"There are ", 120, " pattern sets of type ", [3, 3]

              "They fall into ", 40, " trivial pattern classes."

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 0], [0, 1, 0]}}, " the pattern set ",

        {[0, 0, 0], [0, 1, 0]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 156, 960, 6840, 55440, 504000, 5080320, 56246400]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 18, 6, 0]

                              [24, 96, 36, 0, 0]

                           [120, 600, 240, 0, 0, 0]

                         [720, 4320, 1800, 0, 0, 0, 0]

                      [5040, 35280, 15120, 0, 0, 0, 0, 0]

                   [40320, 322560, 141120, 0, 0, 0, 0, 0, 0]

                [362880, 3265920, 1451520, 0, 0, 0, 0, 0, 0, 0]

             [3628800, 36288000, 16329600, 0, 0, 0, 0, 0, 0, 0, 0]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [1, 0, 0]}}, " the pattern set ",

        {[0, 0, 1], [1, 0, 0]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 133, 781, 5401, 42841, 383041, 3810241, 41731201]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 18, 3, 1]

                              [24, 96, 12, 0, 1]

                            [120, 600, 60, 0, 0, 1]

                         [720, 4320, 360, 0, 0, 0, 1]

                      [5040, 35280, 2520, 0, 0, 0, 0, 1]

                   [40320, 322560, 20160, 0, 0, 0, 0, 0, 1]

                [362880, 3265920, 181440, 0, 0, 0, 0, 0, 0, 1]

             [3628800, 36288000, 1814400, 0, 0, 0, 0, 0, 0, 0, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[1, 0, 2], [2, 0, 1]}}, " the pattern set ",

        {[1, 0, 2], [2, 0, 1]}, " has the scheme ", [[[], {}, {}],

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 125, 646, 3907, 27392, 219193, 1972810, 19728191]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 12, 9, 1]

                              [24, 48, 36, 16, 1]

                          [120, 240, 180, 80, 25, 1]

                      [720, 1440, 1080, 480, 150, 36, 1]

                  [5040, 10080, 7560, 3360, 1050, 252, 49, 1]

             [40320, 80640, 60480, 26880, 8400, 2016, 392, 64, 1]

       [362880, 725760, 544320, 241920, 75600, 18144, 3528, 576, 81, 1]

  [3628800, 7257600, 5443200, 2419200, 756000, 181440, 35280, 5760, 810, 100,

        1]

                "---------------------------------------------"

  "For the equivalence class ", {{[1, 2, 3], [3, 2, 1]}}, " the pattern set ",

        {[1, 2, 3], [3, 2, 1]}, " has the scheme ", [[[], {}, {}],

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

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

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

        [2, 1], {1},

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 157, 726, 2987, 10732, 33777, 94402, 238151]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [4, 18, 9, 1]

                              [4, 64, 72, 16, 1]

                           [0, 100, 400, 200, 25, 1]

                         [0, 0, 900, 1600, 450, 36, 1]

                       [0, 0, 0, 4900, 4900, 882, 49, 1]

                    [0, 0, 0, 0, 19600, 12544, 1568, 64, 1]

                  [0, 0, 0, 0, 0, 63504, 28224, 2592, 81, 1]

                [0, 0, 0, 0, 0, 0, 176400, 57600, 4050, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 0, 0], [0, 0, 1]}, {[0, 0, 0], [1, 0, 0]}}, " the pattern set ",

        {[0, 0, 0], [0, 0, 1]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 156, 960, 6840, 55440, 504000, 5080320, 56246400]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 18, 6, 0]

                              [24, 96, 36, 0, 0]

                           [120, 600, 240, 0, 0, 0]

                         [720, 4320, 1800, 0, 0, 0, 0]

                      [5040, 35280, 15120, 0, 0, 0, 0, 0]

                   [40320, 322560, 141120, 0, 0, 0, 0, 0, 0]

                [362880, 3265920, 1451520, 0, 0, 0, 0, 0, 0, 0]

