"Welcome to gVATTER, a Maple package for the enumeration of"

           "permutations avoiding generalized permutation patterns."

              "To see a list of available functions, type Help();"

    "or to learn more about a particular function type Help(function_name);"

"There are ", 914, " equivalence classes of generalized patterns of lengths ",

    [3, 4]

                              "Class ", 1, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 70, 345, 1961, 12662, 91377, 728949, 6366690, 60415265, 618799585,

    6803149818, 79898615181, 998203446137, 13217492474270, 184888722894713,

    2724183018652777, 42168544049357550]

                                       ""

                              "Class ", 2, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 70, 339, 1859, 11304, 75043, 537927, 4128852, 33710677, 291219757,

    2650140806, 25309886849, 252868392525, 2635575485046, 28587398320851,

    321999635673695, 3759085214905252]

                                       ""

                              "Class ", 3, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 70, 330, 1699, 9317, 53594, 320265, 1974780, 12501797, 80946182,

    534397630, 3588441619, 24459185369, 168944095444, 1180853221621,

    8342201654112, 59504853554799]

                                       ""

                              "Class ", 4, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 284, 1507, 9104, 61766, 465208, 3852642, 34799648, 340496652,

    3587705528, 40501871019, 487705826080, 6239758647782, 84527944150760,

    1208685990485278, 18192939021118240]

                                       ""

                              "Class ", 5, " is:"

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

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

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

                              "Class ", 6, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 59, 247, 1134, 5645, 30025, 169385, 1005798, 6255497, 40560697,

    273246460, 1906553947, 13743690023, 102126146514, 780776436783,

    6130985115331, 49374605672774]

                                       ""

                              "Class ", 7, " is:"

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

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

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

                              "Class ", 8, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 266, 1346, 7744, 49768, 354976, 2779296, 23736488, 219486760,

    2185815120, 23319068984, 265374281984, 3208589794944, 41077406105536,

    555093254690752, 7896038224892416]

                                       ""

                              "Class ", 9, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 262, 1290, 7104, 43064, 285440, 2049280, 15852328, 131300936,

    1159670544, 10872886520, 107862716160, 1128348186240, 12413760505408,

    143251030108096, 1730107187770880]

                                       ""

                              "Class ", 10, " is:"

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

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

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

                              "Class ", 11, " is:"

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

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

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

                              "Class ", 12, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 64, 305, 1701, 10838, 77686, 618850, 5421999, 51825896, 536647821,

    5984335552, 71500271620, 911227502806, 12338872989022, 176908047590908,

    2677323018042734, 42651115297581877]

                                       ""

                              "Class ", 13, " is:"

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

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

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

                              "Class ", 14, " is:"

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

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

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

                              "Class ", 15, " is:"

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

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

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

                              "Class ", 16, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 273, 1432, 8654, 58628, 442310, 3666195, 33170538, 325020557,

    3430253693, 38785386031, 467797514944, 5994689593730, 81340012333068,

    1164984533544267, 17563614560172708]

                                       ""

                              "Class ", 17, " is:"

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

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

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

                              "Class ", 18, " is:"

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

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

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

                              "Class ", 19, " is:"

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

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

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

                              "Class ", 20, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 66, 322, 1847, 12052, 88624, 723710, 6501385, 63717368, 676453108,

    7734414934, 94746943247, 1238053847560, 17188548465632, 252675896401426,

    3920749985796689, 64039935035443740]

                                       ""

                              "Class ", 21, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 63, 298, 1641, 10308, 72675, 568070, 4873845, 45523104, 459722319,

    4990324634, 57936500281, 716262794700, 9393517470475, 130241995833942,

    1903410804893941, 29241521058216688]

                                       ""

                              "Class ", 22, " is:"

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

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

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

                              "Class ", 23, " is:"

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

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

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

                              "Class ", 24, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 281, 1516, 9370, 65198, 503476, 4280017, 39679133, 398540627,

    4310973856, 49960614573, 617615072788, 8112094706561, 112816521850524,

    1656127027124571, 25591198555992118]

                                       ""

                              "Class ", 25, " is:"

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

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

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

                              "Class ", 26, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 250, 1210, 6542, 38796, 250036, 1735682, 12889050, 101797450,

    850961862, 7497871096, 69384956044, 672258658346, 6800789417484,

    71660224436220, 784785689974844]

                                       ""

                              "Class ", 27, " is:"

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

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

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

                              "Class ", 28, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 291, 1583, 9928, 69962, 546785, 4711814, 44214469, 449938465,

    4928760573, 57852293990, 724375238938, 9635849293541, 135730147699184,

    2018004546493613, 31583034212002819]

                                       ""

                              "Class ", 29, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 57, 240, 1149, 6176, 36720, 239220, 1692680, 12923238, 105825684,

    925002698, 8592743190, 84520950540, 877385692952, 9584197068384,

    109878325175412, 1319001942675290]

                                       ""

                              "Class ", 30, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 55, 210, 875, 3942, 18905, 96437, 516162, 2905682, 17013338,

    103929557, 656480791, 4300449239, 29006607198, 201978719000, 1443452416382,

    10611307945196]

                                       ""

                              "Class ", 31, " is:"

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

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

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

                              "Class ", 32, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 941, 2923, 9228, 29536, 95639, 312766, 1031605,

    3427895, 11464605, 38563279, 130374291, 442768709, 1509830427]

                                       ""

                              "Class ", 33, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 103, 301, 895, 2693, 8180, 25030, 77037, 238231, 739566,

    2303297, 7192620, 22511561, 70592276, 221727951, 697421598]

                                       ""

                              "Class ", 34, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}, " has scheme:"

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                              "Class ", 35, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:"

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                              "Class ", 36, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 106, 323, 1008, 3215, 10433, 34308, 114094, 383122, 1297092,

    4422563, 15173196, 52343440, 181451449, 631756805, 2208221581]

                                       ""

                              "Class ", 37, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                              "Class ", 38, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 0, 1]]}, " has scheme:"

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                              "Class ", 39, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 38, 118, 381, 1267, 4303, 14856, 51978, 183880, 656610, 2363531,

    8567117, 31243019, 114553235, 422026959, 1561472627, 5799695276]

                                       ""

                              "Class ", 40, " is:"

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

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

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

                              "Class ", 41, " is:"

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

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

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

                              "Class ", 42, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 38, 119, 385, 1280, 4347, 15004, 52480, 185612, 662665, 2384933,

    8643489, 31517770, 115548610, 425655202, 1574769687, 5848662420]

                                       ""

                              "Class ", 43, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 98, 283, 833, 2477, 7402, 22169, 66461, 199327, 597914,

    1793663, 5380897, 16142585, 48427634, 145282765, 435848141]

                                       ""

                              "Class ", 44, " is:"

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

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

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

                              "Class ", 45, " is:"

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

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

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

                              "Class ", 46, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 106, 324, 1014, 3238, 10516, 34609, 115161, 386852, 1310142,

    4468273, 15333301, 52905102, 183426368, 638715691, 2232793575]

                                       ""

                              "Class ", 47, " is:"

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

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

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

                              "Class ", 48, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 88, 224, 560, 1376, 3328, 7936, 18688, 43520, 100352, 229376,

    520192, 1171456, 2621440, 5832704, 12910592]

                                       ""

                              "Class ", 49, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

    {1, 3, 4},

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 72, 148, 281, 499, 838, 1343, 2069, 3082, 4460, 6294, 8689,

    11765, 15658, 20521, 26525]

                                       ""

                              "Class ", 50, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 84, 210, 564, 1485, 3960, 10868, 29458, 81224, 225836, 626314,

    1757834, 4943192, 13932928, 39533908, 112294180]

                                       ""

                              "Class ", 51, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 29, 53, 80, 106, 136, 170, 208, 250, 296, 346, 400, 458, 520, 586,

    656, 730]

                                       ""

                              "Class ", 52, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    }

            "The first ", 20, " terms of the counting sequence are:"

       [1, 2, 5, 13, 27, 41, 37, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

                                       ""

                              "Class ", 53, " is:"

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

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

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

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

    }

            "The first ", 20, " terms of the counting sequence are:"

        [1, 2, 5, 13, 25, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

                                       ""

                              "Class ", 54, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 70, 339, 1859, 11326, 75533, 545623, 4233832, 35056333, 308036757,

    2859147446, 27922827153, 285954152889, 3061694389090, 34184118042071,

    397082486559995, 4788890186574602]

                                       ""

                              "Class ", 55, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 68, 325, 1763, 10838, 73827, 554241, 4532236, 40151025, 382611829,

    3903918778, 42443412073, 489854252153, 5980071198468, 76987298812701,

    1042282611338431, 14802547304527934]

                                       ""

                              "Class ", 56, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 68, 319, 1685, 9904, 63765, 445435, 3347328, 26880941, 229393559,

    2070451728, 19685412333, 196474678483, 2052249012658, 22374404250663,

    254002765848007, 2996185044863922]

                                       ""

                              "Class ", 57, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 67, 310, 1603, 9263, 58631, 404594, 3012139, 24074131, 205252633,

    1859073998, 17811575033, 179913541265, 1909844642689, 21249231967066,

    247184432673589, 2999751065966681]

                                       ""

                              "Class ", 58, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 67, 304, 1526, 8386, 49758, 316215, 2137000, 15274695, 114949917,

    907348125, 7488079845, 64431009449, 576630525433, 5356165646155,

    51539763437737, 512893471582510]

                                       ""

                              "Class ", 59, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 66, 296, 1448, 7740, 44199, 269107, 1727903, 11668160, 82353750,

    605963066, 4630054002, 36656765191, 299898190568, 2530810508666,

    21986001002672, 196329439543063]

                                       ""

                              "Class ", 60, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 66, 287, 1338, 6603, 34030, 181787, 1000275, 5643827, 32535088,

    191079735, 1140645691, 6907657235, 42370448866, 262884880825, 1647948499717,

    10427327717945]

                                       ""

                              "Class ", 61, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:"

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 260, 1266, 6844, 40548, 261044, 1812044, 13480264, 106903744,

    899732728, 8005012064, 75034738304, 738767782176, 7619725469872,

    82132998671616, 923226325101312]

                                       ""

                              "Class ", 62, " is:"

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

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

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

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

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

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

                              "Class ", 63, " is:"

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

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

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

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

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

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

                              "Class ", 64, " is:"

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

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

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

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

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

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

                              "Class ", 65, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:"

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

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

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

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

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

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

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

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 68, 324, 1762, 10842, 74224, 560246, 4618922, 41305484, 398164098,

    4115578642, 45406725946, 532586071178, 6617584890554, 86831950450732,

    1199781621861714, 17412511362942498]

                                       ""

                              "Class ", 66, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 68, 319, 1683, 9862, 63163, 437899, 3258204, 25847121, 217405529,

    1929981538, 18011731997, 176121521345, 1799076450404, 19149110870871,

    211894493559155, 2432655382039094]

                                       ""

                              "Class ", 67, " is:"

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

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

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

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

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

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

                              "Class ", 68, " is:"

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

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

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

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

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

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

                              "Class ", 69, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 63, 294, 1602, 9961, 69697, 541905, 4634544, 43242203, 437082198,

    4757801674, 55489735756, 690314828567, 9124540858707, 127702155345045,

    1886542471602136, 29336704784339814]

                                       ""

                              "Class ", 70, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:"

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 260, 1266, 6844, 40548, 261044, 1812044, 13480264, 106903744,

    899732728, 8005012064, 75034738304, 738767782176, 7619725469872,

    82132998671616, 923226325101312]

                                       ""

                              "Class ", 71, " is:"

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

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

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

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

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

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

                              "Class ", 72, " is:"

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

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

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

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

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

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

                              "Class ", 73, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 282, 1478, 8764, 58020, 424316, 3396916, 29549144, 277536216,

    2799217416, 30175069704, 346222937824, 4212800538560, 54185328375344,

    734553555025280, 10467850927888672]

                                       ""

                              "Class ", 74, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:"

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

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 59, 246, 1121, 5511, 28825, 159169, 921326, 5563093, 34891428,

    226567578, 1518872789, 10487648392, 74436515078, 542115833405,

    4045127096892, 30883350295301]

                                       ""

                              "Class ", 75, " is:"

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

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

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

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

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

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

                              "Class ", 76, " is:"

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

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

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

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

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

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

                              "Class ", 77, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 277, 1450, 8682, 58343, 436159, 3584782, 32158156, 312461665,

    3270070791, 36664386308, 438512776990, 5572306937731, 74975425890679,

    1064826960466018, 15919092368486544]

                                       ""

                              "Class ", 78, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:"

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 240, 1080, 5299, 27684, 154076, 901523, 5543329, 35531740,

