There all together, 317, different equivalence classes

For the equivalence class of patterns, {

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

                  [1, 1, 2, 6, 21, 73, 202, 382, 396, 144, 0]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

    [[2, 1, 3, 4],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

                [1, 1, 2, 6, 21, 73, 222, 563, 1226, 2376, 4213]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 239, 734, 2134, 5934, 15918]

For the equivalence class of patterns, {

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 236, 745, 2286, 6866, 20285]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 254, 858, 2889, 9775, 33371]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

{[[], {}, {}],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 249, 804, 2540, 7977, 25106]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

{[[], {}, {}],

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

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

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

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

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

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

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

    [2, 1, 4, 3],

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

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

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

    [3, 4, 2, 1],

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

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

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

    [3, 2, 4, 1],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 237, 761, 2415, 7626, 24034]

For the equivalence class of patterns, {

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

                [1, 1, 2, 6, 21, 69, 181, 375, 651, 1009, 1449]

For the equivalence class of patterns, {

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 79, 310, 1251, 5151, 21536, 91137]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

    [4, 2, 3, 1],

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    [[1, 2, 3],

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

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

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

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

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

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

    [[3, 2, 4, 1],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 71, 220, 646, 1835, 5095, 13924]

For the equivalence class of patterns, {

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 77, 290, 1118, 4398, 17595, 71385]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 242, 772, 2409, 7439, 22872]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 243, 777, 2408, 7288, 21661]

For the equivalence class of patterns, {

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

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

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

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

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

    5

                                  here it is:

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

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

    [2, 3, 1, 4],

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

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

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

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

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

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

    [1, 2, 3, 4],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 255, 866, 2927, 9923, 33898]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    [1, 4, 2, 3],

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 233, 739, 2343, 7458, 23801]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 244, 794, 2553, 8179, 26192]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 233, 719, 2146, 6260, 17968]

For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

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

    3

                                  here it is:

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

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

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

    }

                 Using  the scheme, the first, , 21, terms are

[1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299,

    37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946,

    353224531663]

For the equivalence class of patterns, {

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

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

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

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

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

    4

                                  here it is:

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

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

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

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

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

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

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

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

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

    [[2, 4, 1, 3],

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 75, 267, 951, 3407, 12309, 44867]

For the equivalence class of patterns, {

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 75, 259, 862, 2808, 9090, 29489]

For the equivalence class of patterns, {

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

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

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

    5

                                  here it is:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[3, 4, 2, 1], {[0, 1, 0, 2, 0],

    [0, 1, 1, 1, 0], [1, 1, 0, 1, 0], [0, 1, 2, 0, 0], [1, 1, 1, 0, 0],

    [0, 0, 0, 0, 2]}, {1}], [[3, 2, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [

    [4, 3, 5, 1, 2], {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0],

    [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 1, 0],

    [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 2, 0]}, {1}],

    [[3, 2, 1, 4], {[0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [

    [3, 5, 4, 2, 1], {[0, 1, 0, 2, 0, 0], [0, 1, 1, 1, 0, 0],

    [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0],

    [1, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0],

    [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 2]}, {1}],

    [[3, 2, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 3, 1], {[0, 0, 0, 2]}, {}],

    [[3, 2, 1], {[0, 1, 2, 0], [1, 1, 1, 0]}, {}], [[2, 4, 3, 1, 5],

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {2}], [

    [4, 3, 5, 2, 1], {[0, 1, 0, 2, 0, 0], [1, 1, 0, 1, 0, 0],

    [1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0],

    [1, 1, 0, 0, 1, 0], [0, 0, 1, 1, 0, 0]}, {1}], [[2, 5, 3, 1, 4], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}],

    [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {4}], [[2, 5, 4, 1, 3],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1]}, {2}], [[1, 3, 2],

    {[0, 0, 0, 2], [1, 0, 2, 0], [0, 1, 2, 0], [1, 0, 1, 1], [0, 1, 1, 1]}, {}]

    , [[4, 3, 1, 2], %1, {2}], [[4, 3, 1, 5, 2], {[0, 1, 1, 1, 0, 0],

    [1, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 1, 0, 1, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0],

    [0, 0, 0, 0, 2, 0]}, {1}],

    [[3, 2, 4, 1], {[0, 1, 2, 0, 0], [1, 1, 1, 0, 0], [0, 0, 0, 0, 1]}, {}], [

    [4, 3, 2, 1], {[0, 1, 0, 2, 0], [1, 1, 0, 1, 0], [0, 1, 2, 0, 0],

    [1, 1, 1, 0, 0], [0, 0, 1, 1, 0]}, {2}], [[4, 2, 1, 3],

    {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}],

    [[1, 4, 2, 3],

    {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {1}],

    [[1, 3, 2, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}], [

    [3, 2, 1, 5, 4], {[1, 1, 1, 0, 0, 0], [0, 1, 2, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}], [[3, 1, 2, 4],

    {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[4, 2, 1, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [

    [4, 1, 2, 3],

    {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 2]}, {1}],

    [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[4, 2, 5, 1, 3], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}]}

%1 := {[0, 1, 1, 1, 0], [0, 1, 2, 0, 0], [0, 1, 1, 0, 1], [1, 0, 0, 0, 0],

    [0, 0, 0, 2, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 2]}

                 Using  the scheme, the first, , 11, terms are

                [1, 1, 2, 6, 21, 70, 205, 536, 1264, 2722, 5424]

For the equivalence class of patterns, {

    {[1, 3, 4, 2], [2, 1, 4, 3], [3, 1, 2, 4]},

    {[1, 4, 2, 3], [2, 1, 4, 3], [2, 3, 1, 4]},

    {[2, 4, 3, 1], [3, 4, 1, 2], [4, 2, 1, 3]},

    {[3, 2, 4, 1], [3, 4, 1, 2], [4, 1, 3, 2]}}

the member , {[1, 3, 4, 2], [2, 1, 4, 3], [3, 1, 2, 4]}, has a scheme of depth ,

    4

                                  here it is:

{[[1, 4, 3, 2], {[0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {2}],

    [[], {}, {}], [[2, 1, 3], {[0, 1, 0, 1], [0, 0, 1, 0]}, {3}],

    [[1, 3, 2], {[0, 0, 1, 1]}, {}], [[2, 4, 3, 1], {[0, 1, 0, 2, 0],

    [0, 1, 2, 0, 0], [0, 1, 0, 0, 2], [0, 0, 1, 1, 0], [0, 0, 1, 0, 1],

    [0, 0, 0, 1, 1]}, {2}],

    [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}],

    [[1, 2, 3], {[0, 1, 0, 0]}, {1}], [[1, 2], {}, {}], [[1], {}, {}],

    [[2, 3, 1], {[0, 0, 1, 1], [0, 1, 2, 0], [0, 1, 0, 2]}, {2}],

    [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[3, 1, 2], {[0, 0, 0, 1]}, {1}], [[2, 1], {[0, 1, 2]}, {}],

    [[3, 2, 1], {[0, 0, 1, 1], [0, 1, 2, 0], [0, 1, 0, 2]}, {1}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 257, 883, 3019, 10306, 35174]

For the equivalence class of patterns, {

    {[1, 4, 2, 3], [2, 4, 3, 1], [3, 2, 1, 4]},

    {[2, 3, 1, 4], [2, 4, 3, 1], [4, 1, 2, 3]},

    {[1, 4, 2, 3], [2, 3, 4, 1], [4, 2, 1, 3]},

    {[1, 3, 4, 2], [3, 2, 4, 1], [4, 1, 2, 3]},

    {[1, 3, 4, 2], [3, 2, 1, 4], [4, 1, 3, 2]},

    {[1, 4, 3, 2], [3, 1, 2, 4], [3, 2, 4, 1]},

    {[2, 3, 4, 1], [3, 1, 2, 4], [4, 1, 3, 2]},

    {[1, 4, 3, 2], [2, 3, 1, 4], [4, 2, 1, 3]}}

the member , {[1, 4, 2, 3], [2, 4, 3, 1], [3, 2, 1, 4]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}],

    [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}], [

    [1, 3, 2, 4, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 1, 0]}, {4}],

    [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {}], [[3, 1, 2], {}, {}],

    [[2, 1, 3, 4], {[1, 0, 1, 0, 0], [0, 1, 1, 0, 0], [1, 0, 0, 1, 0],

    [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {3}],

    [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}],

    [[1, 2, 3], {[0, 1, 1, 0]}, {2}], [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1]}, {4}], [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}],

    [[1, 2], {}, {}], [[1, 3, 2, 5, 4], %1, {1}],

    [[3, 2, 1], {[0, 0, 0, 1]}, {1}],

    [[2, 1, 3], {[1, 0, 1, 0], [0, 1, 1, 0]}, {}],

    [[2, 3, 1], {[1, 0, 1, 0]}, {}], [[2, 1], {}, {}], [[1], {}, {}],

    [[3, 5, 1, 2, 4], %1, {1}], [[1, 3, 2], {[1, 0, 0, 0], [0, 0, 1, 0]}, {}],

    [[4, 2, 3, 5, 1], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1],

    [1, 0, 1, 0, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0]}, {3}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[2, 1, 4, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}], [

    [4, 5, 1, 2, 3], {[0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 1, 0],

    [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0]}, {4}], [[4, 1, 3, 5, 2], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {3}],

    [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}],

    [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}],

    [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [

    [4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}], [[1, 4, 3, 2],

    {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}],

    [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 0, 1, 0]}, {}],

    [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 5, 4], %1, {2}], [

    [4, 5, 2, 3, 1],

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {1}],

    [[2, 4, 3, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 3, 2], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 0, 0, 1]}, {1}], [[3, 4, 1, 2, 5], {[0, 1, 1, 0, 0, 0],

