [[5, 3, 2, 1, 4], %2, {2, 3, 4}], [[4, 3, 2, 1, 4], {[0, 1, 1, 3, 0, 0],

    [0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 1, 1, 0],

    [1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 0, 1]}, {3, 4}],

    [[5, 4, 2, 1, 3], %2, {1, 2}], [[4, 3, 2, 1, 1], {[0, 0, 3, 1, 1, 0],

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

    [0, 0, 2, 1, 1, 1], [0, 0, 1, 2, 1, 1], [0, 1, 1, 1, 1, 0],

    [0, 0, 2, 1, 2, 0], [0, 0, 1, 2, 2, 0], [0, 0, 1, 1, 3, 0]}, {4, 5}], [

    [4, 3, 2, 1, 5], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0],

    [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1]}, {2, 3, 4}],

    [[4, 3, 1, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 3, 1], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[4, 3, 2, 4, 1], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[4, 2, 1, 4, 3],

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

    [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0], [0, 1, 1, 1, 0, 1]}, {4}], [

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

    [0, 1, 0, 2, 0, 0], [1, 1, 0, 1, 0, 0], [0, 1, 1, 1, 0, 0],

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

    [[3, 2, 1, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3],

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

    [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 1, 1, 0, 1, 0]}, {4, 5}], [

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

    [0, 0, 1, 0, 2, 0], [0, 0, 2, 0, 1, 0], [0, 1, 1, 0, 1, 0],

    [1, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 2, 1], %1, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1], {

    [0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 2, 0],

    [1, 0, 0, 1, 1, 0], [0, 1, 0, 1, 1, 0], [0, 0, 0, 3, 1, 0]}, {2, 4, 5}], [

    [1, 4, 3, 1, 2], {[0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0],

    [1, 0, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0],

    [0, 0, 1, 1, 1, 1]}, {1, 2, 3, 4}], [[2, 1, 3, 2, 4], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 2, 3], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 1, 4, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2],

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

    [0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0]}, {4, 5}]]

%1 := {[0, 1, 0, 1, 1, 0]}

%2 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

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

%3 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 6, 8, 10, 12, 14, 16, 18]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                     [1, 6, 19, 19, 23, 27, 31, 35, 39, 43]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                          [1, 20, 93, 52, 58, 64, 70]

For the equivalence class of patterns, {{[1, 3, 2], [3, 1, 2], [2, 1, 3, 4]},

    {[1, 3, 2], [3, 1, 2], [3, 4, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 4, 3]},

    {[2, 1, 3], [2, 3, 1], [4, 3, 1, 2]}}

  the member , {[1, 3, 2], [3, 1, 2], [2, 1, 3, 4]}, has a scheme of depth , 4

                                  here it is:

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

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

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

    [

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

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

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

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

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

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

    ], [

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}],

    [[1, 2, 3, 4], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}]

    , [[1, 2, 3, 1], %1, {1}], [[2, 3, 4, 1], %2, {1, 2}], [[2, 3, 1, 4],

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

    {1, 2}], [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 3],

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

    {1, 2, 4}], [[2, 3, 1, 1], %1, {3, 4}], [[3, 4, 2, 1], %2, {1, 3}],

    [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4],

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

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

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

    {1, 2, 4}], [[4, 3, 2, 1], %2, {2, 3}], [[3, 2, 1, 1], %1, {3, 4}]]

%1 := {[0, 0, 1, 1, 2], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0]}

%2 := {[0, 1, 1, 1, 2], [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                 [1, 6, 24, 70, 152, 278, 456, 694, 1000, 1382]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                      [1, 20, 148, 813, 2636, 6319, 12645]

For the equivalence class of patterns, {{[2, 1, 3], [3, 2, 1], [2, 3, 4, 1]},

    {[1, 2, 3], [2, 3, 1], [3, 2, 1, 4]}, {[1, 2, 3], [3, 1, 2], [1, 4, 3, 2]},

    {[1, 3, 2], [3, 2, 1], [4, 1, 2, 3]}}

  the member , {[2, 1, 3], [3, 2, 1], [2, 3, 4, 1]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

    [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 4, 1, 2],

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

    [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1],

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

    {3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0],

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

    [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2],

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

    [0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0]}, {4, 5}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 6, 8, 10, 12, 14, 16, 18]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 19, 36, 57, 82, 111, 144, 181, 222]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 93, 238, 482, 852, 1375]