    237233536, 1641203831, 11754107461, 86832065266, 661070955151,

    5173165839419, 41575784087413]

                                       ""

                              "Class ", 79, " is:"

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

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

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

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

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

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

                              "Class ", 80, " is:"

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

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

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

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

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

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

                              "Class ", 81, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:"

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

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 272, 1385, 7936, 50521, 353792, 2702765, 22368256, 199360981,

    1903757312, 19391512145, 209865342976, 2404879675441, 29088885112832,

    370371188237525, 4951498053124096]

                                       ""

                              "Class ", 82, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 240, 1080, 5299, 27684, 154076, 901523, 5543329, 35531740,

    237233536, 1641203831, 11754107461, 86832065266, 661070955151,

    5173165839419, 41575784087413]

                                       ""

                              "Class ", 83, " is:"

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

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

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

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

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

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

                              "Class ", 84, " is:"

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

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

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

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

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

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

                              "Class ", 85, " is:"

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

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

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

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

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

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

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

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

    {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:"

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

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

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

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

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 241, 1093, 5430, 28852, 164014, 984410, 6232479, 41291499,

    285894428, 2057960685, 15380215236, 118912110252, 949882993244,

    7819356088084, 66255836753914]

                                       ""

                              "Class ", 86, " is:"

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

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

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

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

                {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 241, 1093, 5430, 28852, 164014, 984410, 6232479, 41291499,

    285894428, 2057960685, 15380215236, 118912110252, 949882993244,

    7819356088084, 66255836753914]

                                       ""

                              "Class ", 87, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}

                              "Class ", 88, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}

                              "Class ", 89, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 68, 324, 1764, 10833, 74159, 558632, 4599351, 41056291, 395040334,

    4075943756, 44886580308, 525538735910, 6518449651843, 85382518810601,

    1177756559849964, 17064588213923583]

                                       ""

                              "Class ", 90, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 17, 68, 319, 1683, 9862, 63163, 437899, 3258204, 25847121, 217405529,

    1929981538, 18011731997, 176121521345, 1799076450404, 19149110870871,

    211894493559155, 2432655382039094]

                                       ""

                              "Class ", 91, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}

                              "Class ", 92, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}

                              "Class ", 93, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 282, 1478, 8764, 58020, 424316, 3396916, 29549144, 277536216,

    2799217416, 30175069704, 346222937824, 4212800538560, 54185328375344,

    734553555025280, 10467850927888672]

                                       ""

                              "Class ", 94, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}

                              "Class ", 95, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}],

    [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}],

    [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 293, 1600, 10058, 70745, 554914, 4776089, 44922308, 457185790,

    5014937009, 58905465368, 738319044982, 9829799921945, 138595535933882,

    2062431599753245, 32309064111697496]

                                       ""

                              "Class ", 96, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[1, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 59, 257, 1261, 6980, 42536, 284080, 2052692, 15971228, 132825940,

    1175951720, 11029848320, 109234071808, 1138284832568, 12446563087256,

    142430581302760, 1701890250901328]

                                       ""

                              "Class ", 97, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}

                              "Class ", 98, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}

                              "Class ", 99, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 265, 1327, 7516, 47138, 326286, 2459642, 20132224, 177295591,

    1675637317, 16883712723, 180977390644, 2053417327682, 24616892752186,

    310594486535394, 4117960947215777]

                                       ""

                             "Class ", 100, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 240, 1080, 5299, 27684, 154076, 901523, 5543329, 35531740,

    237233536, 1641203831, 11754107461, 86832065266, 661070955151,

    5173165839419, 41575784087413]

                                       ""

                             "Class ", 101, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}

                             "Class ", 102, " is:"

{{[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}

                             "Class ", 103, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 246, 1162, 6146, 35602, 225078, 1535634, 11252520, 87980582,

    730936978, 6424649522, 59542865176, 580017124482, 5922528457026,

    63234234385574, 704404373427440]

                                       ""

                             "Class ", 104, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}

                             "Class ", 105, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 276, 1459, 8873, 60545, 459515, 3834877, 34918395, 344426072,

    3658743075, 41641590856, 505537007078, 6520890948629, 89060420281323,

    1283936507112947, 19484029813045395]

                                       ""

                             "Class ", 106, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 246, 1162, 6146, 35602, 225078, 1535634, 11252520, 87980582,

    730936978, 6424649522, 59542865176, 580017124482, 5922528457026,

    63234234385574, 704404373427440]

                                       ""

                             "Class ", 107, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}

                             "Class ", 108, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}

                             "Class ", 109, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 59, 266, 1372, 8055, 52938, 384654, 3063962, 26541000, 248382032,

    2497513548, 26851035270, 307364169660, 3732280717490, 47916909980098,

    648511949068350, 9228065613117600]

                                       ""

                             "Class ", 110, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 57, 235, 1071, 5395, 29496, 173858, 1095217, 7332252, 51897052,

    386733370, 3023206699, 24715191749, 210726976794, 1869388348938,

    17217964308907, 164340561217279]

                                       ""

                             "Class ", 111, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}

                             "Class ", 112, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}

                             "Class ", 113, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}],

    [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 63, 291, 1560, 9457, 64067, 479343, 3922677, 34858996, 334168379,

    3437124179, 37754352016, 441049534943, 5460032453551, 71399464016582,

    983425159879546, 14230330098774463]

                                       ""

                             "Class ", 114, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}],

    [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}],

    [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 272, 1381, 7844, 49101, 334866, 2465353, 19448558, 163394597,

    1454480618, 13658842677, 134814974292, 1394046194601, 15059192865628,

    169521974511217, 1984193892392004]

                                       ""

                             "Class ", 115, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 63, 305, 1699, 10906, 78347, 627577, 5517013, 52988084, 550802575,

    6169789229, 74016965885, 947405131174, 12882336314219, 185492126955761,

    2819071090517353, 45100707672562420]

                                       ""

                             "Class ", 116, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {}],

    [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 276, 1458, 8768, 58917, 438005, 3564501, 31528216, 301037679,

    3085936138, 33799124342, 393878677474, 4865862392375, 63515924950899,

    873505460940801, 12623299169602904]

                                       ""

                             "Class ", 117, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}],

    [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {2, 3}, {}],

    [[2, 4, 1, 3], {2, 3}, {}], [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {}, {}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 274, 1432, 8550, 56804, 417662, 3353788, 29247346, 274835978,

    2769688512, 29777558982, 340227880284, 4115506849336, 52540603058226,

    705852395170444, 9953537145950506]

                                       ""

                             "Class ", 118, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 3, 2, 4], {1, 2}, {}],

    [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {2}, {}],

    [[2, 3, 1, 4], {2, 3}, {[1, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {2, 3}, {[1, 0, 0, 0, 0]}],

    [[2, 4, 3, 1], {2}, {[1, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 252, 1242, 6872, 41868, 278120, 1995038, 15344114, 125760816,

    1092856812, 10025655348, 96733066474, 978452113060, 10345900827612,

    114068282781962, 1308435045894328]

                                       ""

                             "Class ", 119, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 265, 1327, 7516, 47138, 326286, 2459642, 20132224, 177295591,

    1675637317, 16883712723, 180977390644, 2053417327682, 24616892752186,

    310594486535394, 4117960947215777]

                                       ""

                             "Class ", 120, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 57, 229, 991, 4628, 22870, 119418, 652389, 3721100, 22035467,

    135207321, 856596699, 5593867732, 37563949753, 259021702676, 1830873441634,

    13250245136596]

                                       ""

                             "Class ", 121, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}

                {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}],

    [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 242, 1103, 5525, 29595, 169937, 1029666, 6588461, 44086487,

    308492140, 2242911708, 16936199612, 132232351764, 1066848957406,

    8866237379871, 75847868855822]

                                       ""

                             "Class ", 122, " is:"

{{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {2, 3}, {[0, 0, 1, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 56, 218, 897, 3907, 17677, 82864, 399191, 1970684, 9928426,

    50931050, 265381781, 1402206785, 7500986535, 40574241582, 221679865651,

    1222204655828]

                                       ""

                             "Class ", 123, " is:"

{{[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 59, 266, 1372, 8055, 52938, 384654, 3063962, 26541000, 248382032,

    2497513548, 26851035270, 307364169660, 3732280717490, 47916909980098,

    648511949068350, 9228065613117600]

                                       ""

                             "Class ", 124, " is:"

{{[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}

                {[[1, 2, 3], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}

                             "Class ", 125, " is:"

{{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 58, 253, 1261, 7117, 44746, 310191, 2349777, 19308353, 171039094,

    1624655139, 16471928453, 177538811649, 2027045161202, 24438858713647,

    310253174432089, 4136776437957105]

                                       ""

                             "Class ", 126, " is:"

{{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}],

    [[3, 2, 1, 4], {3}, {[1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {3}, {[1, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2}, {}],

    [[4, 2, 1, 3], {3}, {[1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {3}, {[1, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 4, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 55, 212, 906, 4230, 21216, 114038, 648203, 3896395, 24523384,

    161721186, 1108949538, 7913947648, 58427103155, 446630088759, 3518178364565,

    28579895677072]

                                       ""

                             "Class ", 127, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}

                             "Class ", 128, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {4}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 202, 858, 3910, 18846, 95058, 497753, 2689378, 14922925,

    84723384, 490684063, 2891959557, 17310136848, 105050168977, 645452775947,

    4010312288705]

                                       ""

                             "Class ", 129, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 774, 3355, 15430, 74833, 380844, 2025738, 11224073,

    64599699, 385292336, 2376530794, 15132762345, 99319527470, 670944865852,

    4659403296358]

                                       ""

                             "Class ", 130, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 189, 748, 3128, 13731, 62969, 300552, 1488704, 7634723,

    40464741, 221311617, 1247444859, 7238458309, 43196661875, 264878725516,

    1667564565616]

                                       ""

                             "Class ", 131, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104,

    36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982,

    830830093074]

                                       ""

                             "Class ", 132, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [

    [2, 5, 4, 1, 3], {1, 2, 3},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [

    [3, 5, 4, 1, 2], {1, 2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[3, 5, 4, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645,

    19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775,

    173164232965]

                                       ""

                             "Class ", 133, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3],

    {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}],

    [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865,

    77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932,

    6842825911529]

                                       ""

                             "Class ", 134, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 135, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}

                             "Class ", 136, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}

                             "Class ", 137, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[1, 4, 2, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 791, 3533, 16970, 87119, 475756, 2752618, 16812999,

    108073046, 729045955, 5148347450, 37971933864, 291898543398, 2334232485424,

    19383607067271]

                                       ""

                             "Class ", 138, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]

    , [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879,

    57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734,

    3934345877165]

                                       ""

                             "Class ", 139, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}

                             "Class ", 140, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}

                             "Class ", 141, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 163, 651, 2842, 13464, 68665, 374496, 2172962, 13353087,

    86556359, 589795725, 4211908036, 31439004244, 244700159475, 1981737718395,

    16667383911285]

                                       ""

                             "Class ", 142, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 511, 1950, 7903, 33848, 152529, 720466, 3555715,

    18285538, 97752779, 542107657, 3112916651, 18477588573, 113203102619,

    714836382820]

                                       ""

                             "Class ", 143, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 509, 1922, 7651, 31965, 139685, 636712, 3020203,

    14878176, 75982829, 401654560, 2194564531, 12377765239, 71980880885,

    431114329728]

                                       ""

                             "Class ", 144, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 145, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 3, 2, 4], {2, 3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 4, 3, 2], {3}, {[0, 0, 0, 0, 0, 1]}],

    [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 154, 590, 2449, 10969, 52793, 271632, 1487582, 8640969,

    53060555, 343302845, 2333356129, 16615886986, 123662079003, 959692248484,

    7750147292257]

                                       ""

                             "Class ", 146, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 147, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 509, 1922, 7651, 31965, 139685, 636712, 3020203,

    14878176, 75982829, 401654560, 2194564531, 12377765239, 71980880885,

    431114329728]

                                       ""

                             "Class ", 148, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 149, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 152, 570, 2305, 9982, 46034, 224949, 1159395, 6277554,

    35583262, 210513471, 1296445497, 8292252126, 54973781425, 377068640847,

    2671541279041]

                                       ""

                             "Class ", 150, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 151, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 125, 395, 1283, 4253, 14326, 48905, 168845, 588558, 2068517,

    7321903, 26079650, 93406417, 336189552, 1215348309, 4410991345]

                                       ""

                             "Class ", 152, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3],

    {1, 2, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 114, 324, 920, 2612, 7416, 21056, 59784, 169744, 481952,

    1368400, 3885280, 11031424, 31321376, 88930368, 252498816]

                                       ""