             [3628800, 36288000, 16329600, 0, 0, 0, 0, 0, 0, 0, 0]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 0, 0], [1, 0, 2]}, {[0, 0, 0], [2, 0, 1]}}, " the pattern set ",

        {[0, 0, 0], [1, 0, 2]}, " has the scheme ", [[[], {}, {}],

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 142, 750, 4482, 30450, 234608, 2036016, 19726920]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 9, 0]

                              [24, 64, 54, 0, 0]

                           [120, 320, 310, 0, 0, 0]

                         [720, 1872, 1890, 0, 0, 0, 0]

                      [5040, 12684, 12726, 0, 0, 0, 0, 0]

                    [40320, 98304, 95984, 0, 0, 0, 0, 0, 0]

                 [362880, 860544, 812592, 0, 0, 0, 0, 0, 0, 0]

              [3628800, 8409600, 7688520, 0, 0, 0, 0, 0, 0, 0, 0]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 0, 0], [1, 2, 3]}, {[0, 0, 0], [3, 2, 1]}}, " the pattern set ",

        {[0, 0, 0], [1, 2, 3]}, " has the scheme ", [[[], {}, {}],

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 166, 892, 4794, 25419, 132374, 676676, 3398746]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 9, 0]

                              [14, 80, 72, 0, 0]

                            [42, 350, 500, 0, 0, 0]

                         [132, 1512, 3150, 0, 0, 0, 0]

                       [429, 6468, 18522, 0, 0, 0, 0, 0]

                    [1430, 27456, 103488, 0, 0, 0, 0, 0, 0]

                  [4862, 115830, 555984, 0, 0, 0, 0, 0, 0, 0]

               [16796, 486200, 2895750, 0, 0, 0, 0, 0, 0, 0, 0]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 0, 1], [0, 1, 0]}, {[0, 1, 0], [1, 0, 0]}}, " the pattern set ",

        {[0, 0, 1], [0, 1, 0]}, " has the scheme ",

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 137, 806, 5557, 43940, 391841, 3889450, 42523301]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 18, 3, 1]

                              [24, 96, 12, 4, 1]

                           [120, 600, 60, 20, 5, 1]

                        [720, 4320, 360, 120, 30, 6, 1]

                    [5040, 35280, 2520, 840, 210, 42, 7, 1]

               [40320, 322560, 20160, 6720, 1680, 336, 56, 8, 1]

         [362880, 3265920, 181440, 60480, 15120, 3024, 504, 72, 9, 1]

   [3628800, 36288000, 1814400, 604800, 151200, 30240, 5040, 720, 90, 10, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 1, 0], [1, 0, 2]}, {[0, 1, 0], [2, 0, 1]}}, " the pattern set ",

        {[0, 1, 0], [1, 0, 2]}, " has the scheme ", [[[], {}, {}],

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 127, 661, 3960, 27196, 212365, 1866919, 18290430]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 6, 1]

                              [24, 64, 30, 8, 1]

                          [120, 320, 160, 50, 10, 1]

                       [720, 1872, 960, 320, 75, 12, 1]

                  [5040, 12684, 6552, 2240, 560, 105, 14, 1]

              [40320, 98304, 50736, 17472, 4480, 896, 140, 16, 1]

        [362880, 860544, 442368, 152208, 39312, 8064, 1344, 180, 18, 1]

 [3628800, 8409600, 4302720, 1474560, 380520, 78624, 13440, 1920, 225, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 1, 0], [1, 2, 3]}, {[0, 1, 0], [3, 2, 1]}}, " the pattern set ",

        {[0, 1, 0], [1, 2, 3]}, " has the scheme ", [[[], {}, {}],

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 139, 663, 3197, 15480, 75075, 364347, 1768921]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 6, 1]

                              [14, 80, 36, 8, 1]

                           [42, 350, 200, 60, 10, 1]

                       [132, 1512, 1050, 400, 90, 12, 1]

                   [429, 6468, 5292, 2450, 700, 126, 14, 1]