For the equivalence class of patterns, {

    {[1, 2, 3], [3, 2, 1], [2, 4, 1, 3]}, {[1, 2, 3], [3, 2, 1], [3, 1, 4, 2]}}

  the member , {[1, 2, 3], [3, 2, 1], [2, 4, 1, 3]}, has a scheme of depth , 4

                                  here it is:

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

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

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

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

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

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

    ],

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

    [[1, 2, 2],

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

    {2, 3}],

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

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

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

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

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

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

    [[2, 1, 3],

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

    , [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2], %1, {3, 4}],

    [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 1], {

    [0, 0, 3, 1, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1],

    [0, 0, 1, 2, 0]}, {1, 2, 4}], [[2, 1, 4, 3], {[0, 2, 1, 1, 0],

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

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

    [0, 3, 1, 0, 0], [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1],

    [0, 2, 2, 0, 0]}, {3, 4}], [[3, 1, 4, 2], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0],

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

    [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %1, {3, 4}],

    [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}]]

%1 := {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1],

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

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                         [1, 2, 4, 3, 0, 0, 0, 0, 0, 0]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                        [1, 6, 18, 7, 0, 0, 0, 0, 0, 0]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                            [1, 20, 80, 21, 0, 0, 0]

For the equivalence class of patterns, {{[2, 1, 3], [3, 2, 1], [3, 4, 1, 2]},

    {[1, 2, 3], [2, 3, 1], [2, 1, 4, 3]}, {[1, 2, 3], [3, 1, 2], [2, 1, 4, 3]},

    {[1, 3, 2], [3, 2, 1], [3, 4, 1, 2]}}

  the member , {[2, 1, 3], [3, 2, 1], [3, 4, 1, 2]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

    [1, 1, 2, 0], [0, 2, 2, 0]}, {}], [[1, 2, 3, 4], {[1, 2, 1, 1, 0],

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

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

    [[1, 2, 4, 3],

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

    {1, 2}], [[1, 3, 4, 2], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1],

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

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

    [0, 2, 2, 0, 0], [0, 1, 3, 0, 1]}, {3, 4}], [[1, 2, 3, 2],

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

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

    [0, 0, 1, 1, 1], [0, 0, 1, 2, 0]}, {1}], [[2, 3, 4, 1], {[0, 2, 1, 1, 0],

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

    [[3, 4, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[2, 4, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 1, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 4, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 3, 1, 1], {

    [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1],

    [0, 0, 1, 2, 0]}, {3, 4}], [[2, 3, 1, 2], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0],

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

    [[2, 3, 4, 1, 5], %1, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 4, 5, 1, 3], %1, {1, 2, 3, 4, 5}],

    [[3, 4, 5, 2, 1], %1, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1],

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

    [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}],

    [[3, 4, 5, 1, 2], %1, {1, 2, 3, 4, 5}],

    [[2, 3, 5, 1, 4], %1, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 4, 1, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 1, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 2, 3, 1], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 3, 1, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 3, 1, 2, 2],

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

    [0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0]}, {4, 5}]]

%1 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 6, 8, 10, 12, 14, 16, 18]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 19, 34, 53, 76, 103, 134, 169, 208]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 93, 232, 470, 834, 1351]

For the equivalence class of patterns, {{[1, 3, 2], [2, 3, 1], [1, 2, 3, 4]},

    {[1, 3, 2], [2, 3, 1], [4, 3, 2, 1]}, {[2, 1, 3], [3, 1, 2], [1, 2, 3, 4]},

    {[2, 1, 3], [3, 1, 2], [4, 3, 2, 1]}}

  the member , {[1, 3, 2], [2, 3, 1], [1, 2, 3, 4]}, has a scheme of depth , 4

                                  here it is:

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

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

    [[2, 1], {[0, 1, 3], [0, 3, 1], [0, 2, 2], [0, 4, 0]}, {}],

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

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

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

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

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

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

    {2, 3}],

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

    [[2, 1, 2],

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

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

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

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

    [0, 0, 4, 0], [0, 2, 1, 0], [0, 1, 2, 0]}, {2, 3}], [[3, 2, 1], {

    [0, 4, 1, 0], [0, 3, 2, 0], [0, 2, 3, 0], [0, 1, 3, 1], [0, 3, 1, 1],

    [0, 2, 2, 1], [0, 1, 4, 0], [0, 2, 1, 2], [0, 1, 2, 2], [0, 1, 1, 3]}, {1}]