                             "Class ", 153, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 150, 548, 2125, 8678, 37120, 165541, 766885, 3679078,

    18230700, 93100559, 489037283, 2637743688, 14587090273, 82597362151,

    478300294453]

                                       ""

                             "Class ", 154, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 155, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 125, 395, 1283, 4253, 14326, 48905, 168845, 588558, 2068517,

    7321903, 26079650, 93406417, 336189552, 1215348309, 4410991345]

                                       ""

                             "Class ", 156, " is:"

{{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3],

    {1, 2, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 114, 324, 920, 2612, 7416, 21056, 59784, 169744, 481952,

    1368400, 3885280, 11031424, 31321376, 88930368, 252498816]

                                       ""

                             "Class ", 157, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}],

    [[3, 1, 5, 4, 2], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}],

    [[3, 2, 5, 4, 1], {2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 193, 799, 3577, 17160, 87607, 473331, 2694115, 16092976,

    100559389, 655496474, 4446657704, 31325304206, 228740684791, 1728439184901,

    13495130795651]

                                       ""

                             "Class ", 158, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 774, 3351, 15361, 74043, 373270, 1959528, 10673756,

    60148231, 349756973, 2094116131, 12885558053, 81349014977, 526150688678,

    3481840090140]

                                       ""

                             "Class ", 159, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 786, 3455, 16157, 79828, 414475, 2251807, 12756912,

    75144750, 459145471, 2904137018, 18981839396, 128011946008, 889546078999,

    6361655315141]

                                       ""

                             "Class ", 160, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104,

    36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982,

    830830093074]

                                       ""

                             "Class ", 161, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 159, 610, 2526, 11175, 52535, 261171, 1366731, 7502298,

    43059201, 257676391, 1603855292, 10360712555, 69327442973, 479686571701,

    3426604861543]

                                       ""

                             "Class ", 162, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 163, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 157, 592, 2384, 10151, 45489, 213233, 1041639, 5283914,

    27750937, 150530003, 841448736, 4838152197, 28565898801, 172937366241,

    1072079347567]

                                       ""

                             "Class ", 164, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 165, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 148, 528, 1972, 7647, 30605, 125801, 529131, 2270481, 9914870,

    43973755, 197744417, 900327160, 4145285618, 19280282194, 90507546094]

                                       ""

                             "Class ", 166, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 167, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 148, 528, 1972, 7647, 30605, 125801, 529131, 2270481, 9914870,

    43973755, 197744417, 900327160, 4145285618, 19280282194, 90507546094]

                                       ""

                             "Class ", 168, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {2}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 3, 1], {2, 3}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1}, {[0, 0, 0, 1, 0]}],

    [[3, 2, 4, 1], {1, 3}, {[0, 0, 0, 1, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}],

    [[4, 2, 3, 1], {1, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 169, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 4, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}],

    [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 786, 3458, 16203, 80311, 418797, 2287568, 13040865,

    77352253, 476146324, 3034799869, 19988819454, 135818335121, 950548577932,

    6842825911529]

                                       ""

                             "Class ", 170, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 171, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}

                             "Class ", 172, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}

                             "Class ", 173, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 792, 3547, 17116, 88449, 486971, 2843675, 17543335,

    113946582, 776826147, 5543704417, 41311665744, 320767016895, 2589938380709,

    21706428030664]

                                       ""

                             "Class ", 174, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 4, 3, 1], {1, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 763, 3270, 14844, 70961, 355673, 1862785, 10165879,

    57673186, 339443431, 2068967527, 13039101751, 84846212977, 569306441734,

    3934345877165]

                                       ""

                             "Class ", 175, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}

                             "Class ", 176, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}],

    [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {}, {[0, 0, 1, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 4, 3], {4}, {}],

    [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 4, 2], {4}, {[0, 0, 1, 0, 0, 0]}],

    [[3, 2, 5, 4, 1], {1, 2, 4}, {}],

    [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 5, 3, 2], {4}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[4, 2, 5, 3, 1], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645,

    19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775,

    173164232965]

                                       ""

                             "Class ", 177, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 172, 709, 3204, 15729, 83047, 468720, 2813231, 17869342,

    119646823, 841595247, 6200150985, 47713644735, 382647615183, 3191189820180,

    27623326449417]

                                       ""

                             "Class ", 178, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 164, 660, 2898, 13796, 70669, 386855, 2251488, 13871293,

    90115306, 615221609, 4400766740, 32896421153, 256372020585, 2078626066997,

    17500008323559]

                                       ""

                             "Class ", 179, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}

                             "Class ", 180, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}

                             "Class ", 181, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 4, 3, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 154, 590, 2449, 10969, 52793, 271632, 1487582, 8640969,

    53060555, 343302845, 2333356129, 16615886986, 123662079003, 959692248484,

    7750147292257]

                                       ""

                             "Class ", 182, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}

                             "Class ", 183, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 184, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}

                             "Class ", 185, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 164, 667, 2968, 14285, 73852, 407905, 2393990, 14857645,

    97123306, 666546143, 4788823532, 35924878745, 280751016210, 2280922949747,

    19229165773510]

                                       ""

                             "Class ", 186, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 511, 1950, 7903, 33848, 152529, 720466, 3555715,

    18285538, 97752779, 542107657, 3112916651, 18477588573, 113203102619,

    714836382820]

                                       ""

                             "Class ", 187, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}

                             "Class ", 188, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3],

    {1, 2, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 126, 411, 1428, 5267, 20510, 83935, 359846, 1612345, 7534236,

    36639345, 185057658, 968980753, 5251165342, 29409412955, 169988968164]

                                       ""

                             "Class ", 189, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 510, 1935, 7755, 32644, 143623, 657813, 3125756,

    15364769, 77935525, 407050532, 2184985805, 12034220019, 67907882752,

    392091927591]

                                       ""

                             "Class ", 190, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1}, {[0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 191, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {}, {}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}],

    [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 5, 3, 2], {3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [

    [4, 2, 5, 3, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[5, 1, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 4, 3, 2], {3}, {[0, 0, 0, 1, 0, 0]}], [[5, 2, 4, 3, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 113, 315, 871, 2400, 6607, 18190, 50094, 137985, 380123,

    1047205, 2884966, 7947805, 21895322, 60319000, 166171449]

                                       ""

                             "Class ", 192, " is:"

{{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {}, {}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {3}, {[0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 4, 3], {3}, {[0, 0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 4, 2], {3}, {[0, 0, 0, 0, 1, 0]}],

    [[3, 2, 5, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}],

    [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 5, 3, 2], {3, 4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [

    [4, 2, 5, 3, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 113, 315, 871, 2400, 6607, 18190, 50094, 137985, 380123,

    1047205, 2884966, 7947805, 21895322, 60319000, 166171449]

                                       ""

                             "Class ", 193, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}

                             "Class ", 194, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}

                             "Class ", 195, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}

                             "Class ", 196, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}

                             "Class ", 197, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 169, 691, 3083, 14887, 77187, 427289, 2512003, 15612803,

    102195876, 702197948, 5050241582, 37920986752, 296598019101, 2411510556145,

    20344282029055]

                                       ""

                             "Class ", 198, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 151, 561, 2229, 9413, 41979, 196860, 966823, 4957199,

    26459906, 146679513, 842659238, 5007592446, 30730781759, 194463489383,

    1267169115447]

                                       ""

                             "Class ", 199, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}

                             "Class ", 200, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}

                             "Class ", 201, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 151, 561, 2234, 9464, 42388, 199726, 986076, 5084346,

    27301803, 152307928, 880842734, 5271006575, 32581583929, 207718414778,

    1363979372507]

                                       ""

                             "Class ", 202, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}

                             "Class ", 203, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}

                             "Class ", 204, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}

                             "Class ", 205, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [

    [4, 3, 1, 2], {1, 2, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 166, 652, 2780, 12644, 61136, 312676, 1680592, 9467680,

    55704104, 341185496, 2170853456, 14314313872, 97620050080, 687418278544,

    4989946902176]

                                       ""

                             "Class ", 206, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 166, 652, 2780, 12644, 61136, 312676, 1680592, 9467680,

    55704104, 341185496, 2170853456, 14314313872, 97620050080, 687418278544,

    4989946902176]

                                       ""

                             "Class ", 207, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}

                             "Class ", 208, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}

                             "Class ", 209, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 156, 584, 2322, 9735, 42786, 196042, 933126, 4597647,

    23388334, 122544410, 660019654, 3647807718, 20656436184, 119685898938,

    708715670168]

                                       ""

                             "Class ", 210, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {[0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 156, 584, 2322, 9735, 42786, 196042, 933126, 4597647,

    23388334, 122544410, 660019654, 3647807718, 20656436184, 119685898938,

    708715670168]

                                       ""

                             "Class ", 211, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}

                             "Class ", 212, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}

                             "Class ", 213, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 172, 713, 3226, 15828, 83545, 471064, 2821542, 17874936,

    119309929, 836183548, 6135225538, 47004065712, 375155599641, 3112835462636,

    26801346384659]

                                       ""

                             "Class ", 214, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 151, 561, 2229, 9413, 41979, 196860, 966823, 4957199,

    26459906, 146679513, 842659238, 5007592446, 30730781759, 194463489383,

    1267169115447]

                                       ""

                             "Class ", 215, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}

                             "Class ", 216, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}],

    [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {}, {}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 4, 3], {4}, {}],

    [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 5, 4, 2], {4}, {}], [[3, 2, 5, 4, 1], {1, 2, 4}, {}],

    [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 5, 3, 1], {1, 2, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 217, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 164, 657, 2864, 13524, 68632, 371765, 2139760, 13034231,

    83709409, 564941683, 3995273377, 29532301182, 227642133423, 1826036913659,

    15214273973801]

                                       ""

                             "Class ", 218, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 498, 1839, 7111, 28684, 120377, 524523, 2369290,

    11080464, 53596317, 267895326, 1382620522, 7362469062, 40421370697,

    228640754174]

                                       ""

                             "Class ", 219, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}

                             "Class ", 220, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 1, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {3}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {}, {}],

    [[2, 4, 3, 1], {1, 3}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1}, {[0, 1, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 4, 3], {4}, {}], [[3, 1, 5, 4, 2], {1, 4}, {[0, 1, 0, 0, 0, 0]}],

    [[3, 2, 5, 4, 1], {1, 2, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 221, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 48, 186, 795, 3729, 18949, 103470, 603274, 3734937, 24442163,

    168419418, 1217802237, 9213321266, 72741995834, 597976896008, 5107637247525,

    45246797016193]

                                       ""

                             "Class ", 222, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 170, 691, 3073, 14809, 76666, 423886, 2490514, 15479614,

    101389508, 697513653, 5025406212, 37819960947, 296618360520, 2419362514273,

    20484053318220]

                                       ""

                             "Class ", 223, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 164, 661, 2906, 13829, 70736, 386397, 2242118, 13759933,

    88975628, 604202693, 4296191090, 31904681877, 246886692680, 1986631886029,

    16592212576862]

                                       ""

                             "Class ", 224, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 153, 578, 2346, 10161, 46700, 226618, 1156188, 6180078,

    34506047, 200723708, 1213668400, 7612138774, 49433580135, 331841260249,

    2299237321171]

                                       ""

                             "Class ", 225, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 4, 3, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 163, 653, 2859, 13567, 69280, 378291, 2196956, 13509767,

    87623403, 597388111, 4268272885, 31875143825, 248214101530, 2011174795281,

    16923373842350]

                                       ""

                             "Class ", 226, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}

                             "Class ", 227, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {2}, {}],

    [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 144, 523, 2048, 8597, 38486, 182905, 919146, 4866871,

    27068420, 157693007, 959873708, 6091057009, 40213034874, 275699950381,

    1959625294310]

                                       ""

                             "Class ", 228, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}

                             "Class ", 229, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 172, 713, 3226, 15828, 83545, 471064, 2821542, 17874936,

    119309929, 836183548, 6135225538, 47004065712, 375155599641, 3112835462636,

    26801346384659]

                                       ""

                             "Class ", 230, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 159, 638, 2788, 13214, 67505, 368771, 2142156, 13176720,

    85493737, 583039933, 4166653728, 31121143039, 242366564051, 1963864310862,

    16524849438830]

                                       ""

                             "Class ", 231, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 4, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 150, 572, 2363, 10493, 49800, 251206, 1340438, 7536412,

    44495915, 275061432, 1775644293, 11942283829, 83506399012, 605953774013,

    4555226747377]

                                       ""

                             "Class ", 232, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]

    , [[2, 4, 3, 1], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}], [[3, 4, 1, 2],

    {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 141, 516, 2028, 8506, 37901, 178556, 885480, 4605474,