    [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0],

    [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0],

    [0, 0, 0, 1, 1, 0]}, {1}], [[3, 1, 2, 4, 5], {[0, 1, 1, 0, 0, 0],

    [1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 0, 0],

    [1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 1, 0],

    [0, 0, 0, 1, 1, 0]}, {4}], [[2, 3, 1, 4], {[1, 0, 1, 0, 0], [0, 1, 1, 0, 0],

    [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {1}], [[3, 1, 2, 4],

    {[0, 1, 1, 0, 0], [1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 0, 1, 1, 0]}, {}],

    [[4, 1, 2, 3], {[0, 1, 1, 0, 0]}, {3}]}

%1 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 0, 0, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 228, 670, 1864, 5000, 13099]

For the equivalence class of patterns, {

    {[1, 3, 4, 2], [2, 3, 1, 4], [4, 3, 1, 2]},

    {[1, 4, 2, 3], [3, 1, 2, 4], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [2, 4, 3, 1], [4, 1, 3, 2]},

    {[1, 2, 4, 3], [3, 2, 4, 1], [4, 2, 1, 3]}}

the member , {[1, 3, 4, 2], [2, 3, 1, 4], [4, 3, 1, 2]}, has a scheme of depth ,

    5

                                  here it is:

{[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}],

    [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {2}], [[3, 1, 2], {}, {}],

    [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}],

    [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {}],

    [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}], [[1, 2], {}, {}],

    [[2, 1, 3], {[0, 1, 0, 1]}, {}],

    [[2, 1, 4, 3], {[0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {1}],

    [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {3}],

    [[2, 3, 1], {[0, 0, 0, 1]}, {}], [[2, 1], {}, {}],

    [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}],

    [[3, 1, 4, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}],

    [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[4, 5, 2, 3, 1], %1, {1}], [[3, 1, 4, 2], {[0, 0, 0, 0, 1]}, {}],

    [[1, 2, 4, 3], {[0, 1, 0, 0, 0]}, {1}], [[1, 2, 3], {[0, 1, 0, 0]}, {}],

    [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[1, 3, 2, 4, 5], %2, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}],

    [[1, 3, 2, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [

    [2, 4, 3, 1],

    {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[1, 3, 2], {}, {}], [[2, 4, 3, 5, 1], %1, {1}],

    [[1, 4, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 1, 3, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {}],

    [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}],

    [[3, 2, 4, 5, 1], %1, {1}], [[2, 1, 3, 4, 5], %2, {3}],

    [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[4, 5, 1, 2, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {3}],

    [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}],

    [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {}],

    [[2, 3, 1, 4], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2, 4, 5], %2, {2}],

    [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {3}],

    [[4, 2, 3, 5, 1], %1, {1}], [[3, 1, 2, 5, 4],

    {[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {1}],

    [[3, 4, 1, 2], {[0, 0, 0, 0, 1]}, {}], [[3, 5, 1, 2, 4],

    {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}], [

    [3, 1, 5, 2, 4],

    {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {1}],

    [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}],

    [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {2}],

    [[4, 5, 1, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}],

    [[4, 2, 5, 3, 1], %1, {1}], [[4, 2, 3, 1],

    {[0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[3, 4, 1, 2, 5], {[0, 0, 0, 0, 0, 0]}, {1}]}

%1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}

%2 := {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 71, 219, 626, 1698, 4452, 11428]

For the equivalence class of patterns, {

    {[1, 2, 3, 4], [3, 2, 1, 4], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [4, 1, 2, 3], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [3, 2, 1, 4], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [4, 1, 2, 3], [4, 3, 2, 1]},

    {[1, 2, 4, 3], [2, 3, 4, 1], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 4, 3, 2], [3, 4, 2, 1]},

    {[1, 2, 3, 4], [1, 4, 3, 2], [4, 3, 1, 2]},

    {[2, 1, 3, 4], [2, 3, 4, 1], [4, 3, 2, 1]}}

the member , {[1, 2, 3, 4], [3, 2, 1, 4], [3, 4, 2, 1]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[3, 4, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[4, 1, 2, 3], %4, {1}], [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 3, 1], {[1, 0, 0, 0], [0, 3, 0, 0]}, {}],

    [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3, 4], {[0, 0, 3, 0, 0],

    [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1],

    [1, 0, 1, 0, 0]}, {}], [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}],

    [[1, 2], {}, {}], [[4, 2, 3, 5, 1], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0],

    [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0],

    [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {2}],

    [[3, 1, 2], {[0, 0, 2, 1]}, {}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}],

    [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 4, 3, 1], {[0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}],

    [[2, 1], {}, {}], [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1], {}, {}], [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 5, 2, 4, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 5, 2], %3, {1}],

    [[1, 4, 3, 2], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1]}, {2}],

    [[4, 2, 3, 1], {[0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}],

    [[2, 1, 3], {[0, 3, 0, 0]}, {}], [[3, 4, 1, 2], {[0, 0, 1, 1, 1],

    [0, 0, 0, 2, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {1}],

    [[1, 4, 2, 3], %4, {2}], [[2, 3, 1, 4], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0],

    [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [

    [2, 1, 5, 4, 3], {[0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 0, 0, 2, 1, 0], [1, 0, 1, 0, 1, 0], [1, 0, 0, 1, 1, 0]}, {3}],

    [[2, 4, 5, 1, 3], %2, {1}], [[3, 1, 2, 4],

    {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}],

    [[3, 1, 4, 2], {[0, 0, 1, 1, 1], [0, 0, 0, 2, 1], [1, 0, 0, 0, 0],

    [0, 1, 0, 0, 0], [0, 0, 2, 0, 0]}, {1}],

    [[2, 4, 1, 3], {[0, 3, 0, 0, 0], [0, 0, 0, 2, 1], [1, 0, 0, 0, 0]}, {}], [

    [2, 1, 4, 3],

    {[0, 3, 0, 0, 0], [0, 0, 0, 2, 1], [1, 0, 1, 0, 1], [1, 0, 0, 1, 1]}, {}],

    [[3, 2, 4, 1], {[0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0],

    [0, 3, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}],

    [[3, 4, 2, 5, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1, 5, 3, 4], {

    [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1],

    [1, 0, 1, 0, 0, 0]}, {3}], [[2, 5, 1, 3, 4], %1, {1}], [[1, 3, 4, 2],

    {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {2}],

    [[4, 1, 3, 2], {[0, 0, 2, 1, 0], [0, 0, 0, 0, 1]}, {1}],

    [[1, 2, 3], {[0, 0, 0, 1], [0, 3, 0, 0]}, {}], [[1, 2, 4, 3], %4, {3}], [

    [4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0],

    [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 3, 5, 1, 4], %1, {3}],

    [[1, 3, 2, 5, 4], {[0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {4}],

    [[1, 3, 2], {[0, 0, 2, 1]}, {}], [[2, 5, 1, 4, 3], {[1, 0, 0, 0, 0, 0],

    [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 1, 0]}, {2}], [

    [2, 4, 3, 5, 1], {[0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0],

    [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0],

    [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 2, 0, 0]}, {1}], [

    [1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0],

    [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[1, 4, 2, 5, 3], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}, {1}], [

    [4, 1, 2, 5, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 0, 0]}, {1}], [[3, 2, 4, 5, 1], {[1, 0, 0, 0, 0, 0],

    [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1]}, {1}], [[2, 1, 4, 5, 3], %2, {1}], [[2, 3, 4, 1], {

    [0, 0, 3, 0, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0],

    [1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [[2, 4, 1, 3, 5], {

    [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [1, 0, 0, 0, 0, 0],

    [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0],

    [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 0, 0, 2, 0, 0]}, {1}], [[2, 1, 3, 5, 4], {[0, 0, 3, 0, 0, 0],

    [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {4}], [

    [3, 5, 1, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 1, 1, 1, 0],

    [0, 0, 2, 0, 0, 0]}, {1}], [[3, 1, 4, 5, 2], %3, {1}], [[1, 3, 2, 4],

    {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 2, 0, 0]}, {}],

    [[3, 1, 5, 4, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 1, 1, 1, 0],

    [0, 0, 2, 0, 0, 0]}, {1}], [[3, 2, 5, 4, 1], {[1, 0, 0, 0, 0, 0],

    [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1]}, {2}], [[3, 4, 5, 1, 2], %3, {1}], [[2, 1, 4, 3, 5], {

    [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0],

    [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0],

    [1, 0, 0, 1, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}], [[2, 4, 1, 5, 3], %2, {1}],

    [[3, 1, 2, 5, 4], {[0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {4}],

    [[2, 3, 1, 5, 4], %1, {4}]}

%1 := {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 1, 0, 0, 0],

    [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 0, 0, 1]}

%2 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}

%3 := {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0],

    [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0]}

%4 := {[0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}

                 Using  the scheme, the first, , 11, terms are

                [1, 1, 2, 6, 21, 71, 204, 479, 951, 1687, 2764]