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], {

    [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [0, 1, 1, 0, 1],

    [0, 2, 1, 0, 0]}, {3, 4}], [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 4], {

    [0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

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

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {

    [0, 1, 1, 0, 2], [0, 1, 1, 1, 1], [0, 1, 1, 2, 0], [1, 1, 1, 0, 0],

    [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}]]

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 18, 34, 54, 78, 106, 138, 174, 214]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 80, 149, 227, 314, 410]

For the equivalence class of patterns, {{[1, 3, 2], [3, 1, 2], [1, 2, 3, 4]},

    {[1, 3, 2], [3, 1, 2], [4, 3, 2, 1]}, {[2, 1, 3], [2, 3, 1], [1, 2, 3, 4]},

    {[2, 1, 3], [2, 3, 1], [4, 3, 2, 1]}}

  the member , {[1, 3, 2], [3, 1, 2], [1, 2, 3, 4]}, has a scheme of depth , 3

                                  here it is:

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

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

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

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

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

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

    ], [

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

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

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

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

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

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

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

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                [1, 6, 24, 83, 227, 516, 1026, 1849, 3093, 4882]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                     [1, 20, 148, 1060, 5240, 18925, 54778]

For the equivalence class of patterns, {{[1, 3, 2], [3, 1, 2], [2, 3, 1, 4]},

    {[1, 3, 2], [3, 1, 2], [3, 2, 4, 1]}, {[2, 1, 3], [2, 3, 1], [1, 4, 2, 3]},

    {[2, 1, 3], [2, 3, 1], [4, 1, 3, 2]}}

  the member , {[1, 3, 2], [3, 1, 2], [2, 3, 1, 4]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

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

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

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}], [[1, 2, 3, 1],

    {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 1, 1], [0, 0, 1, 2, 0]}, {4}],

    [[1, 2, 3, 4], %4, {}], [[2, 3, 4, 1],

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

    [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 3], {[0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}, {3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 4, 1],

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

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

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

    {1, 2, 4}], [[2, 1, 3, 4], %4, {}], [[3, 2, 1, 4], %4, {1, 2}],

    [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

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

    [[4, 3, 2, 1], %4, {2, 3}], [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}]

    , [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 4, 5, 2], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 5, 4], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 4, 5, 3], %2, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 2, 3, 4, 1], %3, {1}], [[1, 2, 3, 4, 5], {[0, 1, 2, 1, 1, 0],

    [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {2, 3, 4}], [

    [1, 2, 3, 4, 4],

    {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}],

    [[2, 3, 4, 5, 1], %1, {1, 2, 3, 4}], [[2, 1, 4, 5, 3], %2, {1, 2, 3, 4, 5}],

    [[3, 1, 4, 5, 2], %2, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 4, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 5, 4], %2, {1, 2, 3, 4, 5}], [[2, 1, 3, 4, 1], %3, {2}], [

    [2, 1, 3, 4, 4],

    {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0], [0, 1, 1, 2, 0, 0]}, {4, 5}], [

    [2, 1, 3, 4, 5], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0],

    [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 2, 0]}, {1, 3, 4}],

    [[3, 2, 4, 5, 1], %1, {1, 2}], [[2, 3, 4, 1, 5], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 4, 5, 1, 3], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 5, 1, 2], %2, {1, 2, 3, 4, 5}], [[2, 3, 4, 1, 1], %3, {4, 5}],

    [[2, 3, 5, 1, 4], %2, {1, 2, 3, 4, 5}],

    [[2, 3, 4, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 4, 5, 2, 1], %1, {4}]]

%1 := {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0],

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

%2 := {[0, 1, 1, 1, 1, 0]}

%3 := {[0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [0, 0, 2, 1, 1, 0],

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

%4 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                  [1, 6, 24, 48, 80, 120, 168, 224, 288, 360]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                       [1, 20, 148, 324, 608, 1027, 1608]