              [1430, 27456, 25872, 14112, 4900, 1120, 168, 16, 1]

         [4862, 115830, 123552, 77616, 31752, 8820, 1680, 216, 18, 1]

    [16796, 486200, 579150, 411840, 194040, 63504, 14700, 2400, 270, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 1, 2], [0, 2, 1]}, {[1, 2, 0], [2, 1, 0]}}, " the pattern set ",

        {[0, 1, 2], [0, 2, 1]}, " has the scheme ",

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 125, 646, 3907, 27392, 219193, 1972810, 19728191]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 12, 9, 1]

                              [24, 48, 36, 16, 1]

                          [120, 240, 180, 80, 25, 1]

                      [720, 1440, 1080, 480, 150, 36, 1]

                  [5040, 10080, 7560, 3360, 1050, 252, 49, 1]

             [40320, 80640, 60480, 26880, 8400, 2016, 392, 64, 1]

       [362880, 725760, 544320, 241920, 75600, 18144, 3528, 576, 81, 1]

  [3628800, 7257600, 5443200, 2419200, 756000, 181440, 35280, 5760, 810, 100,

        1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 1, 2], [1, 2, 0]}, {[0, 2, 1], [2, 1, 0]}}, " the pattern set ",

        {[0, 1, 2], [1, 2, 0]}, " has the scheme ", [[[], {}, {}],

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 115, 476, 2059, 9962, 58223, 427864, 3865447]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 12, 9, 1]

                              [24, 32, 42, 16, 1]

                          [120, 80, 140, 110, 25, 1]

                       [720, 192, 390, 480, 240, 36, 1]

                   [5040, 448, 987, 1610, 1365, 462, 49, 1]

               [40320, 1024, 2380, 4592, 5670, 3360, 812, 64, 1]

         [362880, 2304, 5616, 11844, 19152, 17262, 7392, 1332, 81, 1]

    [3628800, 5120, 13140, 28800, 56070, 70056, 46410, 14880, 2070, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[0, 1, 2], [2, 1, 0]}, {[0, 2, 1], [1, 2, 0]}}, " the pattern set ",

        {[0, 1, 2], [2, 1, 0]}, " has the scheme ", [[[], {}, {}],

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

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 109, 426, 1779, 8618, 52217, 401986, 3756223]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 12, 9, 1]

                              [24, 32, 36, 16, 1]

                           [120, 80, 120, 80, 25, 1]

                       [720, 192, 360, 320, 150, 36, 1]

                   [5040, 448, 1008, 1120, 700, 252, 49, 1]

               [40320, 1024, 2688, 3584, 2800, 1344, 392, 64, 1]

          [362880, 2304, 6912, 10752, 10080, 6048, 2352, 576, 81, 1]

     [3628800, 5120, 17280, 30720, 33600, 24192, 11760, 3840, 810, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[1, 0, 2], [1, 2, 3]}, {[2, 0, 1], [3, 2, 1]}}, " the pattern set ",

        {[1, 0, 2], [1, 2, 3]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 141, 698, 3571, 18686, 99385, 535122, 2908863]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 56, 54, 16, 1]

                          [42, 210, 280, 140, 25, 1]

                       [132, 792, 1350, 960, 300, 36, 1]

                   [429, 3003, 6237, 5775, 2625, 567, 49, 1]

             [1430, 11440, 28028, 32032, 19250, 6160, 980, 64, 1]

       [4862, 43758, 123552, 168168, 126126, 54054, 12936, 1584, 81, 1]

 [16796, 167960, 537030, 848640, 764400, 412776, 133770, 24960, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[1, 0, 2], [3, 2, 1]}, {[1, 2, 3], [2, 0, 1]}}, " the pattern set ",

        {[1, 0, 2], [3, 2, 1]}, " has the scheme ", [[[], {}, {}],

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

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

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

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

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 133, 573, 2402, 9992, 42007, 180405, 793936]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 48, 54, 16, 1]