For the equivalence class of patterns, {

    {[1, 3, 4, 2], [2, 1, 3, 4], [2, 3, 4, 1]},

    {[3, 2, 1, 4], [3, 2, 4, 1], [4, 3, 1, 2]},

    {[3, 2, 1, 4], [3, 4, 2, 1], [4, 2, 1, 3]},

    {[1, 4, 3, 2], [3, 4, 2, 1], [4, 1, 3, 2]},

    {[1, 2, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1]},

    {[1, 4, 2, 3], [2, 1, 3, 4], [4, 1, 2, 3]},

    {[1, 2, 4, 3], [3, 1, 2, 4], [4, 1, 2, 3]},

    {[1, 4, 3, 2], [2, 4, 3, 1], [4, 3, 1, 2]}}

the member , {[1, 4, 3, 2], [3, 4, 2, 1], [4, 1, 3, 2]}, has a scheme of depth ,

    4

                                  here it is:

{[[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {1}], [[], {}, {}],

    [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}],

    [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}],

    [[2, 3, 1], {[1, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}], [[1, 2], {}, {}],

    [[2, 1, 3, 4], {}, {1}], [[1, 2, 3], {}, {}], [[2, 1], {}, {}],

    [[3, 2, 1], {}, {2}], [[1], {}, {}], [[1, 2, 3, 4], {}, {2}],

    [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}],

    [[3, 1, 2, 4], {[0, 1, 0, 0, 0]}, {2}],

    [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[1, 3, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[1, 2, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[1, 3, 2], {[0, 1, 0, 0]}, {3}], [[2, 3, 4, 1], {[1, 0, 0, 0, 0]}, {1}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 76, 275, 989, 3541, 12660, 45316]

For the equivalence class of patterns, {

    {[1, 4, 3, 2], [4, 1, 2, 3], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [2, 3, 4, 1], [3, 2, 1, 4]},

    {[2, 3, 4, 1], [3, 2, 1, 4], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [3, 2, 1, 4], [4, 1, 2, 3]},

    {[3, 2, 1, 4], [4, 1, 2, 3], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 4, 3, 2], [2, 3, 4, 1]},

    {[1, 2, 3, 4], [1, 4, 3, 2], [4, 1, 2, 3]},

    {[1, 4, 3, 2], [2, 3, 4, 1], [4, 3, 2, 1]}}

the member , {[1, 4, 3, 2], [4, 1, 2, 3], [4, 3, 2, 1]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1], {[3, 0, 0], [0, 3, 0]}, {}],

    [[3, 1, 2, 4], {[0, 1, 0, 2, 0], [0, 0, 0, 3, 0], [1, 1, 0, 1, 0],

    [2, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {}],

    [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}],

    [[1, 3, 2], {[0, 0, 2, 0], [0, 1, 0, 0], [3, 0, 0, 0]}, {1}],

    [[2, 1, 3], {[0, 2, 0, 0], [3, 0, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}],

    [[1], {}, {}],

    [[3, 1, 2], {[0, 2, 0, 0], [0, 0, 1, 0], [3, 0, 0, 0], [2, 1, 0, 0]}, {}],

    [[3, 1, 2, 4, 5], {[0, 1, 0, 2, 0, 0], [0, 0, 0, 3, 0, 0],

    [1, 1, 0, 1, 0, 0], [2, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 2, 0], [0, 1, 0, 0, 2, 0], [0, 1, 0, 1, 1, 0],

    [0, 0, 0, 2, 1, 0], [1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0],

    [3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0]}, {4}], [[4, 1, 3, 2],

    {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[4, 2, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0],

    [0, 1, 1, 0, 0], [0, 0, 2, 0, 0]}, {1}], [[3, 1, 4, 2],

    {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [3, 0, 0, 0, 0]}, {1}],

    [[2, 1, 4, 3],

    {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0], [3, 0, 0, 0, 0]}, {1}],

    [[3, 2, 4, 1], {[1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 0, 2, 0, 0],

    [0, 0, 1, 1, 0], [0, 0, 0, 2, 0]}, {1}], [[4, 2, 3, 5, 1], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 2, 0, 0, 0, 0],

    [0, 1, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0],

    [0, 0, 0, 0, 2, 0]}, {2}], [[4, 1, 3, 5, 2], {[1, 0, 0, 0, 0, 0],

    [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 0, 2, 0]}, {2}], [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {2}], [

    [3, 1, 2, 5, 4], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {2}],

    [[2, 3, 1], {[0, 0, 2, 0], [3, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0]}, {1}],

    [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}],

    [[3, 2, 1], {[0, 2, 0, 0], [1, 0, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}],

    [[2, 1, 3, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0],

    [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0],

    [0, 2, 0, 0, 0], [3, 0, 0, 0, 0]}, {3}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 232, 717, 2157, 6370, 18557]

For the equivalence class of patterns, {

    {[2, 1, 3, 4], [2, 3, 1, 4], [3, 4, 2, 1]},

    {[1, 2, 4, 3], [4, 1, 3, 2], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [1, 4, 2, 3], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [1, 3, 4, 2], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [4, 2, 1, 3], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [2, 4, 3, 1], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [3, 2, 4, 1], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [3, 1, 2, 4], [4, 3, 1, 2]}}

the member , {[1, 2, 4, 3], [4, 1, 3, 2], [4, 3, 1, 2]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[4, 1, 2, 3], %1, {2}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}],

    [[4, 1, 3, 2], {[0, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {[0, 1, 0, 0]}, {}],

    [[2, 1, 3], {}, {}], [[1, 2], {}, {}],

    [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}],

    [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}],

    [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}],

    [[1, 4, 2, 3], {[0, 0, 1, 0, 0]}, {1}], [[1, 3, 2], {}, {}],

    [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {2}], [[2, 4, 3, 1], %1, {2}],

    [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {1}], [[2, 4, 1, 3], %1, {1}],

    [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}],

    [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}],

    [[4, 2, 3, 1], %1, {1}], [[2, 1, 4, 3], {[0, 2, 0, 0, 0]}, {1}],

    [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}]}

%1 := {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 75, 255, 813, 2443, 6985, 19175]

For the equivalence class of patterns, {

    {[3, 4, 2, 1], [4, 2, 3, 1], [4, 3, 2, 1]},

    {[4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4]},

    {[1, 2, 3, 4], [1, 3, 2, 4], [2, 1, 3, 4]}}

the member , {[3, 4, 2, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth ,

    3

                                  here it is:

{[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1], {}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}],

    [[2, 3, 1], {[1, 0, 0, 0]}, {3}], [[2, 1, 3], {}, {2}],

    [[1, 3, 2], {}, {1}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}]}

                 Using  the scheme, the first, , 21, terms are

[1, 1, 2, 6, 21, 80, 322, 1346, 5783, 25372, 113174, 511649, 2338988, 10793251,

    50205607, 235156609, 1108120540, 5249646137, 24987770893, 119443412277,

    573125649031]

For the equivalence class of patterns, {

    {[2, 1, 3, 4], [3, 2, 1, 4], [4, 1, 2, 3]},

    {[3, 2, 1, 4], [4, 1, 2, 3], [4, 3, 1, 2]},

    {[2, 1, 3, 4], [2, 3, 4, 1], [3, 2, 1, 4]},

    {[1, 4, 3, 2], [4, 1, 2, 3], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [4, 1, 2, 3]},

    {[2, 3, 4, 1], [3, 2, 1, 4], [3, 4, 2, 1]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [2, 3, 4, 1]},

    {[1, 4, 3, 2], [2, 3, 4, 1], [3, 4, 2, 1]}}

the member , {[2, 1, 3, 4], [2, 3, 4, 1], [3, 2, 1, 4]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[1, 2], {}, {}],

    [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {2}],

    [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 1], {}, {}], [[1], {}, {}],

    [[3, 1, 2], {[1, 0, 0, 1]}, {}], [[2, 3, 1], {[1, 0, 0, 1]}, {}],

    [[1, 2, 3], {[1, 0, 0, 0]}, {1}],

    [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}],

    [[4, 2, 3, 1], %1, {1}], [[2, 1, 3], {[0, 0, 0, 1]}, {3}], [

    [3, 5, 1, 2, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {2}], [

    [4, 5, 1, 3, 2],

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}],

    [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {1}], [[3, 4, 1, 2, 5],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 0, 0]}, {2}],

    [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {1}],

    [[1, 3, 2], {[1, 0, 0, 1]}, {}], [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0],

    [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1]}, {3}],

    [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [1, 0, 0, 0, 1], [0, 1, 0, 0, 1]}, {}], [

    [4, 5, 2, 3, 1],

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0]}, {1}],

    [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}],

    [[1, 4, 3, 2], %1, {2}], [[4, 1, 3, 2], %1, {1}],

    [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 1]}, {2}],

    [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1]}, {2}],

    [[2, 4, 3, 1], %1, {2}]}

%1 := {[0, 0, 0, 0, 1], [1, 0, 0, 1, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 256, 876, 2987, 10182, 34726]

For the equivalence class of patterns, {

    {[1, 4, 2, 3], [3, 2, 1, 4], [4, 1, 3, 2]},

    {[2, 3, 1, 4], [3, 2, 4, 1], [4, 1, 2, 3]},

    {[1, 4, 2, 3], [2, 3, 4, 1], [4, 1, 3, 2]},

    {[1, 3, 4, 2], [2, 4, 3, 1], [3, 2, 1, 4]},

    {[1, 3, 4, 2], [2, 4, 3, 1], [4, 1, 2, 3]},

    {[1, 4, 3, 2], [3, 1, 2, 4], [4, 2, 1, 3]},

    {[1, 4, 3, 2], [2, 3, 1, 4], [3, 2, 4, 1]},

    {[2, 3, 4, 1], [3, 1, 2, 4], [4, 2, 1, 3]}}

the member , {[1, 3, 4, 2], [2, 4, 3, 1], [3, 2, 1, 4]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}],