    25046334, 142050411, 838192687, 5134860534, 32596754356, 214063570085,

    1451998278531]

                                       ""

                             "Class ", 233, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 510, 1935, 7755, 32644, 143623, 657813, 3125756,

    15364769, 77935525, 407050532, 2184985805, 12034220019, 67907882752,

    392091927591]

                                       ""

                             "Class ", 234, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 124, 385, 1221, 3940, 12897, 42724, 142971, 482598, 1641263,

    5618421, 19344388, 66945021, 232737815, 812455710, 2846716530]

                                       ""

                             "Class ", 235, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1}, {}],

    [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 126, 404, 1346, 4645, 16556, 60805, 229638, 890228, 3537004,

    14383021, 59787906, 253774985, 1098820926, 4849067432, 21791543502]

                                       ""

                             "Class ", 236, " is:"

{{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {3}, {[0, 0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1}, {}],

    [[2, 4, 3, 1], {1, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 4, 2], {1}, {}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {3}, {[0, 0, 1, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 116, 341, 1014, 3045, 9222, 28137, 86408, 266887, 828560,

    2584111, 8092646, 25438494, 80235386, 253854855, 805447478]

                                       ""

                             "Class ", 237, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}

                             "Class ", 238, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}

                             "Class ", 239, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}

                             "Class ", 240, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 5, 3, 4], {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 2, 4],

    {5}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}],

    [[3, 1, 5, 4, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0]}],

    [[3, 2, 5, 4, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}],

    [[4, 1, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 1, 5, 3, 2],

    {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[4, 2, 5, 3, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 50, 177, 649, 2431, 9230, 35360, 136306, 527782, 2050404, 7986175,

    31169025, 121850895, 477018390, 1869614340, 7335165750, 28804094850]

                                       ""

                             "Class ", 241, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 155, 606, 2599, 12110, 60841, 327464, 1877593, 11413461,

    73252993, 494625939, 3502767572, 25943368434, 200472126922, 1612645708006,

    13477870957065]

                                       ""

                             "Class ", 242, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 147, 560, 2345, 10664, 52308, 275172, 1543313, 9181669,

    57711528, 381901028, 2652142055, 19274120822, 146220736987, 1155408032977,

    9490291814145]

                                       ""

                             "Class ", 243, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}

                             "Class ", 244, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}

                             "Class ", 245, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 246, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 247, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}

                             "Class ", 248, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4],

    {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[2, 1, 5, 4, 3], {4}, {[0, 0, 0, 0, 0, 1]}],

    [[3, 1, 5, 4, 2], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]}],

    [[3, 2, 5, 4, 1], {1, 2, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 110, 288, 722, 1748, 4118, 9496, 21530, 48156, 106526, 233504,

    507938, 1097764, 2359334, 5046312, 10747946]

                                       ""

                             "Class ", 249, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 153, 587, 2460, 11179, 54627, 285370, 1585202, 9324817,

    57860702, 377466967, 2581147862, 18452498284, 137588334279, 1067781363385,

    8608445181936]

                                       ""

                             "Class ", 250, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 438, 1516, 5500, 20728, 81308, 329864, 1384952, 5991216,

    26704104, 122254224, 574704400, 2767755808, 13649774032, 68816419040]

                                       ""

                             "Class ", 251, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}

                             "Class ", 252, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}

                             "Class ", 253, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 254, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 438, 1516, 5500, 20728, 81308, 329864, 1384952, 5991216,

    26704104, 122254224, 574704400, 2767755808, 13649774032, 68816419040]

                                       ""

                             "Class ", 255, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}

                             "Class ", 256, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}

                             "Class ", 257, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 158, 638, 2836, 13716, 71574, 400006, 2380072, 15004623,

    99805064, 697912646, 5114583579, 39172850261, 312799400046, 2598405540813,

    22410894936480]

                                       ""

                             "Class ", 258, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 147, 560, 2345, 10664, 52308, 275172, 1543313, 9181669,

    57711528, 381901028, 2652142055, 19274120822, 146220736987, 1155408032977,

    9490291814145]

                                       ""

                             "Class ", 259, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}

                             "Class ", 260, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}

                             "Class ", 261, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {2}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 147, 561, 2363, 10854, 53914, 287613, 1637430, 9895282,

    63196205, 424934922, 2998429299, 22138577245, 170602189610, 1369037392756,

    11417193986548]

                                       ""

                             "Class ", 262, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 455, 1642, 6273, 25256, 106756, 472352, 2182249,

    10503282, 52554409, 272841606, 1467117830, 8158027910, 46843387855,

    277385156386]

                                       ""

                             "Class ", 263, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}

                             "Class ", 264, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}

                             "Class ", 265, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 165, 680, 3092, 15303, 81662, 466531, 2836599, 18264518,

    124016494, 884803141, 6612309978, 51618936427, 419915032477, 3551995288142,

    31181771080780]

                                       ""

                             "Class ", 266, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 438, 1516, 5500, 20728, 81308, 329864, 1384952, 5991216,

    26704104, 122254224, 574704400, 2767755808, 13649774032, 68816419040]

                                       ""

                             "Class ", 267, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 138, 492, 1896, 7848, 34704, 163152, 812016, 4262688,

    23524704, 136088352, 823085856, 5192599968, 34097965344, 232621882272,

    1645889315616]

                                       ""

                             "Class ", 268, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 116, 338, 988, 2893, 8482, 24893, 73118, 214931, 632230,

    1860939, 5480922, 16151955, 47624838, 140496927, 414680682]

                                       ""

                             "Class ", 269, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 136, 485, 1918, 8341, 39420, 200750, 1094862, 6358927,

    39131350, 254077553, 1734584906, 12412987008, 92856608428, 724349792239,

    5879564020614]

                                       ""

                             "Class ", 270, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 39, 102, 243, 526, 1045, 1930, 3353, 5534, 8747, 13326, 19671,

    28254, 39625, 54418, 73357, 97262]

                                       ""

                             "Class ", 271, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}],

    [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [

    [4, 2, 5, 1, 3], {1, 2, 4},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 116, 340, 1004, 2980, 8876, 26500, 79244, 237220, 710636,

    2129860, 6385484, 19148260, 57428396, 172252420, 516691724]

                                       ""

                             "Class ", 272, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 38, 96, 222, 470, 919, 1678, 2891, 4742, 7460, 11324, 16668,

    23886, 33437, 45850, 61729, 81758]

                                       ""

                             "Class ", 273, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [

    [4, 3, 1, 2], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 149, 560, 2300, 10099, 47120, 233836, 1217231, 6656692,

    38095031, 226737362, 1405055497, 9027028435, 59987273465, 412214278522,

    2920164716720]

                                       ""

                             "Class ", 274, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 121, 384, 1292, 4531, 16659, 63592, 252304, 1035057, 4388141,

    19164274, 86137602, 397584319, 1882716427, 9131770536, 45326650184]

                                       ""

                             "Class ", 275, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 39, 111, 324, 975, 3034, 9690, 32002, 108199, 376968, 1343081,

    4911792, 18352978, 70163584, 273762057, 1090220728, 4425588831]

                                       ""

                             "Class ", 276, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 1, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}], [

    [4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0],

    [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 37, 93, 228, 551, 1322, 3148, 7479, 17704, 41857, 98809, 233073,

    549439, 1294701, 3050133, 7184554, 16922269]

                                       ""

                             "Class ", 277, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 40, 117, 345, 1046, 3341, 11298, 39552, 146097, 551217, 2194542,

    8823510, 37502475, 159371145, 717907410, 3204382860, 15210582345]

                                       ""

                             "Class ", 278, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 37, 90, 188, 340, 558, 854, 1240, 1728, 2330, 3058, 3924, 4940,

    6118, 7470, 9008, 10744]

                                       ""

                             "Class ", 279, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 5, 1, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [

    [4, 2, 5, 1, 3], {1, 2, 4},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [

    [4, 3, 5, 1, 2], {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

     [1, 2, 5, 14, 37, 87, 169, 242, 192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

                                       ""

                             "Class ", 280, " is:"

{{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 2, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1]}],

    [[3, 2, 1, 4], {3}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {}, {[0, 0, 0, 0, 1], [1, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]

    , [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0],

    [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 2, 5, 1, 4],

    {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [

    [4, 2, 5, 1, 3], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0]}], [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

      [1, 2, 5, 14, 35, 71, 106, 100, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

                                       ""

                             "Class ", 281, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 282, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 283, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2],

    {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 1, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 274, 784, 2264, 6583, 19243, 56486, 166371, 491385,

    1454702, 4314977, 12820703, 38148257, 113654312, 338983417]

                                       ""

                             "Class ", 284, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 2, 0]}],

    [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 285, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 286, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 287, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2],

    {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 1, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 274, 784, 2264, 6583, 19243, 56486, 166371, 491385,

    1454702, 4314977, 12820703, 38148257, 113654312, 338983417]

                                       ""

                             "Class ", 288, " is:"

{{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 1], [0, 2, 0]}],

    [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 289, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 290, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}],

    [[2, 1], {1}, {[0, 0, 2]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 291, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 98, 283, 835, 2504, 7611, 23401, 72652, 227433, 717073,

    2275046, 7257975, 23268696, 74926343, 242220993, 785851014]

                                       ""

                             "Class ", 292, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 293, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 4, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 1, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 294, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2],

    {2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 1, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 312, 963, 3040, 9766, 31817, 104856, 348911, 1170602,

    3955460, 13449022, 45980364, 157970838, 545105733, 1888399098]

                                       ""

                             "Class ", 295, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 296, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3],

    {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 297, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1], [0, 1, 1, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 1, 0], [0, 1, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 298, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}

                {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 234, 619, 1649, 4424, 11949, 32475, 88763, 243866, 673127,

    1865867, 5192003, 14498126, 40614479, 114110735]

                                       ""

                             "Class ", 299, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}

                {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 234, 619, 1649, 4424, 11949, 32475, 88763, 243866, 673127,

    1865867, 5192003, 14498126, 40614479, 114110735]

                                       ""

                             "Class ", 300, " is:"

{{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {3}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2], {3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 74, 163, 347, 722, 1480, 3005, 6065, 12196, 24470, 49031,

    98167, 196454, 393044, 786241, 1572653]

                                       ""

                             "Class ", 301, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 310, 947, 2950, 9337, 29945, 97110, 317917, 1049314,

    3488022, 11666966, 39239988, 132626379, 450235112, 1534504202]

                                       ""

                             "Class ", 302, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 4, 1, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 1, 4, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}],

    [[2, 1], {1}, {[0, 1, 1]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 303, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2], {1, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 312, 961, 3022, 9656, 31265, 102359, 338301, 1127219,

    3782498, 12771232, 43356884, 147908455, 506777659, 1743186126]

                                       ""

                             "Class ", 304, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 611, 1607, 4244, 11263, 30051, 80628, 217544, 590191,

    1609643, 4412026, 12150188, 33606499, 93329351]

                                       ""

                             "Class ", 305, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}

                {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 0]]}

                             "Class ", 306, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 1, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 83, 209, 531, 1365, 3552, 9349, 24859, 66693, 180326, 490897,

    1344363, 3701141, 10237522, 28436805, 79288823]

                                       ""

                             "Class ", 307, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [

    [3, 1, 4, 2], {1, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 98, 283, 835, 2504, 7611, 23401, 72652, 227433, 717073,

    2275046, 7257975, 23268696, 74926343, 242220993, 785851014]

                                       ""

                             "Class ", 308, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 309, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}],

    [[2, 1], {1}, {[0, 2, 0]}], [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}], [

    [2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 2, 0], [0, 1, 1, 0], [0, 2, 0, 0]}

    ]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 82, 201, 489, 1185, 2866, 6925, 16725, 40385, 97506, 235409,

    568337, 1372097, 3312546, 7997205, 19306973]

                                       ""

                             "Class ", 310, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662,

    4038909, 13728369, 46919812, 161143157, 555857157, 1924956954]

                                       ""

                             "Class ", 311, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {3}, {[0, 0, 0, 1], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 312, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 312, 961, 3022, 9656, 31265, 102359, 338301, 1127219,

    3782498, 12771232, 43356884, 147908455, 506777659, 1743186126]

                                       ""

                             "Class ", 313, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 91, 252, 720, 2107, 6280, 18998, 58189, 180092, 562306,

    1769019, 5602038, 17842942, 57122359, 183706349, 593221992]

                                       ""

                             "Class ", 314, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 4, 3],

    {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2],

    {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 1, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[4, 5, 1, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 84, 213, 539, 1361, 3430, 8629, 21673, 54353, 136120, 340453,

    850487, 2122209, 5289930, 13172901, 32772421]

                                       ""