                          [42, 155, 210, 140, 25, 1]

                       [132, 528, 765, 640, 300, 36, 1]

                   [429, 1883, 2898, 2590, 1575, 567, 49, 1]

              [1430, 6912, 11508, 10752, 7000, 3360, 980, 64, 1]

         [4862, 25803, 46980, 46872, 31500, 16254, 6468, 1584, 81, 1]

   [16796, 97320, 193995, 210240, 149100, 78624, 33810, 11520, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[1, 3, 2], [2, 1, 3]}, {[2, 3, 1], [3, 1, 2]}}, " the pattern set ",

        {[1, 3, 2], [2, 1, 3]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 161, 842, 4495, 24320, 132865, 731282, 4048727]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [4, 18, 9, 1]

                              [8, 64, 72, 16, 1]

                          [16, 200, 400, 200, 25, 1]

                       [32, 576, 1800, 1600, 450, 36, 1]

                   [64, 1568, 7056, 9800, 4900, 882, 49, 1]

             [128, 4096, 25088, 50176, 39200, 12544, 1568, 64, 1]

        [256, 10368, 82944, 225792, 254016, 127008, 28224, 2592, 81, 1]

  [512, 25600, 259200, 921600, 1411200, 1016064, 352800, 57600, 4050, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[1, 3, 2], [2, 3, 1]}, {[2, 1, 3], [3, 1, 2]}}, " the pattern set ",

        {[1, 3, 2], [2, 3, 1]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 161, 842, 4495, 24320, 132865, 731282, 4048727]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [4, 18, 9, 1]

                              [8, 64, 72, 16, 1]

                          [16, 200, 400, 200, 25, 1]

                       [32, 576, 1800, 1600, 450, 36, 1]

                   [64, 1568, 7056, 9800, 4900, 882, 49, 1]

             [128, 4096, 25088, 50176, 39200, 12544, 1568, 64, 1]

        [256, 10368, 82944, 225792, 254016, 127008, 28224, 2592, 81, 1]

  [512, 25600, 259200, 921600, 1411200, 1016064, 352800, 57600, 4050, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ",

        {{[1, 3, 2], [3, 1, 2]}, {[2, 1, 3], [2, 3, 1]}}, " the pattern set ",

        {[1, 3, 2], [3, 1, 2]}, " has the scheme ", [[[], {}, {}],

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 161, 842, 4495, 24320, 132865, 731282, 4048727]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [4, 18, 9, 1]

                              [8, 64, 72, 16, 1]

                          [16, 200, 400, 200, 25, 1]

                       [32, 576, 1800, 1600, 450, 36, 1]

                   [64, 1568, 7056, 9800, 4900, 882, 49, 1]

             [128, 4096, 25088, 50176, 39200, 12544, 1568, 64, 1]

        [256, 10368, 82944, 225792, 254016, 127008, 28224, 2592, 81, 1]

  [512, 25600, 259200, 921600, 1411200, 1016064, 352800, 57600, 4050, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 0], [0, 1, 2]},

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

        }, " the pattern set ", {[0, 0, 0], [0, 1, 2]}, " has the scheme ", [

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 142, 755, 4611, 32410, 259484, 2335653, 23356945]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 9, 0]

                              [24, 64, 54, 0, 0]

                           [120, 325, 310, 0, 0, 0]

                         [720, 1956, 1935, 0, 0, 0, 0]

                      [5040, 13699, 13671, 0, 0, 0, 0, 0]

                   [40320, 109600, 109564, 0, 0, 0, 0, 0, 0]

                 [362880, 986409, 986364, 0, 0, 0, 0, 0, 0, 0]

              [3628800, 9864100, 9864045, 0, 0, 0, 0, 0, 0, 0, 0]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 0], [1, 3, 2]},

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

        }, " the pattern set ", {[0, 0, 0], [1, 3, 2]}, " has the scheme ", [

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 166, 892, 4794, 25419, 132374, 676676, 3398746]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 9, 0]