For the equivalence class of patterns, {{[1, 3, 2], [2, 3, 1], [3, 2, 1, 4]},

    {[1, 3, 2], [2, 3, 1], [4, 1, 2, 3]}, {[2, 1, 3], [3, 1, 2], [1, 4, 3, 2]},

    {[2, 1, 3], [3, 1, 2], [2, 3, 4, 1]}}

  the member , {[1, 3, 2], [2, 3, 1], [3, 2, 1, 4]}, has a scheme of depth , 4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

    [[1, 2, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[1, 2, 3, 3], %1, {3, 4}],

    [[1, 3, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 3, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 2, 3, 4], %2, {1, 2, 3}],

    [[2, 1, 4, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], %1, {3, 4}],

    [[2, 1, 3, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 4], %2, {1, 2, 3}], [[3, 1, 2, 4], %2, {1, 2, 3}],

    [[4, 1, 3, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 2], {[1, 1, 0, 1, 0], [0, 2, 0, 1, 0]}, {3, 4}],

    [[4, 1, 2, 3], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0]}, {1}], [

    [3, 1, 2, 1],

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

    {1, 2, 4}], [[3, 1, 2, 3], %1, {1}]]

%1 := {[1, 1, 1, 0, 0], [0, 1, 2, 0, 0], [0, 2, 1, 0, 0]}

%2 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                   [1, 6, 18, 34, 54, 78, 106, 138, 174, 214]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                        [1, 20, 80, 149, 227, 314, 410]

For the equivalence class of patterns, {{[1, 2, 3], [2, 3, 1], [4, 3, 2, 1]},

    {[1, 2, 3], [3, 1, 2], [4, 3, 2, 1]}, {[1, 3, 2], [3, 2, 1], [1, 2, 3, 4]},

    {[2, 1, 3], [3, 2, 1], [1, 2, 3, 4]}}

  the member , {[1, 2, 3], [2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth , 5

                                  here it is:

[[[], {}, {}], [[1], {[3, 1], [5, 0], [0, 4]}, {}], [[1, 1], {[5, 0, 0],

    [0, 1, 3], [3, 0, 1], [0, 3, 1], [0, 2, 2], [0, 0, 4], [3, 1, 0], [0, 4, 0]

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

    {[0, 1, 4], [2, 1, 1], [0, 2, 1], [3, 1, 0], [2, 2, 0], [0, 4, 0]}, {}],

    [[1, 2], {[1, 1, 0], [0, 1, 1], [0, 4, 0]}, {}],

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

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

    [1, 2, 1], {[0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 4, 0], [1, 0, 1, 0]}, {1, 3}

    ], [

    [1, 2, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 4, 0, 0]}, {2, 3}

    ],

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

    [[2, 1, 1], {[0, 0, 1, 4], [0, 0, 2, 1], [2, 0, 1, 1], [0, 1, 1, 2],

    [2, 1, 1, 0], [0, 1, 3, 0], [3, 0, 1, 0], [2, 0, 2, 0], [0, 0, 4, 0],

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

    [2, 1, 2], {[1, 1, 0, 0], [0, 1, 1, 0], [0, 1, 0, 1], [0, 4, 0, 0]}, {1, 3}

    ], [[3, 2, 1], {[1, 1, 1, 0], [0, 1, 4, 0], [0, 2, 1, 1], [0, 1, 2, 1],

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

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

    [[2, 1, 3], {[1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 4, 0], [0, 2, 1, 0]}, {}],

    [[2, 4, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 1], {

    [0, 0, 3, 1, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1],

    [0, 0, 1, 2, 0]}, {4}], [[1, 3, 2, 2], %7, {3, 4}], [[1, 4, 3, 2], %6, {}],

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[2, 1, 3, 1], {[0, 0, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 4, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3], {

    [1, 1, 1, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 0, 1], [0, 2, 1, 0, 0],

    [0, 1, 4, 0, 0]}, {3, 4}], [[2, 1, 3, 2], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0],

    [0, 1, 1, 1, 0], [0, 1, 0, 1, 1], [0, 2, 0, 1, 0]}, {}], [[2, 1, 4, 3], {

    [0, 2, 1, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0], [0, 1, 1, 2, 0],

    [0, 1, 3, 1, 0]}, {}], [[3, 1, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}],