    [[3, 2, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {1}],

    [[1, 2, 3], {[0, 1, 0, 0]}, {1}],

    [[1, 4, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {2}],

    [[2, 4, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}],

    [[3, 1, 2], {[0, 1, 0, 1]}, {}],

    [[4, 2, 5, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 2, 1], {[0, 0, 0, 1]}, {1}], [[2, 3, 1], {[1, 0, 1, 0]}, {}],

    [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], %1, {3}],

    [[3, 4, 2, 1], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}],

    [[1, 3, 2], {[0, 1, 0, 1], [1, 0, 0, 0]}, {}],

    [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {3}],

    [[1, 3, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[4, 1, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}, {2}],

    [[2, 3, 1, 4], {[1, 1, 0, 0, 1], [0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {1}],

    [[3, 1, 2, 4], {[1, 0, 1, 0, 1], [0, 1, 0, 0, 0], [1, 0, 0, 1, 0]}, {2}],

    [[2, 1, 4, 3], %1, {1}], [[3, 1, 4, 2, 5], {[1, 0, 0, 0, 0, 0],

    [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [

    [4, 5, 2, 3, 1],

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 1, 0, 0, 0]}, {1}], [

    [3, 1, 5, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {1}], [[4, 1, 5, 3, 2], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 1, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [1, 0, 1, 0, 0]}, {1}], [[4, 5, 1, 3, 2],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 1, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 1, 0, 0, 1],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0]}, {1}],

    [[3, 4, 1, 2], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}], [

    [4, 5, 1, 2, 3], {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0],

    [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {3}], [[3, 5, 1, 2, 4], {

    [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 1, 0, 1]}, {3}], [[2, 1, 3], {[1, 0, 1, 0], [1, 1, 0, 1]}, {}],

    [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]}, {}],

    [[2, 4, 1, 3], %1, {3}], [[4, 1, 5, 2, 3], {[1, 0, 0, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 1, 0, 0, 1]}, {4}],

    [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 1, 0, 1, 0]}, {1}]}

%1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 72, 232, 712, 2116, 6155, 17629]

For the equivalence class of patterns, {

    {[1, 3, 4, 2], [2, 1, 4, 3], [4, 2, 3, 1]},

    {[2, 1, 4, 3], [3, 1, 2, 4], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [2, 4, 3, 1], [3, 4, 1, 2]},

    {[2, 1, 4, 3], [2, 3, 1, 4], [4, 2, 3, 1]},

    {[1, 4, 2, 3], [2, 1, 4, 3], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [3, 4, 1, 2], [4, 1, 3, 2]},

    {[1, 3, 2, 4], [3, 4, 1, 2], [4, 2, 1, 3]},

    {[1, 3, 2, 4], [3, 2, 4, 1], [3, 4, 1, 2]}}

the member , {[1, 4, 2, 3], [2, 1, 4, 3], [4, 2, 3, 1]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[4, 3, 2, 1], {}, {2}],

    [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}], [[1, 2], {}, {}],

    [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {}, {}], [

    [5, 1, 3, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}],

    [[1], {}, {}],

    [[5, 4, 1, 3, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {2}], [

    [3, 5, 1, 2, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[2, 3, 1], {[0, 0, 2, 0]}, {}], [[4, 3, 1, 2], {[1, 0, 0, 0, 0]}, {}],

    [[3, 2, 4, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {3}],

    [[1, 4, 2, 3], {[0, 0, 0, 0, 0]}, {1}],

    [[3, 1, 4, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[1, 2, 3], {}, {2}], [[5, 1, 4, 3, 2],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {3}],

    [[3, 4, 2, 1], {[0, 0, 0, 2, 0]}, {1}], [[1, 3, 2], {[0, 0, 1, 0]}, {}],

    [[1, 3, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}],

    [[5, 1, 4, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 1, 2], {[1, 0, 0, 0]}, {}],

    [[5, 4, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}], [[5, 3, 1, 2, 4], {

    [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0, 0]}, {1}], [[3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}],

    [[5, 4, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}], [

    [4, 3, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3],

    {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {3}],

    [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 0, 0, 2, 0]}, {}],

    [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}],

    [[3, 2, 1, 4], %1, {1}], [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [

    [4, 5, 1, 3, 2],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 2, 0]}, {1}],

    [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 1, 0, 0]}, {3}],

    [[2, 4, 3, 1], {[0, 0, 0, 1, 0], [0, 0, 2, 0, 0]}, {2}], [[4, 1, 3, 2, 5],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0]}, {1}],

    [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}],

    [[2, 1, 3], {[0, 0, 1, 0], [1, 2, 0, 0]}, {}], [[2, 3, 1, 4], %1, {1}],

    [[2, 1, 3, 4], %1, {3}], [[5, 2, 4, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}]}

%1 := {[1, 2, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 239, 740, 2194, 6298, 17653]

For the equivalence class of patterns, {

    {[3, 2, 1, 4], [4, 1, 2, 3], [4, 1, 3, 2]},

    {[1, 4, 3, 2], [4, 1, 2, 3], [4, 2, 1, 3]},

    {[2, 3, 1, 4], [3, 2, 1, 4], [4, 1, 2, 3]},

    {[2, 3, 4, 1], [3, 1, 2, 4], [3, 2, 1, 4]},

    {[1, 3, 4, 2], [1, 4, 3, 2], [4, 1, 2, 3]},

    {[1, 4, 2, 3], [1, 4, 3, 2], [2, 3, 4, 1]},

    {[2, 3, 4, 1], [2, 4, 3, 1], [3, 2, 1, 4]},

    {[1, 4, 3, 2], [2, 3, 4, 1], [3, 2, 4, 1]}}

the member , {[1, 4, 3, 2], [4, 1, 2, 3], [4, 2, 1, 3]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[1, 2], {[0, 3, 0]}, {}], [[2, 1], {[0, 3, 0]}, {}],

    [[2, 1, 3], {[0, 2, 0, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {}], [[1], {}, {}],

    [[2, 1, 3, 4], {[0, 1, 0, 2, 0], [0, 0, 1, 2, 0], [0, 0, 0, 3, 0],

    [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 1, 2, 0, 0],

    [0, 2, 0, 0, 0]}, {3}], [[3, 2, 1], {[0, 0, 1, 0], [0, 3, 0, 0]}, {1}],

    [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}], [

    [3, 2, 4, 1],

    {[0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}],

    [[3, 1, 4, 2], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}],

    [[1, 2, 3], {[0, 3, 0, 0], [0, 2, 1, 0], [0, 1, 2, 0], [0, 0, 3, 0]}, {2}],

    [[2, 3, 1], {[0, 0, 2, 0], [0, 3, 0, 0], [0, 2, 1, 0]}, {1}],

    [[3, 1, 2], {[0, 2, 0, 0], [0, 0, 1, 0]}, {3}],

    [[1, 3, 2], {[0, 0, 2, 0], [0, 1, 0, 0]}, {1}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 260, 913, 3206, 11258, 39533]

For the equivalence class of patterns, {

    {[1, 2, 3, 4], [3, 1, 4, 2], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [2, 4, 1, 3], [4, 3, 2, 1]}}

the member , {[1, 2, 3, 4], [3, 1, 4, 2], [4, 3, 2, 1]}, has a scheme of depth ,

    5

                                  here it is:

{[[4, 1, 3, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[], {}, {}], [[3, 4, 5, 2, 1],

    {[0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0],

    [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 0], [0, 0, 1, 1, 1, 0],

    [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {3}],

    [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 3, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}],

    [[2, 3, 4, 1], {[0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 1]}, {}], [

    [3, 1, 2, 4],

    {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}],

    [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}],

    [[3, 1, 2, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}],

    [[2, 3, 4, 1, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}],

    [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 3, 2], {[0, 0, 1, 1], [0, 3, 0, 0], [0, 0, 3, 0]}, {}],

    [[3, 1, 4, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 4, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 4, 5, 1, 2], {

    [0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0], [0, 2, 0, 1, 0, 0],

    [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0],

    [0, 0, 0, 0, 3, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0],

    [0, 0, 0, 1, 1, 0]}, {2}], [[3, 4, 2, 1], {[0, 1, 1, 1, 0], [0, 2, 0, 1, 0],

    [0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 1, 0, 1, 1], [0, 0, 1, 1, 1],

    [0, 1, 1, 0, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0]}, {}], [[3, 4, 2, 5, 1],

    {[1, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0],

    [0, 0, 0, 0, 3, 0]}, {4}], [[1, 3, 2, 4],

    {[0, 0, 0, 3, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}],

    [[3, 2, 1],

    {[1, 0, 0, 0], [0, 3, 0, 0], [0, 2, 1, 0], [0, 2, 0, 1], [0, 1, 1, 1]}, {}]

    , [[3, 1, 2], {[0, 0, 1, 1], [0, 3, 0, 0], [0, 0, 3, 0], [0, 2, 0, 1]}, {}],

    [[1, 2, 3], {[0, 0, 0, 1], [0, 0, 3, 0]}, {}], [[2, 4, 1, 3], {

    [0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 0, 2, 0, 1], [0, 1, 0, 0, 0],

    [0, 0, 0, 1, 1]}, {1}], [[4, 2, 3, 5, 1], {[1, 0, 0, 0, 0, 0],

    [0, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}],

    [[4, 1, 2, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], {

    [0, 0, 0, 3, 0], [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0],

    [0, 2, 0, 1, 0], [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0],

    [0, 1, 1, 0, 1], [0, 0, 2, 0, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0],