                              [14, 80, 72, 0, 0]

                            [42, 350, 500, 0, 0, 0]

                         [132, 1512, 3150, 0, 0, 0, 0]

                       [429, 6468, 18522, 0, 0, 0, 0, 0]

                    [1430, 27456, 103488, 0, 0, 0, 0, 0, 0]

                  [4862, 115830, 555984, 0, 0, 0, 0, 0, 0, 0]

               [16796, 486200, 2895750, 0, 0, 0, 0, 0, 0, 0, 0]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [0, 1, 2]},

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

        }, " the pattern set ", {[0, 0, 1], [0, 1, 2]}, " has the scheme ", [

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 127, 666, 4059, 28540, 228575, 2057686, 20577883]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 6, 1]

                              [24, 64, 30, 8, 1]

                          [120, 325, 160, 50, 10, 1]

                       [720, 1956, 975, 320, 75, 12, 1]

                  [5040, 13699, 6846, 2275, 560, 105, 14, 1]

             [40320, 109600, 54796, 18256, 4550, 896, 140, 16, 1]

        [362880, 986409, 493200, 164388, 41076, 8190, 1344, 180, 18, 1]

 [3628800, 9864100, 4932045, 1644000, 410970, 82152, 13650, 1920, 225, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [1, 0, 2]},

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

        }, " the pattern set ", {[0, 0, 1], [1, 0, 2]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 127, 661, 3960, 27196, 212365, 1866919, 18290430]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 6, 1]

                              [24, 64, 30, 8, 1]

                          [120, 320, 160, 50, 10, 1]

                       [720, 1872, 960, 320, 75, 12, 1]

                  [5040, 12684, 6552, 2240, 560, 105, 14, 1]

              [40320, 98304, 50736, 17472, 4480, 896, 140, 16, 1]

        [362880, 860544, 442368, 152208, 39312, 8064, 1344, 180, 18, 1]

 [3628800, 8409600, 4302720, 1474560, 380520, 78624, 13440, 1920, 225, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [1, 2, 0]},

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

        }, " the pattern set ", {[0, 0, 1], [1, 2, 0]}, " has the scheme ", [

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 115, 526, 2889, 19258, 151127, 1352014, 13498933]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 6, 1]

                              [24, 64, 18, 8, 1]

                           [120, 325, 40, 30, 10, 1]

                        [720, 1956, 75, 80, 45, 12, 1]

                    [5040, 13699, 126, 175, 140, 63, 14, 1]

                [40320, 109600, 196, 336, 350, 224, 84, 16, 1]

             [362880, 986409, 288, 588, 756, 630, 336, 108, 18, 1]

        [3628800, 9864100, 405, 960, 1470, 1512, 1050, 480, 135, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [1, 2, 3]},

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

        }, " the pattern set ", {[0, 0, 1], [1, 2, 3]}, " has the scheme ", [

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

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 139, 663, 3197, 15480, 75075, 364347, 1768921]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 6, 1]

                              [14, 80, 36, 8, 1]

                           [42, 350, 200, 60, 10, 1]

                       [132, 1512, 1050, 400, 90, 12, 1]

                   [429, 6468, 5292, 2450, 700, 126, 14, 1]

              [1430, 27456, 25872, 14112, 4900, 1120, 168, 16, 1]

         [4862, 115830, 123552, 77616, 31752, 8820, 1680, 216, 18, 1]

    [16796, 486200, 579150, 411840, 194040, 63504, 14700, 2400, 270, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [1, 3, 2]},

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

        }, " the pattern set ", {[0, 0, 1], [1, 3, 2]}, " has the scheme ", [

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

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 139, 663, 3197, 15480, 75075, 364347, 1768921]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 6, 1]

                              [14, 80, 36, 8, 1]

                           [42, 350, 200, 60, 10, 1]

                       [132, 1512, 1050, 400, 90, 12, 1]

                   [429, 6468, 5292, 2450, 700, 126, 14, 1]