                             "Class ", 315, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 2, 0, 0], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 76, 176, 400, 896, 1984, 4352, 9472, 20480, 44032, 94208,

    200704, 425984, 901120, 1900544, 3997696]

                                       ""

                             "Class ", 316, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}

                {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [

    [2, 4, 3, 1], {1, 2},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 196, 470, 1126, 2699, 6487, 15633, 37788, 91589, 222572,

    542145, 1323446, 3237074, 7932108, 19469151]

                                       ""

                             "Class ", 317, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}

                {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [

    [2, 4, 3, 1], {1, 2},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}], [

    [4, 2, 3, 1], {1, 2},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 31, 67, 133, 246, 429, 712, 1133, 1739, 2587, 3745, 5293, 7324,

    9945, 13278, 17461, 22649]

                                       ""

                             "Class ", 318, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}

                {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    ,

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 31, 68, 139, 270, 505, 919, 1639, 2880, 5005, 8626, 14773, 25177,

    42743, 72340, 122119, 205710]

                                       ""

                             "Class ", 319, " is:"

{{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]

    , [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 30, 61, 112, 190, 303, 460, 671, 947, 1300, 1743, 2290, 2956,

    3757, 4710, 5833, 7145]

                                       ""

                             "Class ", 320, " is:"

{{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 98, 284, 843, 2543, 7767, 23976, 74698, 234573, 741657,

    2358898, 7542201, 24228227, 78157091, 253080046, 822310166]

                                       ""

                             "Class ", 321, " is:"

{{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[3, 2, 1], {2}, {[0, 1, 1, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}], [[3, 1, 4, 2],

    {1, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 72, 148, 281, 499, 838, 1343, 2069, 3082, 4460, 6294, 8689,

    11765, 15658, 20521, 26525]

                                       ""

                             "Class ", 322, " is:"

{{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 3, 2],

    {1, 2, 3, 4}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 30, 61, 112, 202, 354, 651, 1155, 2156, 3861, 7293, 13156, 25090,

    45526, 87516, 159562, 308788]

                                       ""

                             "Class ", 323, " is:"

{{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 2, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 2, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[1, 3, 2], {1}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 2, 0, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1, 2}, {[0, 2, 0, 0], [1, 0, 0, 0]}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {

    [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 2, 0, 0], [0, 1, 1, 0, 0],

    [0, 2, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [

    [3, 1, 4, 2], {1, 2},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}], [

    [3, 2, 4, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 3, 2], {1, 2},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 2, 0, 0, 0]}], [

    [4, 2, 3, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 2, 0, 0, 0], [1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

        [1, 2, 5, 13, 27, 38, 30, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

                                       ""

                             "Class ", 324, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 234, 1147, 6409, 40109, 278790, 2131561, 17770527, 160520515,

    1561497766, 16273913375, 180920965809, 2137026192025, 26727133637226,

    352841047850509, 4903211943667855]

                                       ""

                             "Class ", 325, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 212, 954, 4752, 25969, 154361, 990487, 6819786, 50109385,

    391140040, 3230526785, 28134637874, 257579143318, 2472303560791,

    24817627091303, 259976485672830]

                                       ""

                             "Class ", 326, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 2, 4, 3], {3}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}],

    [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 4, 1], {}, {}],

    [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}],

    [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 3, 5, 2, 4], {3, 4}, {}],

    [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {3}, {}],

    [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}],

    [[2, 3, 4, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 5, 1, 4], {3, 4}, {}],

    [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[2, 4, 5, 3, 1], {3}, {}],

    [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}],

    [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {3}, {}],

    [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}],

    [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 219, 1001, 5046, 27775, 165695, 1062340, 7283557, 53113319,

    410235084, 3343663861, 28663973241, 257717117236, 2423929128723,

    23794401863655, 243281124966296]

                                       ""

                             "Class ", 327, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}

                             "Class ", 328, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}],

    [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}],

    [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}],

    [[1, 4, 5, 3, 2], {4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 228, 1079, 5663, 32647, 205010, 1388603, 10098277, 78354341,

    646001512, 5636288125, 51858287793, 501651549633, 5087825411994,

    53971234830357, 597486949585175]

                                       ""

                             "Class ", 329, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1]}],

    [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [

    [1, 4, 5, 2, 3], {2, 3},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}],

    [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 209, 914, 4325, 21974, 118536, 674890, 4031722, 25167504,

    163568498, 1103602098, 7710545608, 55666084237, 414491623490, 3177955746047,

    25052617962334]

                                       ""

                             "Class ", 330, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {}, {}],

    [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}],

    [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {4}, {}],

    [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 5, 3, 1], {2, 3}, {}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 216, 964, 4646, 24013, 131593, 759099, 4586500, 28881836,

    188957320, 1280246412, 8961562463, 64664061806, 480087274666, 3661253920830,

    28638215769069]

                                       ""

                             "Class ", 331, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}], [

    [1, 4, 5, 2, 3], {2, 3},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 0, 1]}],

    [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 0, 1]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 198, 816, 3561, 16283, 77266, 378058, 1897839, 9737300,

    50908895, 270571932, 1459009348, 7969270383, 44032902349, 245831281893,

    1385392555808]

                                       ""

                             "Class ", 332, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 257, 1228, 6452, 36925, 228407, 1518083, 10784591, 81521786,

    653070719, 5524746781, 49198466694, 459881456225, 4500838695337,

    46015297680328, 490428280382058]

                                       ""

                             "Class ", 333, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}

                             "Class ", 334, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 255, 1195, 6071, 33067, 191572, 1173560, 7565572, 51122021,

    360844593, 2652748304, 20259114000, 160367896395, 1313186353309,

    11104070769446, 96805461173077]

                                       ""

                             "Class ", 335, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}],

    [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2, 5], {2, 3},

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}],

    [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}],

    [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 257, 1218, 6274, 34620, 202638, 1248696, 8055604, 54166570,

    378298651, 2736286925, 20449012083, 157573513543, 1249776687177,

    10187191864992, 85224046587245]

                                       ""

                             "Class ", 336, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}

                             "Class ", 337, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}],

    [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {}, {[0, 0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 3, 4, 2, 5],

    {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0]}],

    [[1, 4, 5, 3, 2], {4}, {[0, 0, 0, 0, 1, 0]}],

    [[2, 4, 5, 3, 1], {2, 3}, {[0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 255, 1188, 5939, 31359, 172944, 988066, 5812511, 35045590,

    215794033, 1353167357, 8621417002, 55707025821, 364479136268, 2411580125396,

    16118232095406]

                                       ""

                             "Class ", 338, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}

                             "Class ", 339, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}

                             "Class ", 340, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 283, 1485, 8806, 58201, 424138, 3378503, 29201571, 272185232,

    2721407941, 29052853374, 329832647149, 3967866398315, 50419466017366,

    674808433239472, 9488327874233227]

                                       ""

                             "Class ", 341, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}],

    [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 3, 5, 2, 4], {2, 3}, {[0, 0, 0, 0, 0, 1]}],

    [[1, 4, 5, 2, 3], {2, 3}, {[0, 0, 0, 0, 0, 1]}], [[1, 4, 5, 3, 2], {4},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 280, 1434, 8155, 50727, 341334, 2463540, 18944172, 154373953,

    1327093675, 11989658314, 113467604012, 1121667427105, 11553148211808,

    123714418435525, 1374567557730910]

                                       ""

                             "Class ", 342, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}

                             "Class ", 343, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}

                             "Class ", 344, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 216, 1003, 5261, 30917, 201798, 1450469, 11388351, 96959521,

    889450892, 8743616507, 91682659773, 1021369686065, 12046826393442,

    149976650013757, 1965357120739559]

                                       ""

                             "Class ", 345, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 346, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}

                             "Class ", 347, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}

                             "Class ", 348, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437,

    190899322, 1382958545, 10480142147, 82864869804, 682076806159,

    5832742205057, 51724158235372]

                                       ""

                             "Class ", 349, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 350, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}

                             "Class ", 351, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}

                             "Class ", 352, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}

                             "Class ", 353, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}

                             "Class ", 354, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 271, 1371, 7779, 48900, 337246, 2531308, 20538784, 179121627,

    1670789896, 16597062037, 174919209206, 1949347785525, 22902975398463,

    282932506370403, 3666170733941919]

                                       ""

                             "Class ", 355, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 267, 1305, 6987, 40433, 250451, 1648435, 11463265, 83839564,

    642488106, 5142699941, 42880786675, 371596750893, 3339915863015,

    31079317910984, 298937766549892]

                                       ""

                             "Class ", 356, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}

                             "Class ", 357, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}

                             "Class ", 358, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}

                             "Class ", 359, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}

                             "Class ", 360, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}],

    [[2, 3, 4, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 282, 1478, 8764, 58020, 424316, 3396916, 29549144, 277536216,

    2799217416, 30175069704, 346222937824, 4212800538560, 54185328375344,

    734553555025280, 10467850927888672]

                                       ""

                             "Class ", 361, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 278, 1408, 7912, 48639, 323726, 2313771, 17640592, 142681797,

    1218678524, 10948964653, 103122539696, 1015206288131, 10419655582692,

    111238936481903, 1232757715352112]

                                       ""

                             "Class ", 362, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}

                             "Class ", 363, " is:"

{{[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}

                             "Class ", 364, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 236, 1175, 6702, 43057, 307873, 2423961, 20823695, 193804280,

    1942369811, 20856123848, 238863111338, 2906620671345, 37449834847975,

    509323114653295, 7291456743619788]

                                       ""

                             "Class ", 365, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 227, 1104, 6121, 38119, 263546, 2001935, 16567001, 148342608,

    1428826334, 14730441781, 161843623703, 1887816736795, 23299010402379,

    303330456642286, 4154470532283076]

                                       ""

                             "Class ", 366, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 223, 1045, 5490, 31899, 203323, 1410404, 10574109, 85207843,

    734306376, 6738349045, 65594715269, 675081851048, 7323396509583,

    83515731242687, 998773216624064]

                                       ""

                             "Class ", 367, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 2, 4], {2}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 213, 963, 4833, 26606, 159312, 1029531, 7133223, 52700869,

    413203132, 3423952396, 29877913175, 273686998709, 2624327668961,

    26275637217953, 274083199917675]

                                       ""

                             "Class ", 368, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 200, 840, 3790, 18179, 91959, 487465, 2694614, 15470190,

    91940680, 564062078, 3563925339, 23143688998, 154195928810, 1052393848368,

    7347759401161]

                                       ""

                             "Class ", 369, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 4, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 189, 750, 3137, 13681, 61730, 286464, 1361085, 6598135,

    32544047, 162954194, 826817907, 4244709536, 22020654628, 115316593500,

    609026306475]

                                       ""

                             "Class ", 370, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}],

    [[1, 4, 3, 2], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}],

    [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {3}, {}],

    [[2, 4, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[2, 5, 4, 3, 1], {3}, {}],

    [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {3}, {}],

    [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 200, 840, 3790, 18179, 91959, 487465, 2694614, 15470190,

    91940680, 564062078, 3563925339, 23143688998, 154195928810, 1052393848368,

    7347759401161]

                                       ""

                             "Class ", 371, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[2, 4, 3, 1], {2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {}, {}],

    [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 3, 1, 2], {1, 2, 3}, {}], [[4, 5, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 189, 750, 3137, 13681, 61730, 286464, 1361085, 6598135,

    32544047, 162954194, 826817907, 4244709536, 22020654628, 115316593500,

    609026306475]

                                       ""

                             "Class ", 372, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 272, 1395, 8089, 52397, 375072, 2939923, 25044256, 230366510,

    2275433564, 24019980848, 269855683744, 3214730968041, 40475835775360,

    537054578045551, 7489852551207675]

                                       ""

                             "Class ", 373, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 282, 1477, 8744, 57714, 420152, 3342913, 28853528, 268470546,

    2678372216, 28516602003, 322706772376, 3867602263506, 48934415811968,

    651760309017429, 9114834595279936]

                                       ""

                             "Class ", 374, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 2, 4], {2}, {[0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}],

    [[2, 1, 3, 4, 5], {3},

    {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 4, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 266, 1302, 7030, 41403, 263794, 1805259, 13192124, 102433517,

    841481234, 7286038350, 66275525831, 631483556132, 6286222953992,

    65226848832627, 703983399464268]

                                       ""

                             "Class ", 375, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}

                             "Class ", 376, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {}, {[0, 0, 0, 1, 0]}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {}],

    [[4, 2, 3, 1], {1, 2}, {}],

    [[3, 1, 2, 4, 5], {4}, {[0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 2, 5, 3], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}],

    [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 279, 1422, 8056, 50031, 337086, 2443586, 18931005, 155869316,

    1357537718, 12456831979, 120011900240, 1210289973564, 12742266859527,

    139723544159576, 1592357411178332]