    [0, 0, 0, 1, 1]}, {}],

    [[2, 1, 3, 4], {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1]}, {}], [

    [3, 2, 4, 1], {[0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 1, 0, 1, 1],

    [0, 2, 0, 0, 1], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}],

    [[2, 1, 3], {[0, 1, 0, 0]}, {}], [[2, 3, 1, 4],

    {[0, 0, 0, 3, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}],

    [[2, 4, 3, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0],

    [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 1, 2, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 1, 0, 1, 0],

    [0, 0, 2, 0, 1, 0], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}], [

    [1, 3, 2, 5, 4], {[0, 2, 0, 1, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 0, 0, 2, 0, 0]}, {1}],

    [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[1, 2, 4, 3], %3, {1}], [[2, 1, 4, 5, 3], {[0, 0, 0, 3, 0, 0],

    [0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0]}, {1}], [[3, 5, 1, 2, 4], %1, {1}],

    [[1, 3, 4, 2], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 3, 0, 0, 0],

    [0, 0, 0, 0, 1], [0, 0, 1, 1, 0]}, {2}], [[2, 3, 1], {[0, 1, 1, 1]}, {}],

    [[1, 4, 3, 2], %4, {2}], [[3, 2, 5, 1, 4], {[0, 0, 0, 2, 0, 1],

    [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 1, 1]}, {1}],

    [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 4, 1, 5, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 5, 1, 4], %1, {1}],

    [[3, 4, 2, 1, 5], %2, {3}], [[1, 4, 2, 3], %3, {1}],

    [[3, 1, 2, 5, 4], %1, {1}], [[3, 4, 1, 2], {[0, 0, 0, 3, 0],

    [0, 0, 3, 0, 0], [0, 2, 0, 1, 0], [0, 3, 0, 0, 0], [0, 2, 0, 0, 1],

    [0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}, {}], [[5, 2, 3, 1, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}],

    [[4, 2, 3, 1, 5], %2, {1}], [[3, 4, 1, 2, 5], {[0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 0, 3, 0]}, {1}], [[4, 5, 2, 1, 3], {[0, 0, 2, 0, 0, 1],

    [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0], [0, 0, 0, 0, 3, 0],

    [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {2}], [

    [5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0],

    [0, 0, 0, 2, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0],

    [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [

    [4, 5, 2, 3, 1], {[0, 2, 0, 0, 0, 1], [0, 1, 1, 0, 0, 1],

    [0, 0, 2, 0, 0, 1], [0, 1, 1, 1, 0, 0], [0, 0, 2, 1, 0, 0],

    [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0],

    [0, 2, 0, 1, 0, 0], [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0],

    [0, 1, 2, 0, 0, 0], [0, 1, 1, 0, 1, 0], [0, 0, 2, 0, 1, 0],

    [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0],

    [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[4, 3, 1, 2], %4, {1}], [

    [2, 5, 4, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 2, 0, 0],

    [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}],

    [[4, 1, 3, 2], %4, {1}], [[4, 2, 5, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [

    [4, 2, 1, 3], {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 0, 2, 0, 1],

    [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {2}], [[3, 5, 4, 1, 2],

    {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0],

    [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 2, 0, 0],

    [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1],

    [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}],

    [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 5, 1, 2, 3], {

    [0, 2, 1, 0, 0, 0], [0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 2, 0, 0, 0]}, {1}], [

    [2, 1, 3, 5, 4], {[0, 0, 2, 1, 0, 0], [0, 0, 3, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 2, 0, 0]}, {1}], [[3, 5, 2, 1, 4], {[0, 0, 0, 2, 0, 1],

    [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 0, 0, 1, 1]}, {1}], [

    [4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0],

    [0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1]}, {1}],

    [[4, 1, 2, 3], %3, {2}], [[3, 2, 4, 1, 5], %2, {1}], [[4, 5, 3, 1, 2], {

    [0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0],

    [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1],

    [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 4, 3, 1, 5], %2, {2}],

    [[2, 4, 5, 1, 3], {[0, 0, 0, 3, 0, 0], [0, 0, 3, 0, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 1, 0],

    [0, 0, 0, 0, 3, 0], [0, 0, 0, 1, 1, 0]}, {1}],

    [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 5, 3, 1, 4], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}, {1}],

    [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[5, 2, 4, 1, 3], {

    [1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0],

    [0, 0, 0, 0, 3, 0], [0, 0, 0, 2, 0, 0], [0, 0, 0, 1, 1, 0],

    [0, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1]}, {1}], [[2, 3, 1, 5, 4], %1, {1}],

    [[1, 4, 3, 5, 2], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0],

    [0, 0, 2, 0, 0, 0], [0, 0, 1, 0, 1, 0]}, {2}],

    [[3, 1, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1], {[0, 0, 0, 3, 0],

    [0, 1, 1, 1, 0], [0, 0, 2, 1, 0], [0, 0, 3, 0, 0], [0, 2, 0, 1, 0],

    [0, 2, 1, 0, 0], [0, 1, 2, 0, 0], [0, 3, 0, 0, 0], [0, 1, 1, 0, 1],

    [0, 0, 2, 0, 1], [0, 2, 0, 0, 1], [1, 0, 0, 0, 0], [0, 0, 0, 1, 1]}, {}], [

    [2, 1, 4, 3],

    {[0, 0, 0, 3, 0], [0, 0, 3, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1]}, {1}],

    [[3, 2, 4, 5, 1], {[1, 0, 0, 0, 0, 0], [0, 2, 0, 1, 0, 0],

    [0, 3, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 1, 1, 0], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 3, 0]}, {4}], [

    [4, 5, 1, 3, 2], {[0, 0, 0, 3, 0, 0], [1, 0, 0, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0], [0, 0, 2, 0, 0, 0],

    [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 0],

    [0, 0, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 1]}, {1}]}

%1 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0]}

%2 := {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0]}

%3 := {[0, 2, 1, 0, 0], [0, 3, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0],

    [0, 0, 2, 0, 0]}

%4 := {[0, 0, 0, 3, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0],

    [0, 0, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 1]}

                 Using  the scheme, the first, , 11, terms are

                   [1, 1, 2, 6, 21, 69, 164, 252, 221, 85, 0]

For the equivalence class of patterns, {

    {[2, 4, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]},

    {[2, 4, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]},

    {[3, 1, 4, 2], [3, 4, 1, 2], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [2, 1, 4, 3], [3, 1, 4, 2]},

    {[1, 2, 4, 3], [2, 1, 4, 3], [2, 4, 1, 3]},

    {[2, 1, 3, 4], [2, 1, 4, 3], [2, 4, 1, 3]},

    {[3, 1, 4, 2], [3, 4, 1, 2], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [2, 1, 4, 3], [3, 1, 4, 2]}}

the member , {[2, 4, 1, 3], [3, 4, 1, 2], [4, 3, 1, 2]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}],

    [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}],

    [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {2}],

    [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[3, 1, 2], {}, {2}], [[1, 4, 2, 3], {}, {3}],

    [[2, 3, 1], {[0, 1, 0, 0], [0, 0, 1, 0]}, {1}], [[1, 3, 2, 4], {}, {1}]}

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 79, 310, 1251, 5151, 21536, 91137]

For the equivalence class of patterns, {

    {[1, 2, 4, 3], [4, 1, 2, 3], [4, 3, 1, 2]},

    {[2, 1, 3, 4], [4, 1, 2, 3], [4, 3, 1, 2]},

    {[2, 1, 3, 4], [3, 2, 1, 4], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [2, 3, 4, 1], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [3, 2, 1, 4], [3, 4, 2, 1]},

    {[1, 2, 4, 3], [2, 3, 4, 1], [3, 4, 2, 1]}}

the member , {[1, 2, 4, 3], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[2, 1, 3], {}, {}],

    [[1, 3, 2], {[0, 0, 2, 0]}, {}], [[1, 2], {}, {}],

    [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 2], {[0, 0, 1, 0]}, {}],

    [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}],

    [[1, 4, 2, 3], %1, {1}], [[2, 1], {}, {}], [[1], {}, {}],

    [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {1}],

    [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}],

    [[3, 4, 1, 2], %1, {1}], [[4, 1, 3, 2], %1, {1}],

    [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[3, 1, 2, 4], %1, {2}],

    [[3, 1, 4, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {1}],

    [[2, 1, 4, 3], {[0, 0, 0, 2, 0]}, {1}], [[1, 2, 3], {[0, 0, 1, 0]}, {2}],

    [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 2, 0]}, {2}],

    [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}], [[1, 3, 2, 4], %1, {1}],

    [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}],

    [[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {1}]}

%1 := {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 246, 763, 2227, 6191, 16567]

For the equivalence class of patterns, {

    {[2, 4, 1, 3], [4, 3, 1, 2], [4, 3, 2, 1]},

    {[3, 1, 4, 2], [3, 4, 2, 1], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 2, 4, 3], [2, 4, 1, 3]},

    {[1, 2, 3, 4], [1, 2, 4, 3], [3, 1, 4, 2]},

    {[1, 2, 3, 4], [2, 1, 3, 4], [2, 4, 1, 3]},

    {[1, 2, 3, 4], [2, 1, 3, 4], [3, 1, 4, 2]},

    {[3, 1, 4, 2], [4, 3, 1, 2], [4, 3, 2, 1]},

    {[2, 4, 1, 3], [3, 4, 2, 1], [4, 3, 2, 1]}}

the member , {[3, 1, 4, 2], [3, 4, 2, 1], [4, 3, 2, 1]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[1, 2, 3], {}, {1}], [[3, 1, 2], {}, {}],