              [1430, 27456, 25872, 14112, 4900, 1120, 168, 16, 1]

         [4862, 115830, 123552, 77616, 31752, 8820, 1680, 216, 18, 1]

    [16796, 486200, 579150, 411840, 194040, 63504, 14700, 2400, 270, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 0, 1], [2, 1, 3]},

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

        }, " the pattern set ", {[1, 0, 0], [1, 3, 2]}, " has the scheme ", [

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 139, 663, 3197, 15480, 75075, 364347, 1768921]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 6, 1]

                              [14, 80, 36, 8, 1]

                           [42, 350, 200, 60, 10, 1]

                       [132, 1512, 1050, 400, 90, 12, 1]

                   [429, 6468, 5292, 2450, 700, 126, 14, 1]

              [1430, 27456, 25872, 14112, 4900, 1120, 168, 16, 1]

         [4862, 115830, 123552, 77616, 31752, 8820, 1680, 216, 18, 1]

    [16796, 486200, 579150, 411840, 194040, 63504, 14700, 2400, 270, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 0], [0, 1, 2]},

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

        }, " the pattern set ", {[0, 1, 0], [0, 1, 2]}, " has the scheme ", [

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 127, 666, 4059, 28540, 228575, 2057686, 20577883]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 15, 6, 1]

                              [24, 64, 30, 8, 1]

                          [120, 325, 160, 50, 10, 1]

                       [720, 1956, 975, 320, 75, 12, 1]

                  [5040, 13699, 6846, 2275, 560, 105, 14, 1]

             [40320, 109600, 54796, 18256, 4550, 896, 140, 16, 1]

        [362880, 986409, 493200, 164388, 41076, 8190, 1344, 180, 18, 1]

 [3628800, 9864100, 4932045, 1644000, 410970, 82152, 13650, 1920, 225, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 0], [1, 3, 2]},

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

        }, " the pattern set ", {[0, 1, 0], [1, 3, 2]}, " has the scheme ", [

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 139, 663, 3197, 15480, 75075, 364347, 1768921]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 18, 6, 1]

                              [14, 80, 36, 8, 1]

                           [42, 350, 200, 60, 10, 1]

                       [132, 1512, 1050, 400, 90, 12, 1]

                   [429, 6468, 5292, 2450, 700, 126, 14, 1]

              [1430, 27456, 25872, 14112, 4900, 1120, 168, 16, 1]

         [4862, 115830, 123552, 77616, 31752, 8820, 1680, 216, 18, 1]

    [16796, 486200, 579150, 411840, 194040, 63504, 14700, 2400, 270, 20, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [1, 0, 2]},

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

        }, " the pattern set ", {[0, 1, 2], [1, 0, 2]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 123, 596, 3246, 20280, 146931, 1229716, 11717418]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 12, 9, 1]

                              [24, 40, 42, 16, 1]

                          [120, 170, 170, 110, 25, 1]

                       [720, 924, 765, 560, 240, 36, 1]

                  [5040, 6118, 4305, 2765, 1540, 462, 49, 1]

             [40320, 47312, 30212, 15904, 8610, 3696, 812, 64, 1]

       [362880, 416106, 251748, 114492, 51282, 23814, 7980, 1332, 81, 1]

  [3628800, 4091140, 2395215, 1002720, 371700, 150192, 59640, 15840, 2070, 100,

        1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [1, 2, 3]},

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

        }, " the pattern set ", {[0, 1, 2], [1, 2, 3]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 141, 698, 3571, 18686, 99385, 535122, 2908863]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 56, 54, 16, 1]

                          [42, 210, 280, 140, 25, 1]

                       [132, 792, 1350, 960, 300, 36, 1]

                   [429, 3003, 6237, 5775, 2625, 567, 49, 1]

             [1430, 11440, 28028, 32032, 19250, 6160, 980, 64, 1]

       [4862, 43758, 123552, 168168, 126126, 54054, 12936, 1584, 81, 1]