                                       ""

                             "Class ", 377, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}

                             "Class ", 378, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 250, 1298, 7703, 51467, 381951, 3117345, 27758002, 267770646,

    2781689142, 30961218359, 367586670410, 4636917881385, 61932970235412,

    873164233670970, 12958252984098685]

                                       ""

                             "Class ", 379, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 216, 994, 5076, 28403, 172538, 1129511, 7919314, 59150556,

    468504022, 3919569708, 34518111783, 319030219223, 3086250047021,

    31174921402976, 328110078110137]

                                       ""

                             "Class ", 380, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}

                             "Class ", 381, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}

                             "Class ", 382, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 0, 1, 0]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 247, 1257, 7278, 47147, 337515, 2647102, 22567640, 207755781,

    2054014818, 21704741360, 244103974517, 2911166155596, 36695268945491,

    487451496893356, 6805956072906951]

                                       ""

                             "Class ", 383, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 1, 0]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 214, 961, 4715, 24972, 141474, 851457, 5415799, 36256594,

    254588417, 1869567813, 14321698479, 114191646047, 945809186436,

    8123312069013, 72231752386891]

                                       ""

                             "Class ", 384, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}

                             "Class ", 385, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}

                             "Class ", 386, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3}, {}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 222, 1087, 6113, 38771, 273156, 2116043, 17876769, 163608325,

    1612640390, 17031119279, 191858941845, 2296393841867, 29102639656296,

    389313504492343, 5482049793803645]

                                       ""

                             "Class ", 387, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 206, 920, 4580, 25154, 150932, 981386, 6866406, 51395168,

    409532644, 3459452232, 30867433056, 289984316988, 2860158012088,

    29541687402732, 318793110781220]

                                       ""

                             "Class ", 388, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}

                             "Class ", 389, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}

                             "Class ", 390, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 204, 892, 4297, 22587, 128505, 785859, 5135380, 35679658,

    262432764, 2035859488, 16603448562, 141946540173, 1268878840828,

    11832933358298, 114880851228387]

                                       ""

                             "Class ", 391, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 0, 1, 0]}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 392, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}

                             "Class ", 393, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}

                             "Class ", 394, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 241, 1230, 7168, 47011, 342752, 2749156, 24053385, 227982835,

    2327114126, 25450633537, 296897460287, 3679954208730, 48295017981188,

    669027020081538, 9755764841318196]

                                       ""

                             "Class ", 395, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 216, 994, 5076, 28403, 172538, 1129511, 7919314, 59150556,

    468504022, 3919569708, 34518111783, 319030219223, 3086250047021,

    31174921402976, 328110078110137]

                                       ""

                             "Class ", 396, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}

                             "Class ", 397, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}

                             "Class ", 398, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 0, 1, 0]}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 228, 1106, 6055, 36910, 247839, 1817055, 14439295, 123598699,

    1133643737, 11090461818, 115265065188, 1268207399102, 14725415966647,

    179934053991331, 2307986244575397]

                                       ""

                             "Class ", 399, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}

                             "Class ", 400, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}

                             "Class ", 401, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}

                             "Class ", 402, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}

                             "Class ", 403, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}

                             "Class ", 404, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 281, 1467, 8673, 57259, 417786, 3338240, 28987974, 271836538,

    2737761532, 29472409569, 337728438080, 4104467100697, 52731110006168,

    714054279822292, 10165022913806921]

                                       ""

                             "Class ", 405, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2, 3}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 62, 278, 1408, 7912, 48639, 323726, 2313771, 17640592, 142681797,

    1218678524, 10948964653, 103122539696, 1015206288131, 10419655582692,

    111238936481903, 1232757715352112]

                                       ""

                             "Class ", 406, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}

                             "Class ", 407, " is:"

{{[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}

                             "Class ", 408, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 247, 1276, 7538, 50147, 370699, 3014047, 26732635, 256855009,

    2657782571, 29465593978, 348450020008, 4378193940555, 58246930717200,

    817960088005676, 12091148294626003]

                                       ""

                             "Class ", 409, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 227, 1099, 6018, 36731, 247023, 1814046, 14439997, 123824523,

    1137790027, 11151616241, 116115627311, 1279928772367, 14888831026123,

    182262280804594, 2342061985577646]

                                       ""

                             "Class ", 410, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}

                             "Class ", 411, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}

                             "Class ", 412, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 213, 962, 4809, 26330, 156572, 1003959, 6901907, 50614730,

    394239503, 3249033929, 28234754941, 257950702659, 2470792105206,

    24752985813569, 258796735760664]

                                       ""

                             "Class ", 413, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}],

    [[2, 4, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 202, 867, 4050, 20347, 108929, 616960, 3676696, 22953705,

    149585164, 1014496168, 7141764886, 52067670500, 392350943328, 3050449550117,

    24432012338969]

                                       ""

                             "Class ", 414, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}

                             "Class ", 415, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}

                             "Class ", 416, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 61, 272, 1397, 8120, 52713, 378198, 2971149, 25362997, 233762818,

    2313399979, 24465513080, 275348881614, 3285827712887, 41440345640210,

    550749986349220, 7693077351474040]

                                       ""

                             "Class ", 417, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [0, 1, 0]]}

                             "Class ", 418, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}

                             "Class ", 419, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 0, 1]]}

                             "Class ", 420, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [0, 1, 1]]}

                             "Class ", 421, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 4, 1, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 1, 4, 2], [1, 1, 1]]}

                             "Class ", 422, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}],

    [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 58, 266, 1425, 8735, 60217, 461323, 3887873, 35743902, 356005407,

    3818526028, 43883100528, 537932180981, 7006265650585, 96620486597858,

    1406478000845326, 21551279697085645]

                                       ""

                             "Class ", 423, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 247, 1261, 7344, 47938, 346669, 2751161, 23761398, 221875801,

    2227118818, 23912139251, 273450099712, 3318030253127, 42576643292747,

    576044218136968, 8195370874140308]

                                       ""

                             "Class ", 424, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}

                             "Class ", 425, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}

                             "Class ", 426, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 246, 1254, 7260, 46958, 335861, 2631126, 22400332, 205941934,

    2033268218, 21454658696, 240945992881, 2869382583437, 36116725449993,

    479084488705909, 6679724829687238]

                                       ""

                             "Class ", 427, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1}, {[0, 1, 0, 0]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 225, 1060, 5559, 31946, 199011, 1333383, 9542676, 72548093,

    583246195, 4938969826, 43903762028, 408473224908, 3967214764869,

    40128867353594, 421864138684363]

                                       ""

                             "Class ", 428, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}

                             "Class ", 429, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}

                             "Class ", 430, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 247, 1306, 7873, 53284, 400659, 3315305, 29931131, 292722593,

    3082861040, 34787046402, 418711026536, 5354767435073, 72508617184297,

    1036380957679262, 15592857992580145]

                                       ""

                             "Class ", 431, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 234, 1186, 6838, 44147, 315442, 2470671, 21048026, 193737691,

    1915792141, 20253504248, 227941718928, 2720789253831, 34330180125028,

    456545563593478, 6382140627558919]

                                       ""

                             "Class ", 432, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}

                             "Class ", 433, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}

                             "Class ", 434, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}],

    [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 207, 938, 4749, 26405, 159442, 1037966, 7242298, 53873264,

    425211530, 3546365003, 31144379957, 287123104249, 2771249597447,

    27935108814362, 293456939305590]

                                       ""

                             "Class ", 435, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 1, 0, 0]}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 1, 0, 0, 0]}],

    [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2}, {[0, 0, 1, 0, 0]}],

    [[4, 3, 1, 2], {2}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 790, 3502, 16523, 82292, 430181, 2350019, 13367964,

    78947723, 482846080, 3051776257, 19896783391, 133602311011, 922662248900,

    6545341183117]

                                       ""

                             "Class ", 436, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}

                             "Class ", 437, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}

                             "Class ", 438, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 231, 1151, 6561, 42105, 300293, 2355931, 20162545, 186931557,

    1866389567, 19965740365, 227823415297, 2762105533781, 35457317044945,

    480454769716359, 6852917584220089]

                                       ""

                             "Class ", 439, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 214, 967, 4813, 26085, 152638, 957937, 6412451, 45570321,

    342402934, 2710436095, 22533280701, 196195621437, 1784690607510,

    16923333452477, 166952531526511]

                                       ""

                             "Class ", 440, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {1, 2, 3}, {}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2, 3}, {}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3}, {}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {2, 3}, {}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 205, 907, 4442, 23805, 138313, 864968, 5787919, 41234987,

    311428270, 2484043073, 20855769931, 183774151796, 1695118310937,

    16328941230491, 163924431859610]

                                       ""

                             "Class ", 441, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 202, 858, 3914, 18941, 96415, 513091, 2841508, 16316350,

    96854062, 592845948, 3733887761, 24152746790, 160194862656, 1087880052560,

    7554511381289]

                                       ""

                             "Class ", 442, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1}, {[0, 1, 0, 0]}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 218, 1027, 5461, 32345, 211115, 1505184, 11637861, 96987450,

    866643053, 8265521498, 83805239469, 900138980460, 10209856205272,

    121948691830751, 1529954324547961]

                                       ""

                             "Class ", 443, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 0, 1]]}

                             "Class ", 444, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 1, 0, 0]}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}],

    [[1, 4, 3, 2], {2}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[2, 4, 3, 1], {2}, {[0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 2, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 3, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[4, 5, 3, 2, 1],

    {3}, {[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 194, 817, 3759, 18684, 99429, 562650, 3367674, 21225647,

    140336250, 970078051, 6990435263, 52378574562, 407173070312, 3277282569299,

    27263558457936]

                                       ""

                             "Class ", 445, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 4, 1, 2], [1, 1, 1]]}

                             "Class ", 446, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 222, 1081, 6003, 37541, 260838, 1993313, 16620903, 150129385,

    1460358714, 15220486013, 169206987027, 1998659329745, 24996780567666,

    329996243490637, 4585756271798223]

                                       ""

                             "Class ", 447, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 50, 183, 743, 3314, 15975, 82603, 456466, 2681825, 16665635,

    109129660, 750666249, 5408224521, 40701459996, 319234025975, 2604093290649,

    22051341226220]

                                       ""

                             "Class ", 448, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {}, {}],

    [[3, 4, 1, 2], {3}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4, 5], {1, 2, 3}, {}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2, 3}, {}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3}, {}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {2, 3}, {}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 209, 963, 4982, 28605, 180581, 1242008, 9243071, 73997287,

    633955362, 5786698881, 56059604719, 574403977712, 6205937371557,

    70506729095863, 840260345868434]

                                       ""

                             "Class ", 449, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3}, {[1, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 50, 180, 698, 2888, 12559, 56821, 266183, 1286822, 6398328,

    32626550, 170245278, 907398767, 4932364916, 27305407720, 153767581048,

    879942988175]

                                       ""

                             "Class ", 450, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {1, 2}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 222, 1081, 6003, 37541, 260838, 1993313, 16620903, 150129385,

    1460358714, 15220486013, 169206987027, 1998659329745, 24996780567666,

    329996243490637, 4585756271798223]

                                       ""

                             "Class ", 451, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 2, 3}, {}],

    [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {2}, {[0, 0, 1, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 50, 183, 743, 3314, 15975, 82603, 456466, 2681825, 16665635,

    109129660, 750666249, 5408224521, 40701459996, 319234025975, 2604093290649,

    22051341226220]

                                       ""

                             "Class ", 452, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2}, {}],

    [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 1, 2, 4, 5], {4}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3}, {}], [[4, 1, 2, 5, 3], {1, 2, 3}, {}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {}],

    [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 208, 945, 4777, 26566, 160989, 1053507, 7394824, 55365599,

    439950772, 3694768020, 32674630663, 303301203600, 2946734984779,

    29889227087350, 315799107374715]

                                       ""

                             "Class ", 453, " is:"

{{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {2}, {[0, 0, 1, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 1, 2, 4, 5], {4}, {}], [[3, 1, 2, 5, 4], {1, 2, 3}, {}],

    [[4, 1, 2, 5, 3], {1, 2, 3}, {}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {[0, 0, 1, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 50, 180, 692, 2794, 11677, 50122, 219969, 983364, 4464335,

    20534940, 95533507, 448860988, 2127350417, 10160304084, 48860199333,

    236417283997]

                                       ""

                             "Class ", 454, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 236, 1179, 6719, 43044, 306534, 2400432, 20508890, 189823714,

    1892071059, 20206816110, 230187259638, 2786094731351, 35705369933482,

    483005364212036, 6877762415656366]

                                       ""