    [[3, 1, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 1], {

    [0, 0, 3, 1, 0], [1, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 1, 1, 1],

    [0, 0, 1, 2, 0]}, {4}], [[4, 1, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 2, 3, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 1, 2, 2], %7, {3, 4}],

    [[4, 1, 3, 2], %6, {}], [[3, 2, 1, 2], %7, {2}],

    [[4, 3, 2, 1], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4],

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

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

    [0, 1, 1, 1, 0], [0, 0, 1, 4, 0], [0, 0, 2, 1, 1], [0, 0, 1, 2, 1]}, {3, 4}

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

    [0, 2, 1, 0, 0], [0, 1, 4, 0, 0]}, {1}], [[4, 3, 1, 2], %6, {}], [

    [4, 2, 1, 3], {[0, 2, 1, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

    [0, 1, 1, 2, 0], [0, 1, 3, 1, 0]}, {}], [[1, 4, 3, 2, 2], %3, {4, 5}],

    [[1, 4, 3, 2, 1], %5, {1, 2, 3, 4, 5}],

    [[1, 5, 4, 3, 2], %2, {1, 2, 3, 4, 5}],

    [[1, 4, 3, 2, 5], %2, {1, 2, 3, 4, 5}],

    [[2, 5, 4, 3, 1], %2, {1, 2, 3, 4, 5}],

    [[1, 5, 4, 2, 3], %2, {1, 2, 3, 4, 5}],

    [[1, 4, 3, 2, 3], %1, {1, 2, 3, 4, 5}],

    [[1, 5, 3, 2, 4], %2, {1, 2, 3, 4, 5}],

    [[1, 4, 3, 2, 4], %4, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 3, 1], %5, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 3, 5], %2, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 3, 4], %4, {1, 2, 3, 4, 5}],

    [[2, 1, 5, 3, 4], %2, {1, 2, 3, 4, 5}],

    [[3, 1, 5, 4, 2], %2, {1, 2, 3, 4, 5}], [[2, 1, 4, 3, 2], %3, {1, 3, 4}], [

    [2, 1, 5, 4, 3], {[0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0],

    [1, 1, 1, 1, 1, 0], [0, 1, 1, 2, 1, 0], [0, 1, 1, 1, 1, 1],

    [0, 1, 1, 1, 2, 0]}, {1, 2}], [[3, 2, 5, 4, 1], %2, {1, 2, 3, 4, 5}], [

    [2, 1, 4, 3, 3], {[0, 1, 3, 0, 1, 0], [0, 2, 1, 0, 1, 0],

    [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0],

    [0, 1, 1, 0, 1, 1]}, {4, 5}], [[4, 1, 3, 2, 5], %2, {1, 2, 3, 4, 5}],

    [[5, 1, 3, 2, 4], %2, {1, 2, 3, 4, 5}],

    [[4, 1, 3, 2, 4], %4, {1, 2, 3, 4, 5}],

    [[4, 1, 3, 2, 1], %5, {1, 2, 3, 4, 5}],

    [[5, 1, 4, 3, 2], %2, {1, 2, 3, 4, 5}],

    [[5, 2, 4, 3, 1], %2, {1, 2, 3, 4, 5}], [[4, 1, 3, 2, 2], %3, {4, 5}],

    [[4, 1, 3, 2, 3], %1, {1, 2, 3, 4, 5}],

    [[5, 1, 4, 2, 3], %2, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 3, 4], %4, {1, 2, 3, 4, 5}],

    [[5, 3, 1, 4, 2], %2, {1, 2, 3, 4, 5}], [[4, 2, 1, 3, 3], {

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

    [0, 1, 1, 1, 1, 0], [1, 1, 1, 0, 1, 0], [0, 1, 1, 0, 1, 1]}, {4, 5}],

    [[4, 2, 1, 3, 2], %3, {1, 2}], [[4, 2, 1, 3, 1], %5, {1, 2, 3, 4, 5}],

    [[5, 2, 1, 3, 4], %2, {1, 2, 3, 4, 5}],

    [[5, 3, 2, 4, 1], %2, {1, 2, 3, 4, 5}],

    [[4, 2, 1, 3, 5], %2, {1, 2, 3, 4, 5}], [[5, 2, 1, 4, 3], {

    [0, 1, 2, 1, 1, 0], [0, 2, 1, 1, 1, 0], [1, 1, 1, 1, 1, 0],

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

    [[5, 4, 2, 3, 1], %2, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 2, 1], %5, {1, 2, 3, 4, 5}],