 [16796, 167960, 537030, 848640, 764400, 412776, 133770, 24960, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [1, 3, 2]},

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

        }, " the pattern set ", {[0, 1, 2], [1, 3, 2]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 137, 638, 2995, 14136, 67061, 319803, 1533248]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 52, 54, 16, 1]

                          [42, 180, 250, 140, 25, 1]

                       [132, 636, 1050, 840, 300, 36, 1]

                   [429, 2296, 4284, 4235, 2275, 567, 49, 1]

              [1430, 8432, 17416, 19768, 13650, 5320, 980, 64, 1]

         [4862, 31365, 71028, 89460, 72576, 37674, 11172, 1584, 81, 1]

  [16796, 117790, 290655, 400200, 363510, 227556, 92610, 21600, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [2, 0, 1]},

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

        }, " the pattern set ", {[0, 1, 2], [2, 0, 1]}, " has the scheme ", [

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 28, 117, 536, 2851, 18068, 135241, 1167400, 11362311]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [6, 12, 9, 1]

                              [24, 40, 36, 16, 1]

                          [120, 170, 140, 80, 25, 1]

                       [720, 924, 660, 360, 150, 36, 1]

                   [5040, 6118, 3948, 1890, 770, 252, 49, 1]

             [40320, 47312, 28784, 12432, 4480, 1456, 392, 64, 1]

        [362880, 416106, 244368, 99288, 32256, 9324, 2520, 576, 81, 1]

 [3628800, 4091140, 2346660, 919440, 280560, 73080, 17640, 4080, 810, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [2, 1, 3]},

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

        }, " the pattern set ", {[1, 2, 0], [1, 3, 2]}, " has the scheme ", [

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 141, 698, 3571, 18686, 99385, 535122, 2908863]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 56, 54, 16, 1]

                          [42, 210, 280, 140, 25, 1]

                       [132, 792, 1350, 960, 300, 36, 1]

                   [429, 3003, 6237, 5775, 2625, 567, 49, 1]

             [1430, 11440, 28028, 32032, 19250, 6160, 980, 64, 1]

       [4862, 43758, 123552, 168168, 126126, 54054, 12936, 1584, 81, 1]

 [16796, 167960, 537030, 848640, 764400, 412776, 133770, 24960, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [2, 3, 1]},

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

        }, " the pattern set ", {[1, 2, 0], [3, 1, 2]}, " has the scheme ", [

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 137, 638, 2995, 14136, 67061, 319803, 1533248]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 52, 54, 16, 1]

                          [42, 180, 250, 140, 25, 1]

                       [132, 636, 1050, 840, 300, 36, 1]

                   [429, 2296, 4284, 4235, 2275, 567, 49, 1]

              [1430, 8432, 17416, 19768, 13650, 5320, 980, 64, 1]

         [4862, 31365, 71028, 89460, 72576, 37674, 11172, 1584, 81, 1]

  [16796, 117790, 290655, 400200, 363510, 227556, 92610, 21600, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [3, 1, 2]},

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

        }, " the pattern set ", {[0, 1, 2], [3, 1, 2]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 141, 698, 3571, 18686, 99385, 535122, 2908863]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 56, 54, 16, 1]

                          [42, 210, 280, 140, 25, 1]

                       [132, 792, 1350, 960, 300, 36, 1]

                   [429, 3003, 6237, 5775, 2625, 567, 49, 1]

             [1430, 11440, 28028, 32032, 19250, 6160, 980, 64, 1]

       [4862, 43758, 123552, 168168, 126126, 54054, 12936, 1584, 81, 1]

 [16796, 167960, 537030, 848640, 764400, 412776, 133770, 24960, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[0, 1, 2], [3, 2, 1]},

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

        }, " the pattern set ", {[0, 1, 2], [3, 2, 1]}, " has the scheme ", [

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 133, 583, 2552, 11301, 50883, 232839, 1080166]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 48, 54, 16, 1]

                          [42, 165, 210, 140, 25, 1]