    [[2, 3, 1], {[1, 0, 0, 0]}, {}], [[3, 2, 1], {[1, 0, 0, 0]}, {}],

    [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}],

    [[3, 4, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}],

    [[3, 4, 1, 2], %1, {3}], [[2, 1], {}, {}], [[1], {}, {}],

    [[4, 1, 3, 2], %1, {2}], [[4, 3, 1, 2], %1, {3}], [[1, 3, 2], {}, {1}],

    [[2, 1, 3], {[0, 1, 0, 0]}, {1}], [[4, 2, 1, 3], %1, {2}],

    [[2, 4, 1, 3], %1, {1}],

    [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[4, 1, 2, 3], {}, {3}],

    [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {2}]}

%1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 75, 265, 925, 3201, 11017, 37793]

For the equivalence class of patterns, {

    {[1, 3, 4, 2], [2, 1, 4, 3], [2, 3, 1, 4]},

    {[1, 4, 2, 3], [2, 1, 4, 3], [3, 1, 2, 4]},

    {[3, 2, 4, 1], [3, 4, 1, 2], [4, 2, 1, 3]},

    {[2, 4, 3, 1], [3, 4, 1, 2], [4, 1, 3, 2]}}

the member , {[1, 3, 4, 2], [2, 1, 4, 3], [2, 3, 1, 4]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {}, {1}], [[1, 2], {}, {}],

    [[2, 1, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}], [

    [1, 2, 4, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[1, 5, 2, 4, 3], {[0, 1, 0, 0, 0, 0]}, {2}],

    [[2, 1, 4, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 1], {}, {}],

    [[1, 3, 4, 2], {[0, 0, 0, 0, 0]}, {1}], [[1], {}, {}],

    [[1, 2, 3, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[1, 2, 3], {[0, 1, 0, 0]}, {}],

    [[2, 3, 4, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[2, 3, 5, 4, 1], %2, {1}], [[1, 3, 2], {}, {}],

    [[1, 2, 5, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[5, 1, 2, 4, 3], {[0, 1, 0, 0, 0, 0]}, {1}], [[4, 2, 3, 1], %1, {1}],

    [[1, 3, 5, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[1, 4, 2, 3, 5], {

    [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0, 0]}, {1}], [[1, 5, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 5, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}],

    [[2, 5, 3, 4, 1], %2, {1}], [[3, 1, 4, 2], %1, {1}],

    [[4, 1, 2, 3], {[0, 1, 0, 0, 0]}, {}],

    [[5, 1, 3, 4, 2], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[2, 1, 3], {[0, 1, 0, 1], [0, 0, 1, 0]}, {}], [[3, 2, 4, 1], %1, {1}],

    [[1, 4, 2, 3], {[0, 1, 0, 0, 0]}, {}],

    [[1, 2, 4, 3], {[0, 1, 0, 0, 0]}, {}], [[5, 2, 3, 4, 1], %2, {1}],

    [[4, 1, 3, 2], {}, {1}], [[1, 2, 5, 4, 3], {[0, 1, 0, 0, 0, 0]}, {3}],

    [[3, 1, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 1]}, {4}], [

    [4, 1, 2, 3, 5], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1]}, {2}], [[1, 4, 3, 2], {}, {2}],

    [[2, 3, 1], {[0, 0, 0, 1]}, {2}], [[2, 4, 3, 1], %1, {2}],

    [[5, 1, 2, 3, 4], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {2}]}

%1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}

%2 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 74, 255, 863, 2891, 9638, 32068]

For the equivalence class of patterns, {

    {[1, 4, 3, 2], [2, 4, 3, 1], [4, 1, 3, 2]},

    {[1, 3, 4, 2], [2, 3, 1, 4], [2, 3, 4, 1]},

    {[1, 4, 2, 3], [3, 1, 2, 4], [4, 1, 2, 3]},

    {[3, 2, 1, 4], [3, 2, 4, 1], [4, 2, 1, 3]}}

the member , {[1, 4, 3, 2], [2, 4, 3, 1], [4, 1, 3, 2]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[3, 4, 2, 1], {}, {3}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}],

    [[2, 1], {}, {}], [[3, 2, 1], {}, {2}], [[1], {}, {}],

    [[3, 4, 1, 2], {[0, 1, 0, 0, 0]}, {3}], [[3, 1, 2], {[0, 1, 0, 0]}, {2}],

    [[1, 2, 3], {}, {2}], [[2, 1, 3], {}, {1}],

    [[1, 3, 2], {[1, 0, 0, 0], [0, 1, 0, 0]}, {1}], [[2, 3, 1, 4], {}, {1}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}]}

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 79, 309, 1237, 5026, 20626, 85242]

For the equivalence class of patterns, {

    {[1, 4, 2, 3], [2, 4, 3, 1], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [3, 1, 2, 4], [4, 1, 3, 2]},

    {[3, 1, 2, 4], [3, 2, 4, 1], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [2, 3, 1, 4], [2, 4, 3, 1]},

    {[1, 3, 2, 4], [1, 4, 2, 3], [4, 2, 1, 3]},

    {[2, 3, 1, 4], [4, 2, 1, 3], [4, 2, 3, 1]},

    {[1, 3, 4, 2], [4, 1, 3, 2], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [1, 3, 4, 2], [3, 2, 4, 1]}}

the member , {[1, 3, 2, 4], [1, 4, 2, 3], [4, 2, 1, 3]}, has a scheme of depth ,

    5

                                  here it is:

{[[3, 2, 1], {[0, 0, 1, 0]}, {1}], [[], {}, {}], [[3, 1, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[1, 2], {}, {}], [[4, 5, 1, 2, 3], {}, {4}],

    [[2, 1, 3, 4], {}, {3}],

    [[2, 1, 4, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {3}],

    [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}],

    [[3, 2, 4, 1], {[0, 0, 1, 0, 0]}, {1}], [[4, 5, 2, 3, 1],

    {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}],

    [[1, 2, 3], {}, {2}],

    [[4, 2, 3, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[3, 1, 2, 4], {}, {3}],

    [[2, 4, 1, 3], {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}, {1}],

    [[1, 3, 2], {[0, 0, 1, 0], [0, 0, 0, 1]}, {2}],

    [[4, 1, 3, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}],

    [[3, 1, 4, 2], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}],

    [[3, 4, 1, 2, 5], {}, {1}], [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0],

    [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}, {1}],

    [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {1}],

    [[4, 1, 2, 3], {}, {3}], [[3, 4, 1, 2], {}, {}], [[2, 3, 1, 4], {}, {1}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 76, 271, 938, 3146, 10252, 32583]

For the equivalence class of patterns, {

    {[2, 3, 4, 1], [4, 2, 3, 1], [4, 3, 2, 1]},

    {[4, 1, 2, 3], [4, 2, 3, 1], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 3, 2, 4], [1, 4, 3, 2]},

    {[1, 2, 3, 4], [1, 3, 2, 4], [3, 2, 1, 4]}}

the member , {[2, 3, 4, 1], [4, 2, 3, 1], [4, 3, 2, 1]}, has a scheme of depth ,

    4

                                  here it is:

{[[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}],

    [[1, 2], {}, {}], [[2, 3, 1, 4], %1, {1}], [[2, 1, 3, 4], %1, {1}],

    [[2, 3, 1], {}, {}], [[2, 1], {}, {}], [[1], {}, {}],

    [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[3, 2, 1], {[1, 0, 0, 0]}, {3}],

    [[1, 4, 3, 2], %1, {1}], [[1, 3, 2], {}, {}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0]}, {3}],

    [[2, 4, 3, 1], {[1, 0, 0, 0, 0]}, {4}], [[3, 1, 2], {[1, 0, 0, 0]}, {2}],

    [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {4}],

    [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {4}], [[2, 1, 4, 3], {}, {2}],

    [[3, 4, 1, 2], {[1, 0, 0, 0, 0]}, {3}], [[1, 4, 2, 3], %1, {1}],

    [[3, 1, 4, 2], {[1, 0, 0, 0, 0]}, {2}]}

%1 := {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 76, 278, 1019, 3734, 13678, 50100]

For the equivalence class of patterns, {

    {[2, 3, 1, 4], [2, 4, 3, 1], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [1, 4, 2, 3], [2, 4, 3, 1]},

    {[3, 1, 2, 4], [4, 1, 3, 2], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [3, 1, 2, 4], [3, 2, 4, 1]},

    {[1, 4, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [1, 3, 4, 2], [4, 1, 3, 2]},

    {[1, 3, 4, 2], [3, 2, 4, 1], [4, 2, 3, 1]},

    {[1, 3, 2, 4], [2, 3, 1, 4], [4, 2, 1, 3]}}

the member , {[1, 4, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[3, 4, 1, 2, 5],

    {[1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0]}, {1}],

    [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [

    [3, 5, 1, 2, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}], [

    [4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0],

    [0, 0, 1, 1, 0, 0], [0, 0, 1, 0, 1, 0]}, {3}], [[1, 2], {}, {}],

    [[2, 1], {[1, 1, 0]}, {}], [[1], {}, {}],

    [[3, 4, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 1, 0]}, {}],

    [[1, 2, 3], {}, {2}], [[4, 5, 1, 3, 2], {[1, 0, 0, 0, 0, 0],

    [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[0, 0, 0, 0, 0]}, {1}],

    [[4, 5, 2, 3, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 2, 1], {[1, 1, 0, 0], [0, 0, 1, 0]}, {1}],