                             "Class ", 455, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 223, 1055, 5602, 33104, 215344, 1530306, 11794859, 98013354,

    873507804, 8311011758, 84081594967, 901291065446, 10204041482437,

    121671969721616, 1524086989451724]

                                       ""

                             "Class ", 456, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 0]]}

                             "Class ", 457, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 0]]}

                             "Class ", 458, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 214, 976, 4952, 27628, 167835, 1100907, 7745877, 58132563,

    463220323, 3903496616, 34667437595, 323500012593, 3163283249122,

    32334233509147, 344747601451995]

                                       ""

                             "Class ", 459, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 202, 867, 4050, 20347, 108929, 616960, 3676696, 22953705,

    149585164, 1014496168, 7141764886, 52067670500, 392350943328, 3050449550117,

    24432012338969]

                                       ""

                             "Class ", 460, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [0, 1, 1]]}

                             "Class ", 461, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 3, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 2, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 3, 4, 1], [1, 1, 1]]}

                             "Class ", 462, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 259, 1276, 7088, 43768, 297077, 2197790, 17600992, 151691557,

    1399698327, 13766525311, 143761544661, 1588539799612, 18516601520605,

    227059829467695, 2921868308618943]

                                       ""

                             "Class ", 463, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 0]]}

                             "Class ", 464, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 0]]}

                             "Class ", 465, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 16, 60, 250, 1133, 5518, 28629, 157145, 907268, 5482163, 34525009,

    225830465, 1529933838, 10710185393, 77323758331, 574775698288,

    4392582679927, 34467720910533]

                                       ""

                             "Class ", 466, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [0, 1, 1]]}

                             "Class ", 467, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 4, 2, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 1, 3, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[3, 2, 4, 1], [1, 1, 1]]}

                             "Class ", 468, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}],

    [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 57, 256, 1343, 8072, 54504, 409204, 3379450, 30440319, 297074928,

    3122128613, 35155614027, 422255657647, 5388664849655, 72813384066529,

    1038539443957024, 15592310196052078]

                                       ""

                             "Class ", 469, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 237, 1177, 6658, 42148, 295649, 2277780, 19111497, 173548274,

    1695888125, 17743425328, 197923711716, 2344804072222, 29402689208218,

    389069634493942, 5417992949815810]

                                       ""

                             "Class ", 470, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 0]]}

                             "Class ", 471, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 0]]}

                             "Class ", 472, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}],

    [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 238, 1190, 6760, 42928, 301351, 2317878, 19383367, 175117517,

    1699908027, 17645470136, 195047019402, 2287401731818, 28367041354814,

    370917308549738, 5100139026133440]

                                       ""

                             "Class ", 473, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 225, 1060, 5559, 31946, 199011, 1333383, 9542676, 72548093,

    583246195, 4938969826, 43903762028, 408473224908, 3967214764869,

    40128867353594, 421864138684363]

                                       ""

                             "Class ", 474, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [0, 1, 1]]}

                             "Class ", 475, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 4, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 1, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[2, 4, 3, 1], [1, 1, 1]]}

                             "Class ", 476, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 246, 1285, 7632, 51047, 379882, 3107866, 27729984, 268101742,

    2791548987, 31140262687, 370537287994, 4684669114142, 62711399684009,

    886121712012865, 13180076574164335]

                                       ""

                             "Class ", 477, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 221, 1070, 5864, 35758, 240149, 1761640, 14010804, 120052784,

    1102363141, 10797517031, 112363629915, 1237920255867, 14393258314859,

    176118237604992, 2262196092304674]

                                       ""

                             "Class ", 478, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 1, 0]]}

                             "Class ", 479, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}

                             "Class ", 480, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 207, 938, 4749, 26405, 159442, 1037966, 7242298, 53873264,

    425211530, 3546365003, 31144379957, 287123104249, 2771249597447,

    27935108814362, 293456939305590]

                                       ""

                             "Class ", 481, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 2}, {[1, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 193, 806, 3663, 17865, 92578, 506380, 2909544, 17492997,

    109683801, 715149867, 4836556044, 33854618565, 244806687510, 1825708550099,

    14021681288156]

                                       ""

                             "Class ", 482, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [0, 1, 1]]}

                             "Class ", 483, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 3, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 0]], [[4, 2, 3, 1], [1, 1, 1]]}

                             "Class ", 484, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 57, 260, 1383, 8425, 57743, 439565, 3681065, 33629352, 332823949,

    3547316195, 40508844337, 493431911516, 6386071062647, 87511272349645,

    1265829561461280, 19273601627136534]

                                       ""

                             "Class ", 485, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 248, 1270, 7418, 48527, 351365, 2790693, 24110965, 225124000,

    2258982597, 24240618298, 276999343636, 3358128619967, 43048216016420,

    581792117032546, 8267596128531881]

                                       ""

                             "Class ", 486, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}],

    [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {3, 4}, {}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}],

    [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}],

    [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 2, 3, 4, 1], {3, 4}, {}],

    [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 2, 4, 1], {3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 231, 1149, 6499, 41087, 286737, 2188198, 18121195, 161799130,

    1548992809, 15824566325, 171798746059, 1974840643211, 23958978569249,

    305900851911104, 4099672644898555]

                                       ""

                             "Class ", 487, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 4, 5, 2], {1, 2, 3}, {}],

    [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}],

    [[4, 1, 2, 3, 5], {3}, {}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {}],

    [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}],

    [[5, 1, 2, 3, 4], {3}, {}],

    [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 3, 4, 2], {1, 2, 3}, {}],

    [[5, 2, 3, 4, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 228, 1099, 5928, 35254, 228484, 1599182, 11999272, 95939844,

    813258367, 7277365519, 68489954954, 675750666393, 6969854753885,

    74963616455266, 838874111945721]

                                       ""

                             "Class ", 488, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 55, 238, 1182, 6611, 41079, 280585, 2088887, 16831290, 145909376,

    1353901925, 13387543865, 140519928409, 1560307755943, 18272340868257,

    225062872092644, 2908510777842370]

                                       ""

                             "Class ", 489, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 225, 1053, 5426, 30324, 181813, 1160411, 7836953, 55736543,

    415794255, 3242908244, 26368927090, 222997498250, 1957208758466,

    17794720730953, 167316030294374]

                                       ""

                             "Class ", 490, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}],

    [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {3}, {}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}],

    [[3, 2, 1, 4, 5], {3}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 4, 5, 1], {3}, {}],

    [[3, 2, 5, 1, 4], {1, 2}, {}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 5, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3}, {}],

    [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 216, 991, 5008, 27435, 161170, 1007538, 6662962, 46387180,

    338594463, 2582270707, 20514754368, 169336055698, 1448996452225,

    12827760409816, 117280585941812]

                                       ""

                             "Class ", 491, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 4, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}],

    [[3, 2, 4, 5, 1], {1, 2, 3}, {[0, 1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 213, 944, 4505, 22751, 120121, 657392, 3705967, 21419694,

    126470428, 760656025, 4649557583, 28829675978, 181047194819, 1149992355028,

    7380101908123]

                                       ""

                             "Class ", 492, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 57, 264, 1415, 8651, 59629, 456644, 3845073, 35324187, 351585801,

    3768402336, 43275699299, 530107592163, 6899416639309, 95078750786212,

    1383043889551237, 21177025711771971]

                                       ""

                             "Class ", 493, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 236, 1209, 7029, 45767, 330218, 2614237, 22527407, 209874172,

    2101910000, 22518892761, 256972938001, 3111690495917, 39849368301170,

    538101809031509, 7641181186053727]

                                       ""

                             "Class ", 494, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}],

    [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {3}, {}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 1, 4, 5], {3}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 5, 1], {3, 4}, {}], [[4, 1, 2, 3, 5], {3}, {}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {}], [[4, 2, 1, 3, 5], {3}, {}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {3, 4}, {}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 1, 2, 3, 4], {3}, {}],

    [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 3, 4, 2], {1, 2, 3}, {}], [[5, 2, 1, 3, 4], {3}, {}],

    [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 2, 3, 4, 1], {3, 4}, {}],

    [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 2, 4, 1], {3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 235, 1195, 6887, 44411, 316985, 2478706, 21068723, 193375564,

    1905610837, 20064439731, 224768968815, 2668948264883, 33481592728473,

    442441350484104, 6142447900513459]

                                       ""

                             "Class ", 495, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4], {}, {[1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {}, {[1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {3}, {[1, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 2, 4, 5], {3}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 1, 4, 5, 2], {1, 2, 3}, {}],

    [[3, 2, 1, 4, 5], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 5, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}], [[4, 1, 2, 3, 5], {3}, {}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3}, {}],

    [[4, 2, 1, 3, 5], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 2, 3, 4], {3}, {}],

    [[5, 1, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 1, 3, 4, 2], {1, 2, 3}, {}],

    [[5, 2, 1, 3, 4], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 2, 3, 4, 1], {3, 4}, {[1, 0, 0, 0, 0, 0]}],

    [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 209, 972, 5096, 29396, 184428, 1249882, 9086671, 70418689,

    578759617, 5023327332, 45874451866, 439379350747, 4401165356010,

    45990073037889, 500214087475177]

                                       ""

                             "Class ", 496, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 2}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 56, 252, 1306, 7680, 50586, 368510, 2942407, 25549553, 239672786,

    2415506709, 26028045628, 298597722346, 3633563186411, 46746185609074,

    633939579594122, 9038318339760517]

                                       ""

                             "Class ", 497, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[1, 0, 0, 0]}], [[3, 1, 2, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {2}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 53, 222, 1069, 5708, 33340, 211524, 1444491, 10537633, 81678722,

    669562113, 5780868727, 52384735427, 496730713583, 4915670565949,

    50648099914113, 542187229167601]

                                       ""

                             "Class ", 498, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}],

    [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {3}, {}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}],

    [[3, 2, 1, 4, 5], {3}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 4, 5, 1], {3}, {}],

    [[3, 2, 5, 1, 4], {1, 2}, {}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 5, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3}, {}], [[4, 3, 5, 1, 2], {4}, {}],

    [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 54, 230, 1115, 6006, 35526, 228248, 1578694, 11678932, 91899108,

    765491968, 6722838027, 62035830448, 599632605681, 6055020298466,

    63723526216260, 697447163334784]

                                       ""

                             "Class ", 499, " is:"

{{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 0]], [[1, 2, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}], [[2, 1, 3, 4], {}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {2}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4], {}, {[1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {2}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2}, {[1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2}, {[1, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 1, 3, 4, 5], {3}, {}],

    [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}],

    [[3, 2, 1, 4, 5], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 5, 1], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 5, 1, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 5, 1, 3], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 52, 205, 896, 4207, 20785, 106918, 568684, 3110265, 17417093,

    99540184, 579076184, 3421761720, 20500330247, 124342023191, 762555221046,

    4723371050545]

                                       ""

                             "Class ", 500, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 501, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 502, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 503, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [

    [2, 3, 1, 4], {1, 2, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 504, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 505, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 506, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 507, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [

    [2, 3, 1, 4], {1, 2, 3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 508, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 509, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 510, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 511, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 512, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 513, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 514, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 515, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 516, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 517, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 518, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 519, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 520, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 521, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 522, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 523, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 524, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 525, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 526, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 527, " is:"

{{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:"

  {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 528, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 310, 947, 2950, 9337, 29945, 97110, 317917, 1049314,

    3488022, 11666966, 39239988, 132626379, 450235112, 1534504202]

                                       ""

                             "Class ", 529, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 530, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 531, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 532, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}

                             "Class ", 533, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}

                             "Class ", 534, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 535, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 536, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 537, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 538, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 539, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 540, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662,

    4038909, 13728369, 46919812, 161143157, 555857157, 1924956954]

                                       ""

                             "Class ", 541, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 542, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}

                             "Class ", 543, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 544, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}

                             "Class ", 545, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}

                             "Class ", 546, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}

                             "Class ", 547, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}

                             "Class ", 548, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 549, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 550, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}

                             "Class ", 551, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}

                             "Class ", 552, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}

                             "Class ", 553, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}

                             "Class ", 554, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}

                             "Class ", 555, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}

                             "Class ", 556, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}

                             "Class ", 557, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}

                             "Class ", 558, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}

                             "Class ", 559, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}

                             "Class ", 560, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}

                             "Class ", 561, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}

                             "Class ", 562, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}

                             "Class ", 563, " is:"

{{[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}

                             "Class ", 564, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 565, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 566, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}

                             "Class ", 567, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}

                             "Class ", 568, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}

                             "Class ", 569, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}

                             "Class ", 570, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}

                             "Class ", 571, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}

                             "Class ", 572, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}

                             "Class ", 573, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}

                             "Class ", 574, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}

                             "Class ", 575, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}

                             "Class ", 576, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 577, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 578, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}