                       [132, 588, 855, 640, 300, 36, 1]

                   [429, 2142, 3528, 3010, 1575, 567, 49, 1]

              [1430, 7920, 14616, 14112, 8400, 3360, 980, 64, 1]

         [4862, 29601, 60588, 65520, 44100, 20034, 6468, 1584, 81, 1]

  [16796, 111540, 250965, 300960, 226800, 116424, 42630, 11520, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[1, 0, 2], [1, 3, 2]},

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

        }, " the pattern set ", {[1, 0, 2], [1, 3, 2]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 141, 698, 3571, 18686, 99385, 535122, 2908863]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 56, 54, 16, 1]

                          [42, 210, 280, 140, 25, 1]

                       [132, 792, 1350, 960, 300, 36, 1]

                   [429, 3003, 6237, 5775, 2625, 567, 49, 1]

             [1430, 11440, 28028, 32032, 19250, 6160, 980, 64, 1]

       [4862, 43758, 123552, 168168, 126126, 54054, 12936, 1584, 81, 1]

 [16796, 167960, 537030, 848640, 764400, 412776, 133770, 24960, 2430, 100, 1]

                "---------------------------------------------"

  "For the equivalence class ", {{[1, 0, 2], [2, 3, 1]},

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

        }, " the pattern set ", {[1, 0, 2], [3, 1, 2]}, " has the scheme ", [

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

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

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

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 30, 137, 638, 2995, 14136, 67061, 319803, 1533248]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [5, 15, 9, 1]

                              [14, 52, 54, 16, 1]

                          [42, 180, 250, 140, 25, 1]

                       [132, 636, 1050, 840, 300, 36, 1]

                   [429, 2296, 4284, 4235, 2275, 567, 49, 1]

              [1430, 8432, 17416, 19768, 13650, 5320, 980, 64, 1]

         [4862, 31365, 71028, 89460, 72576, 37674, 11172, 1584, 81, 1]

  [16796, 117790, 290655, 400200, 363510, 227556, 92610, 21600, 2430, 100, 1]

                "---------------------------------------------"

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

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

        }, " the pattern set ", {[1, 2, 3], [1, 3, 2]}, " has the scheme ",

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 161, 842, 4495, 24320, 132865, 731282, 4048727]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [4, 18, 9, 1]

                              [8, 64, 72, 16, 1]

                          [16, 200, 400, 200, 25, 1]

                       [32, 576, 1800, 1600, 450, 36, 1]

                   [64, 1568, 7056, 9800, 4900, 882, 49, 1]

             [128, 4096, 25088, 50176, 39200, 12544, 1568, 64, 1]

        [256, 10368, 82944, 225792, 254016, 127008, 28224, 2592, 81, 1]

  [512, 25600, 259200, 921600, 1411200, 1016064, 352800, 57600, 4050, 100, 1]

                "---------------------------------------------"

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

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

        }, " the pattern set ", {[1, 2, 3], [2, 3, 1]}, " has the scheme ", [

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

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

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

  "First ", 10, " terms of the counting sequence are ",

        [2, 7, 32, 160, 812, 4074, 20064, 96954, 460460, 2153866]

                "First ", 10, " rows of the 0s triangle are: "

                                    [1, 1]

                                   [2, 4, 1]

                                 [4, 18, 9, 1]

                              [7, 64, 72, 16, 1]

                          [11, 175, 400, 200, 25, 1]

                       [16, 396, 1575, 1600, 450, 36, 1]

                    [22, 784, 4851, 8575, 4900, 882, 49, 1]

              [29, 1408, 12544, 34496, 34300, 12544, 1568, 64, 1]

         [37, 2349, 28512, 112896, 174636, 111132, 28224, 2592, 81, 1]

    [46, 3700, 58725, 316800, 705600, 698544, 308700, 57600, 4050, 100, 1]

                "---------------------------------------------"

  "Overall, we found schemes for ", 40, " out of ", 40,

        " trivial classes, for a success rate of ", 1.