    [[3, 1, 2], {[0, 1, 1, 0], [1, 0, 0, 0]}, {}],

    [[1, 3, 2], {[0, 0, 1, 0]}, {2}],

    [[2, 3, 1, 4], {[1, 1, 0, 0, 0], [1, 0, 1, 0, 0]}, {1}],

    [[3, 4, 2, 1], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0]}, {1}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[2, 3, 1], {[1, 1, 0, 0], [1, 0, 1, 0]}, {}],

    [[4, 1, 2, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 0]}, {2}],

    [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 1, 1, 0, 0]}, {1}],

    [[2, 1, 3], {[1, 1, 0, 0]}, {1}]}

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 77, 287, 1079, 4082, 15522, 59280]

For the equivalence class of patterns, {

    {[1, 4, 2, 3], [3, 2, 4, 1], [4, 3, 1, 2]},

    {[1, 3, 4, 2], [2, 1, 3, 4], [4, 2, 1, 3]},

    {[2, 4, 3, 1], [3, 1, 2, 4], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [2, 3, 1, 4], [4, 1, 3, 2]},

    {[1, 4, 2, 3], [2, 1, 3, 4], [3, 2, 4, 1]},

    {[2, 3, 1, 4], [3, 4, 2, 1], [4, 1, 3, 2]},

    {[1, 3, 4, 2], [3, 4, 2, 1], [4, 2, 1, 3]},

    {[1, 2, 4, 3], [2, 4, 3, 1], [3, 1, 2, 4]}}

the member , {[1, 4, 2, 3], [3, 2, 4, 1], [4, 3, 1, 2]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[3, 4, 1, 2], {}, {3}], [[1, 2], {}, {}], [[2, 3, 1], {}, {}],

    [[2, 1], {}, {}], [[1], {}, {}], [[1, 2, 3], {}, {2}],

    [[2, 1, 3], {[1, 0, 0, 0]}, {1}],

    [[4, 2, 1, 3], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {2}],

    [[3, 2, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[3, 1, 2], {}, {2}], [[1, 3, 2], {[0, 0, 1, 0]}, {1}],

    [[4, 3, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}],

    [[2, 4, 1, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[4, 3, 1, 2], {[0, 0, 0, 0, 0]}, {1}],

    [[2, 3, 1, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 2, 1], {[0, 1, 0, 0]}, {}],

    [[4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}],

    [[4, 5, 3, 2, 1], {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {3}],

    [[4, 5, 3, 1, 2], {[0, 0, 0, 0, 0, 0]}, {1}], [[3, 5, 2, 1, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 244, 787, 2468, 7570, 22809]

For the equivalence class of patterns, {

    {[1, 2, 3, 4], [2, 3, 4, 1], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [3, 2, 1, 4], [4, 3, 2, 1]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [4, 1, 2, 3], [4, 3, 1, 2]}}

the member , {[1, 2, 4, 3], [1, 4, 3, 2], [4, 3, 2, 1]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[2, 4, 1, 3], {[0, 0, 1, 0, 0]}, {1}],

    [[2, 3, 1, 4], {[0, 0, 0, 1, 0]}, {1}], [[3, 1, 2], {}, {}],

    [[4, 3, 1, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[3, 2, 1], {[1, 0, 0, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 1, 0, 0]}, {3}],

    [[4, 1, 3, 2], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[2, 1, 3], {}, {}], [[1, 3, 2], {[0, 1, 0, 0]}, {}],

    [[4, 3, 2, 1], {[0, 0, 0, 0, 0]}, {1}], [[1, 2], {}, {}],

    [[3, 1, 4, 2], {[0, 1, 0, 0, 0]}, {1}],

    [[4, 3, 5, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {}, {}],

    [[2, 1], {}, {}], [[1], {}, {}], [[3, 4, 1, 2], {}, {1}],

    [[1, 2, 3], {[0, 0, 1, 0]}, {2}], [[2, 1, 3, 4], {[0, 0, 0, 1, 0]}, {3}],

    [[1, 3, 2, 4], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[2, 1, 4, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[1, 4, 2, 3], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[1, 4, 3, 2], {[0, 0, 0, 0, 0]}, {1}],

    [[3, 2, 1, 4], {[1, 0, 0, 0, 0]}, {1}],

    [[4, 2, 1, 3], {[1, 0, 0, 0, 0]}, {1}],

    [[5, 3, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 4, 3, 1, 5], {

    [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0]}, {1}], [[3, 5, 4, 1, 2],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}], [

    [2, 5, 3, 1, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}],

    [[2, 5, 4, 1, 3], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 4, 2, 1], {[1, 0, 0, 0, 0]}, {}],

    [[4, 2, 5, 1, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]}, {1}], [

    [3, 2, 5, 1, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}],

    [[3, 2, 4, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}],

    [[4, 3, 5, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[4, 5, 2, 1, 3], {[1, 0, 0, 0, 0, 0]}, {1}],

    [[4, 5, 3, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[4, 5, 3, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 5, 4, 2, 1], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[3, 5, 2, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}],

    [[3, 4, 2, 1, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {1}], [

    [4, 2, 3, 1, 5],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}, {1}],

    [[5, 3, 4, 1, 2], {[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[5, 2, 3, 1, 4], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {1}], [

    [5, 2, 4, 1, 3],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[4, 2, 3, 1], {[1, 0, 0, 0, 0]}, {}],

    [[2, 4, 3, 1], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {}],

    [[3, 2, 4, 1], {[1, 0, 0, 0, 0]}, {}],

    [[3, 1, 2, 4], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {4}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 75, 248, 735, 1952, 4697, 10378]

For the equivalence class of patterns, {

    {[2, 3, 4, 1], [2, 4, 1, 3], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [2, 4, 1, 3], [3, 2, 1, 4]},

    {[2, 4, 1, 3], [3, 4, 2, 1], [4, 1, 2, 3]},

    {[1, 4, 3, 2], [2, 1, 3, 4], [3, 1, 4, 2]},

    {[1, 4, 3, 2], [2, 1, 3, 4], [2, 4, 1, 3]},

    {[3, 1, 4, 2], [3, 4, 2, 1], [4, 1, 2, 3]},

    {[2, 3, 4, 1], [3, 1, 4, 2], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [3, 1, 4, 2], [3, 2, 1, 4]}}

the member , {[2, 3, 4, 1], [2, 4, 1, 3], [4, 3, 1, 2]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[3, 1, 2], {}, {}],

    [[4, 1, 3, 2], {[0, 0, 1, 0, 0]}, {3}], [[2, 1, 3], {}, {}],

    [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}],

    [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}], [[2, 1], {}, {}],

    [[1], {}, {}],

    [[4, 5, 1, 2, 3], {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]}, {3}],

    [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[4, 5, 2, 3, 1],

    {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {5}],

    [[3, 4, 1, 2], {[0, 0, 0, 1, 0]}, {}],

    [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}],

    [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {1}],

    [[2, 1, 4, 3], {[1, 0, 0, 1, 0], [0, 1, 0, 1, 0]}, {2}],

    [[1, 4, 2, 3], {[1, 0, 0, 0, 0]}, {1}],

    [[3, 1, 4, 2], {[0, 0, 0, 1, 0], [1, 0, 1, 0, 0]}, {2}],

    [[1, 3, 2], {[1, 0, 1, 0]}, {}],

    [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {2}],

    [[3, 1, 2, 4], {[1, 0, 0, 0, 0]}, {2}],

    [[4, 1, 2, 3], {[1, 0, 0, 0, 0]}, {2}],

    [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {1}], [[2, 3, 1], {[0, 0, 1, 0]}, {}],

    [[3, 5, 1, 2, 4], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[4, 5, 1, 3, 2], {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {4}],

    [[3, 4, 2, 1], {[0, 1, 0, 0, 0], [0, 0, 0, 1, 0]}, {3}],

    [[3, 2, 4, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}], [

    [3, 4, 1, 2, 5], {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[1, 4, 3, 2], {[0, 0, 1, 0, 0], [1, 0, 0, 1, 0]}, {3}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 245, 804, 2617, 8511, 27709]

For the equivalence class of patterns, {

    {[2, 3, 4, 1], [3, 4, 2, 1], [4, 1, 2, 3]},

    {[2, 3, 4, 1], [4, 1, 2, 3], [4, 3, 1, 2]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [3, 2, 1, 4]},

    {[1, 4, 3, 2], [2, 1, 3, 4], [3, 2, 1, 4]}}

the member , {[2, 3, 4, 1], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth ,

    5

                                  here it is:

{[[3, 2, 4, 1], {[0, 1, 0, 0, 0]}, {2}], [[], {}, {}],

    [[1, 3, 2, 4], {[1, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}],

    [[1, 2], {}, {}], [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[3, 1, 4, 2, 5],

    {[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[3, 1, 2], {[0, 0, 1, 0]}, {}], [[4, 1, 2, 3], {[0, 0, 0, 0, 0]}, {1}],

    [[2, 3, 1, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[2, 1, 3, 4], {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]}, {1}],

    [[2, 3, 1], {}, {}], [[2, 1], {}, {}],

    [[4, 1, 5, 2, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[1], {}, {}],

    [[4, 1, 3, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[4, 2, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[1, 2, 3], {[1, 0, 0, 0]}, {1}], [[1, 4, 3, 2], {[0, 0, 1, 0, 0]}, {3}],