    [[5, 3, 1, 2, 4], %2, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 2, 3], %1, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 2, 5], %2, {1, 2, 3, 4, 5}],

    [[5, 4, 1, 3, 2], %2, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 2, 4], %4, {1, 2, 3, 4, 5}], [[4, 3, 1, 2, 2], %3, {4, 5}],

    [[5, 4, 1, 2, 3], %2, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 4, 3, 1], %1, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 2, 1], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 1, 4, 3, 2], %1, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 2], {

    [0, 1, 0, 0, 1, 1], [0, 2, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0],

    [0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0]}, {4, 5}]]

%1 := {[0, 1, 1, 0, 1, 0]}

%2 := {[0, 1, 1, 1, 1, 0]}

%3 := {[0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 1, 0], [0, 2, 0, 1, 1, 0],

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

%4 := {[0, 1, 1, 1, 0, 0]}

%5 := {[0, 0, 1, 1, 1, 0]}

%6 := {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1], [1, 1, 1, 1, 0],

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

%7 := {[0, 1, 0, 2, 0], [0, 3, 0, 1, 0], [1, 1, 0, 1, 0], [0, 1, 1, 1, 0],

    [0, 1, 0, 1, 1]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                         [1, 2, 4, 6, 3, 1, 0, 0, 0, 0]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                        [1, 6, 19, 23, 5, 1, 0, 0, 0, 0]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                            [1, 20, 93, 99, 7, 1, 0]

For the equivalence class of patterns, {{[1, 2, 3], [2, 3, 1], [4, 3, 1, 2]},

    {[1, 2, 3], [3, 1, 2], [3, 4, 2, 1]}, {[1, 3, 2], [3, 2, 1], [2, 1, 3, 4]},

    {[2, 1, 3], [3, 2, 1], [1, 2, 4, 3]}}

  the member , {[1, 2, 3], [3, 1, 2], [3, 4, 2, 1]}, has a scheme of depth , 5

                                  here it is:

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

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

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

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

    ],

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

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

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

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

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

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

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

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

    [[1, 4, 2, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[1, 3, 2, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[1, 4, 3, 2],

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

    {2, 3}], [[1, 3, 2, 3], {[0, 1, 1, 0, 0]}, {1, 2, 3, 4}], [[1, 3, 2, 2],

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

    {3, 4}], [[1, 3, 2, 1], {[2, 0, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0],

    [0, 0, 1, 1, 1], [0, 0, 1, 2, 0]}, {}], [[2, 4, 3, 1], {[0, 2, 1, 1, 0],

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

    [[2, 1, 3, 4], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 1, 4, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}], [[2, 1, 3, 3],

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

    {3, 4}], [[3, 2, 4, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 1, 1],

    [1, 1, 1, 1, 0], [0, 1, 1, 2, 0]}, {1, 2}], [[2, 1, 4, 3],

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

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

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

    [0, 1, 0, 2, 0], [2, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 1],

    [0, 2, 0, 1, 0]}, {}], [[4, 2, 1, 3], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[4, 3, 2, 1], {[0, 2, 1, 1, 0], [0, 1, 2, 1, 0], [0, 1, 1, 2, 0]}, {2, 3}]

    , [[4, 3, 1, 2], {[0, 1, 1, 1, 0]}, {1, 2, 3, 4}],

    [[3, 2, 1, 1], {[0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 1, 2, 0]}, {3, 4}]

    , [[3, 2, 1, 2], {[0, 1, 0, 1, 0]}, {1, 2, 3, 4}], [[3, 2, 1, 4],

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

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

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

    [[2, 4, 3, 1, 5], %1, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 1, 3], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 5, 4, 1, 3], %1, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 1, 4], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 5, 4, 1, 2], %1, {1, 2, 3, 4, 5}],