    [[1, 3, 2], {}, {}], [[3, 4, 2, 1], {[0, 1, 0, 0, 0]}, {3}],

    [[2, 1, 4, 3], {}, {2}],

    [[2, 4, 3, 1], {[0, 1, 0, 0, 0], [0, 0, 1, 0, 0]}, {4}],

    [[1, 4, 2, 3], {[1, 0, 0, 0, 0], [0, 0, 0, 1, 0]}, {1}],

    [[2, 4, 1, 3], {[0, 0, 0, 1, 0]}, {3}],

    [[3, 1, 2, 4], {[1, 0, 0, 0, 0], [0, 0, 1, 0, 0]}, {2}],

    [[4, 1, 5, 3, 2], {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]}, {4}], [

    [3, 1, 5, 2, 4],

    {[1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}, {1}], [

    [4, 2, 5, 3, 1],

    {[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}, {1}],

    [[3, 1, 4, 2], {[0, 0, 1, 0, 0]}, {}],

    [[3, 4, 1, 2], {[0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 73, 241, 766, 2399, 7514, 23648]

For the equivalence class of patterns, {

    {[1, 2, 3, 4], [2, 4, 1, 3], [3, 2, 1, 4]},

    {[2, 3, 4, 1], [3, 1, 4, 2], [4, 3, 2, 1]},

    {[2, 3, 4, 1], [2, 4, 1, 3], [4, 3, 2, 1]},

    {[2, 4, 1, 3], [4, 1, 2, 3], [4, 3, 2, 1]},

    {[3, 1, 4, 2], [4, 1, 2, 3], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 4, 3, 2], [2, 4, 1, 3]},

    {[1, 2, 3, 4], [1, 4, 3, 2], [3, 1, 4, 2]},

    {[1, 2, 3, 4], [3, 1, 4, 2], [3, 2, 1, 4]}}

the member , {[1, 2, 3, 4], [2, 4, 1, 3], [3, 2, 1, 4]}, has a scheme of depth ,

    5

                                  here it is:

{[[], {}, {}], [[3, 1, 2], {}, {}],

    [[2, 1, 3, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}],

    [[1, 2, 3, 4], {[0, 0, 0, 0, 0]}, {1}], [[2, 1, 3], {}, {}],

    [[1, 2], {}, {}], [[2, 4, 3, 1], %2, {1}],

    [[3, 4, 1, 2], {[0, 0, 0, 1, 0]}, {1}], [[3, 2, 4, 1], %2, {1}],

    [[1, 3, 4, 2], %1, {2}], [[1, 2, 4, 3], %1, {3}],

    [[2, 1, 3, 5, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {4}],

    [[3, 1, 4, 5, 2], %3, {1}],

    [[2, 1, 4, 5, 3], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}],

    [[3, 2, 4, 5, 1], %4, {1}], [[3, 1, 5, 4, 2], %3, {1}],

    [[3, 2, 5, 4, 1], %4, {1}], [[3, 2, 1], {[0, 0, 0, 1]}, {1}],

    [[3, 4, 2, 5, 1], %4, {1}], [[1, 2, 3], {[0, 0, 0, 1]}, {}],

    [[3, 4, 1, 5, 2], %3, {1}], [[2, 3, 1, 5, 4],

    {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1]}, {4}],

    [[2, 1], {}, {}], [[1], {}, {}], [[1, 4, 2, 3], %1, {2}],

    [[2, 3, 1, 4, 5], {[0, 0, 0, 0, 0, 0]}, {1}], [[2, 3, 4, 1], %2, {1}],

    [[3, 4, 2, 1], %1, {1}], [[3, 1, 2, 4], {[0, 0, 0, 0, 1]}, {1}],

    [[2, 3, 1, 4], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {}], [[1, 3, 2], {}, {}],

    [[1, 3, 2, 4], {[0, 0, 0, 0, 1]}, {2}],

    [[2, 4, 1, 5, 3], {[0, 0, 0, 0, 0, 0]}, {1}], [[4, 1, 2, 3], %1, {1}],

    [[1, 4, 3, 2], {[0, 0, 0, 0, 1]}, {2}],

    [[2, 1, 5, 4, 3], {[0, 0, 0, 0, 0, 1]}, {3}],

    [[2, 1, 4, 3, 5], {[0, 0, 0, 0, 0, 1]}, {3}],

    [[2, 4, 1, 3], {[0, 0, 0, 0, 0]}, {1}],

    [[2, 1, 5, 3, 4], {[0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]}, {3}],

    [[2, 3, 1], {[0, 0, 1, 0]}, {}], [[4, 1, 3, 2], {[0, 0, 0, 0, 1]}, {1}],

    [[2, 1, 4, 3], {}, {}], [[2, 1, 3, 4], {[0, 0, 0, 0, 1]}, {}],

    [[3, 1, 4, 2], {[0, 0, 0, 1, 0]}, {1}],

    [[4, 2, 3, 1], {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}, {1}]}

%1 := {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}

%2 := {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}

%3 := {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1]}

%4 := {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 0, 0, 0, 1]}

                 Using  the scheme, the first, , 11, terms are

               [1, 1, 2, 6, 21, 71, 229, 726, 2299, 7296, 23180]

For the equivalence class of patterns, {

    {[3, 4, 1, 2], [4, 1, 2, 3], [4, 3, 1, 2]},

    {[2, 3, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1]},

    {[2, 1, 3, 4], [2, 1, 4, 3], [3, 2, 1, 4]},

    {[1, 2, 4, 3], [1, 4, 3, 2], [2, 1, 4, 3]}}

the member , {[3, 4, 1, 2], [4, 1, 2, 3], [4, 3, 1, 2]}, has a scheme of depth ,

    3

                                  here it is:

{[[], {}, {}], [[1, 2, 3], {}, {1}], [[1, 2], {}, {}],

    [[3, 2, 1], {[0, 1, 0, 0]}, {2}], [[2, 1], {}, {}], [[1], {}, {}],

    [[2, 1, 3], {}, {2}], [[1, 3, 2], {}, {1}],

    [[2, 3, 1], {[0, 1, 0, 0]}, {1}], [[3, 1, 2], {[0, 0, 1, 0]}, {2}]}

                 Using  the scheme, the first, , 21, terms are

[1, 1, 2, 6, 21, 79, 313, 1290, 5475, 23764, 105001, 470738, 2136022, 9791501,

    45275765, 210931962, 989153896, 4665405537, 22117490066, 105333232395,

    503705307121]

For the equivalence class of patterns, {

    {[1, 3, 4, 2], [1, 4, 2, 3], [3, 1, 4, 2]},

    {[1, 3, 4, 2], [1, 4, 2, 3], [2, 4, 1, 3]},

    {[2, 4, 3, 1], [3, 1, 4, 2], [3, 2, 4, 1]},

    {[2, 4, 1, 3], [4, 1, 3, 2], [4, 2, 1, 3]},

    {[3, 1, 4, 2], [4, 1, 3, 2], [4, 2, 1, 3]},

    {[2, 3, 1, 4], [3, 1, 2, 4], [3, 1, 4, 2]},

    {[2, 4, 1, 3], [2, 4, 3, 1], [3, 2, 4, 1]},

    {[2, 3, 1, 4], [2, 4, 1, 3], [3, 1, 2, 4]}}

the member , {[1, 3, 4, 2], [1, 4, 2, 3], [2, 4, 1, 3]}, has a scheme of depth ,

    3

                                  here it is:

{[[], {}, {}], [[1, 2, 3], {[0, 1, 0, 0]}, {1}],

    [[2, 3, 1], {[0, 0, 1, 0]}, {1}], [[1, 2], {}, {}], [[2, 1], {}, {1}],

    [[1], {}, {}], [[1, 3, 2], {[0, 0, 1, 0]}, {2}]}

                 Using  the scheme, the first, , 21, terms are

[1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143, 8377299,

    37704042, 170870106, 779058843, 3571051579, 16447100702, 76073821946,

    353224531663]

For the equivalence class of patterns, {

    {[1, 2, 4, 3], [1, 3, 4, 2], [2, 3, 4, 1]},

    {[2, 1, 3, 4], [2, 3, 1, 4], [2, 3, 4, 1]},

    {[1, 4, 3, 2], [4, 1, 3, 2], [4, 3, 1, 2]},

    {[3, 2, 1, 4], [4, 2, 1, 3], [4, 3, 1, 2]},

    {[3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 2, 1]},

    {[1, 2, 4, 3], [1, 4, 2, 3], [4, 1, 2, 3]},

    {[2, 1, 3, 4], [3, 1, 2, 4], [4, 1, 2, 3]},

    {[1, 4, 3, 2], [2, 4, 3, 1], [3, 4, 2, 1]}}

the member , {[1, 2, 4, 3], [1, 3, 4, 2], [2, 3, 4, 1]}, has a scheme of depth ,

    4

                                  here it is:

{[[3, 4, 1, 2], {}, {1, 2}], [[], {}, {}], [[1, 3, 2], {}, {2}],

    [[3, 4, 2, 1], {}, {3}], [[1, 2], {}, {}], [[2, 1], {}, {1}], [

    [2, 3, 1, 4],

    {[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0]}, {3}],

    [[2, 3, 1], {}, {}], [[1], {}, {}], [[2, 4, 1, 3], {}, {1, 2}],

    [[1, 2, 3], {[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]}, {1}]}

                 Using  the scheme, the first, , 11, terms are

              [1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900]

For the equivalence class of patterns, {

    {[3, 4, 1, 2], [4, 1, 3, 2], [4, 3, 2, 1]},

    {[3, 4, 1, 2], [4, 2, 1, 3], [4, 3, 2, 1]},

    {[1, 2, 3, 4], [1, 3, 4, 2], [2, 1, 4, 3]},

    {[1, 2, 3, 4], [1, 4, 2, 3], [2, 1, 4, 3]},