    [[2, 5, 3, 1, 4], %1, {1, 2, 3, 4, 5}], [[2, 4, 3, 1, 1], {

    [0, 0, 1, 1, 2, 0], [0, 1, 1, 1, 1, 0], [1, 0, 1, 1, 1, 0],

    [0, 0, 2, 1, 1, 0], [0, 0, 1, 2, 1, 0], [0, 0, 1, 1, 1, 1]}, {4, 5}],

    [[3, 5, 4, 2, 1], %1, {1, 2, 3, 4, 5}],

    [[2, 4, 3, 1, 2], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 1],

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

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

    {1, 2, 3, 4, 5}], [[4, 3, 2, 4, 1], {[0, 2, 1, 1, 0, 0], [0, 1, 2, 1, 0, 0],

    [0, 1, 1, 1, 1, 0], [1, 1, 1, 1, 0, 0], [0, 1, 1, 2, 0, 0],

    [0, 1, 1, 1, 0, 1]}, {1, 2, 3, 4}],

    [[4, 2, 1, 4, 3], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[4, 3, 1, 4, 2], {[0, 1, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 3, 2], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[3, 2, 1, 3, 4], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[3, 2, 1, 3, 3],

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

    [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [2, 1, 1, 0, 0, 0]}, {4, 5}],

    [[1, 4, 3, 1, 2], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 4, 3, 2, 1],

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

    [0, 1, 0, 2, 1, 0], [0, 1, 0, 1, 2, 0], [0, 1, 0, 1, 1, 1]}, {4}],

    [[1, 3, 2, 1, 2], {[0, 0, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 1, 4], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 4, 2, 1, 3], {[0, 0, 1, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[1, 3, 2, 1, 3], {[0, 0, 1, 1, 0, 0]}, {1, 2, 3, 4, 5}], [[1, 3, 2, 1, 1],

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

    [0, 0, 0, 2, 1, 0], [0, 1, 0, 1, 1, 0], [2, 0, 0, 1, 1, 0]}, {4, 5}],

    [[2, 1, 3, 2, 4], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 3, 2, 3], {[0, 1, 0, 1, 0, 0]}, {1, 2, 3, 4, 5}],

    [[2, 1, 4, 2, 3], {[0, 1, 0, 1, 1, 0]}, {1, 2, 3, 4, 5}],

    [[3, 1, 4, 3, 2], {[0, 1, 1, 0, 1, 0]}, {1, 2, 3, 4, 5}], [[2, 1, 3, 2, 1],

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

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

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

    [0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 0, 0, 2, 0],

    [2, 1, 0, 0, 1, 0]}, {4, 5}], [[3, 2, 4, 3, 1], {[0, 1, 2, 0, 1, 0],

    [0, 2, 1, 0, 1, 0], [0, 1, 1, 0, 2, 0], [0, 1, 1, 1, 1, 0],

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

%1 := {[0, 1, 1, 1, 1, 0]}

 Using  the scheme, the first, , 10, terms for , 1,  copies of each letter are

                      [1, 2, 4, 6, 8, 10, 12, 14, 16, 18]

 Using  the scheme, the first, , 10, terms for , 2,  copies of each letter are

                     [1, 6, 19, 21, 27, 33, 39, 45, 51, 57]

 Using  the scheme, the first, , 7, terms for , 3,  copies of each letter are

                          [1, 20, 93, 58, 70, 82, 94]

                         Out of a total of , 31, cases

                      27, were successful and , 4, failed

                             Success Rate: , 0.871

                             Here are the failures

{{{[2, 3, 1], [3, 1, 2], [1, 2, 3, 4]}, {[1, 3, 2], [2, 1, 3], [4, 3, 2, 1]}},

    {{[1, 2, 3], [2, 3, 1], [4, 2, 1, 3]}, {[1, 2, 3], [3, 1, 2], [2, 4, 3, 1]},

    {[1, 3, 2], [3, 2, 1], [3, 1, 2, 4]}, {[2, 1, 3], [3, 2, 1], [1, 3, 4, 2]}}

    , {{[2, 3, 1], [3, 1, 2], [2, 1, 3, 4]},

    {[2, 3, 1], [3, 1, 2], [1, 2, 4, 3]}, {[1, 3, 2], [2, 1, 3], [3, 4, 2, 1]},

    {[1, 3, 2], [2, 1, 3], [4, 3, 1, 2]}}, {

    {[2, 3, 1], [3, 1, 2], [1, 3, 2, 4]}, {[1, 3, 2], [2, 1, 3], [4, 2, 3, 1]}}

    }