                             "Class ", 579, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 82, 202, 497, 1224, 3017, 7439, 18343, 45228, 111514, 274945,

    677894, 1671393, 4120937, 10160465, 25051354]

                                       ""

                             "Class ", 580, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}

                             "Class ", 581, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 582, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}

                             "Class ", 583, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 82, 202, 497, 1224, 3017, 7439, 18343, 45228, 111514, 274945,

    677894, 1671393, 4120937, 10160465, 25051354]

                                       ""

                             "Class ", 584, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 318, 990, 3147, 10170, 33312, 110349, 369043, 1244332,

    4225451, 14437860, 49603122, 171248961, 593796453, 2067041691]

                                       ""

                             "Class ", 585, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 586, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}

                             "Class ", 587, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}

                             "Class ", 588, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}

                             "Class ", 589, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}

                             "Class ", 590, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}

                             "Class ", 591, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}

                             "Class ", 592, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 318, 990, 3147, 10170, 33312, 110349, 369043, 1244332,

    4225451, 14437860, 49603122, 171248961, 593796453, 2067041691]

                                       ""

                             "Class ", 593, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 594, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 595, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 596, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}

                             "Class ", 597, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}

                             "Class ", 598, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}

                             "Class ", 599, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}

                             "Class ", 600, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 601, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 602, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 603, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {[0, 0, 1, 0], [1, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2, 3},

    {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 604, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}

                             "Class ", 605, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}

                             "Class ", 606, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}

                             "Class ", 607, " is:"

{{[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}

                             "Class ", 608, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 609, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 311, 955, 2995, 9553, 30896, 101082, 333946, 1112496,

    3732955, 12605029, 42800317, 146046819, 500555447, 1722402303]

                                       ""

                             "Class ", 610, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}

                             "Class ", 611, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}

                             "Class ", 612, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 613, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 614, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 615, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 616, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}

                             "Class ", 617, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}

                             "Class ", 618, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 619, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 620, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 621, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 622, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}

                             "Class ", 623, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 624, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 625, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 626, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}

                             "Class ", 627, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 628, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662,

    4038909, 13728369, 46919812, 161143157, 555857157, 1924956954]

                                       ""

                             "Class ", 629, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 90, 243, 671, 1893, 5442, 15896, 47055, 140856, 425644,

    1296651, 3977669, 12276601, 38093996, 118768897, 371875733]

                                       ""

                             "Class ", 630, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}

                             "Class ", 631, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}

                             "Class ", 632, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 633, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 634, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}

                             "Class ", 635, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}

                {[[2, 1, 3], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}

                             "Class ", 636, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 310, 947, 2950, 9337, 29945, 97110, 317917, 1049314,

    3488022, 11666966, 39239988, 132626379, 450235112, 1534504202]

                                       ""

                             "Class ", 637, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 638, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 639, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 640, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 641, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 642, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 643, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 644, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 645, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 83, 209, 531, 1365, 3552, 9349, 24859, 66693, 180326, 490897,

    1344363, 3701141, 10237522, 28436805, 79288823]

                                       ""

                             "Class ", 646, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 647, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {[1, 0, 0, 0]}], [

    [3, 2, 1, 4], {1, 2, 3},

    {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}], [

    [4, 2, 1, 3], {1, 2, 3},

    {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 31, 66, 127, 225, 373, 586, 881, 1277, 1795, 2458, 3291, 4321,

    5577, 7090, 8893, 11021]

                                       ""

                             "Class ", 648, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 649, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 74, 163, 347, 722, 1480, 3005, 6065, 12196, 24470, 49031,

    98167, 196454, 393044, 786241, 1572653]

                                       ""

                             "Class ", 650, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 651, " is:"

{{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {[1, 0, 0, 0]}], [

    [3, 2, 1, 4], {1, 2, 3},

    {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}]

    , [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 31, 66, 127, 225, 373, 586, 881, 1277, 1795, 2458, 3291, 4321,

    5577, 7090, 8893, 11021]

                                       ""

                             "Class ", 652, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 166, 652, 2780, 12644, 61136, 312676, 1680592, 9467680,

    55704104, 341185496, 2170853456, 14314313872, 97620050080, 687418278544,

    4989946902176]

                                       ""

                             "Class ", 653, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 156, 584, 2322, 9735, 42786, 196042, 933126, 4597647,

    23388334, 122544410, 660019654, 3647807718, 20656436184, 119685898938,

    708715670168]

                                       ""

                             "Class ", 654, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}],

    [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 157, 592, 2384, 10151, 45489, 213233, 1041639, 5283914,

    27750937, 150530003, 841448736, 4838152197, 28565898801, 172937366241,

    1072079347567]

                                       ""

                             "Class ", 655, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 148, 528, 1972, 7647, 30605, 125801, 529131, 2270481, 9914870,

    43973755, 197744417, 900327160, 4145285618, 19280282194, 90507546094]

                                       ""

                             "Class ", 656, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 166, 652, 2780, 12644, 61136, 312676, 1680592, 9467680,

    55704104, 341185496, 2170853456, 14314313872, 97620050080, 687418278544,

    4989946902176]

                                       ""

                             "Class ", 657, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 156, 584, 2322, 9735, 42786, 196042, 933126, 4597647,

    23388334, 122544410, 660019654, 3647807718, 20656436184, 119685898938,

    708715670168]

                                       ""

                             "Class ", 658, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}],

    [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 157, 592, 2384, 10151, 45489, 213233, 1041639, 5283914,

    27750937, 150530003, 841448736, 4838152197, 28565898801, 172937366241,

    1072079347567]

                                       ""

                             "Class ", 659, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 0, 1]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {}, {[0, 0, 0, 0, 1]}],

    [[2, 3, 4, 1], {3}, {[0, 0, 0, 0, 1]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {3, 4}, {[0, 0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 148, 528, 1972, 7647, 30605, 125801, 529131, 2270481, 9914870,

    43973755, 197744417, 900327160, 4145285618, 19280282194, 90507546094]

                                       ""

                             "Class ", 660, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 661, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104,

    36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982,

    830830093074]

                                       ""

                             "Class ", 662, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 663, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 759, 3203, 14129, 64645, 304984, 1476932, 7315104,

    36948515, 189871563, 990732313, 5240487838, 28060898517, 151925192982,

    830830093074]

                                       ""

                             "Class ", 664, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [0, 1, 0]]}

                             "Class ", 665, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]}

                             "Class ", 666, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [0, 1, 1]]}

                             "Class ", 667, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]}

                             "Class ", 668, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 669, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]}

                             "Class ", 670, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 773, 3336, 15207, 72697, 362447, 1876392, 10051083,

    55544661, 315899245, 1845139684, 11048651523, 67719859612, 424287619507,

    2714074517843]

                                       ""

                             "Class ", 671, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]}

                             "Class ", 672, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [0, 1, 0]]}

                             "Class ", 673, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]}

                             "Class ", 674, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [0, 1, 1]]}

                             "Class ", 675, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]}

                             "Class ", 676, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]}

                             "Class ", 677, " is:"

{{[[1, 3, 2], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]}

                             "Class ", 678, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 169, 684, 3027, 14506, 74704, 410959, 2402759, 14864628,

    96931862, 664053595, 4765304949, 35727127967, 279199931117, 2269526565287,

    19153084489750]

                                       ""

                             "Class ", 679, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 160, 621, 2618, 11896, 57931, 301051, 1662754, 9724694,

    60028955, 389924896, 2657899936, 18964287491, 141308877382, 1097273410797,

    8861877157967]

                                       ""

                             "Class ", 680, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {2, 3}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 159, 611, 2529, 11180, 52495, 260512, 1361144, 7463590,

    42832869, 256675107, 1602835688, 10411663977, 70240383875, 491433828181,

    3561093801155]

                                       ""

                             "Class ", 681, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {[0, 0, 0, 1]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 2, 4], {3}, {[0, 0, 0, 0, 1]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {2, 3}, {[0, 0, 0, 0, 1]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 150, 548, 2127, 8717, 37562, 169661, 801485, 3953194,

    20330168, 108881372, 606597507, 3511580257, 21099348404, 131429120398,

    847704815326]

                                       ""

                             "Class ", 682, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 683, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 684, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 685, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 686, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 789, 3504, 16694, 84844, 457903, 2614361, 15738974,

    99622074, 661276128, 4592428258, 33297012678, 251545861356, 1976465482616,

    16124678393524]

                                       ""

                             "Class ", 687, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {[0, 0, 1, 0]}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 2, 4], {3}, {[0, 0, 0, 1, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 190, 761, 3237, 14500, 67998, 332436, 1689268, 8902753,

    48584899, 274240305, 1599727591, 9637474722, 59930980746, 384504930820,

    2543948121073]

                                       ""

                             "Class ", 688, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]}

                             "Class ", 689, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]}

                             "Class ", 690, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 170, 691, 3073, 14809, 76666, 423886, 2490514, 15479614,

    101389508, 697513653, 5025406212, 37819960947, 296618360520, 2419362514273,

    20484053318220]

                                       ""

                             "Class ", 691, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 509, 1922, 7651, 31965, 139685, 636712, 3020203,

    14878176, 75982829, 401654560, 2194564531, 12377765239, 71980880885,

    431114329728]

                                       ""

                             "Class ", 692, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]}

                             "Class ", 693, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1]}],

    [[2, 4, 3, 1], {2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1]}],

    [[3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[3, 5, 2, 4, 1], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}], [

    [4, 5, 2, 3, 1], {1, 2},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 694, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 170, 691, 3073, 14809, 76666, 423886, 2490514, 15479614,

    101389508, 697513653, 5025406212, 37819960947, 296618360520, 2419362514273,

    20484053318220]

                                       ""

                             "Class ", 695, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 509, 1922, 7651, 31965, 139685, 636712, 3020203,

    14878176, 75982829, 401654560, 2194564531, 12377765239, 71980880885,

    431114329728]

                                       ""

                             "Class ", 696, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]}

                             "Class ", 697, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 2, 4], {1, 2, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]}],

    [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2, 4},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 0, 1, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 698, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 699, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[1, 0, 0, 0]}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}],

    [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 700, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {4}, {}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 701, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 702, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 703, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 704, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {4}, {}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 705, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 706, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}],

    [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 163, 650, 2819, 13205, 66394, 356108, 2026961, 12193784,

    77257390, 513893880, 3578535238, 26022556390, 197171537342, 1553524616544,

    12705149238638]

                                       ""

                             "Class ", 707, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 509, 1922, 7651, 31965, 139685, 636712, 3020203,

    14878176, 75982829, 401654560, 2194564531, 12377765239, 71980880885,

    431114329728]

                                       ""

                             "Class ", 708, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 0]]}

                             "Class ", 709, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]}

                             "Class ", 710, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 153, 579, 2356, 10224, 47037, 228317, 1164422, 6217150,

    34644804, 200954104, 1210498098, 7557073290, 48806078579, 325546568953,

    2239382613122]

                                       ""

                             "Class ", 711, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 712, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [0, 1, 1]]}

                             "Class ", 713, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]}

                             "Class ", 714, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]}

                             "Class ", 715, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]}

                             "Class ", 716, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]}

                             "Class ", 717, " is:"

{{[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]}

                             "Class ", 718, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 170, 696, 3108, 15033, 78145, 433719, 2556086, 15926179,

    104515924, 720019737, 5191868276, 39084412481, 306474245502, 2498076845435,

    21126885133724]

                                       ""

                             "Class ", 719, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 0, 1]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 153, 580, 2371, 10371, 48247, 237493, 1231441, 6699860,

    38119342, 226144337, 1395333767, 8933949540, 59239521088, 406073656561,

    2872934746018]

                                       ""

                             "Class ", 720, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 1, 0]]}

                             "Class ", 721, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 0]]}

                             "Class ", 722, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 723, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 724, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 725, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 3, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 3, 4, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 726, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[0, 1, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 192, 791, 3530, 16928, 86710, 472118, 2721105, 16542806,

    105755071, 708978461, 4972092924, 36396332778, 277532143421, 2200421394355,

    18109227996017]

                                       ""

                             "Class ", 727, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 0]]}

                             "Class ", 728, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 0, 1]]}

                             "Class ", 729, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 4, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 4, 1, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 1, 4, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 1, 4, 2], [1, 1, 1]]}

                             "Class ", 730, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2}, {}], [[4, 3, 1, 2], {1, 2}, {}],

    [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 47, 178, 748, 3447, 17244, 92835, 534204, 3267576, 21146313,

    144208503, 1032738971, 7743248516, 60622626001, 494425356400, 4191848590776,

    36874490881252]

                                       ""

                             "Class ", 731, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 162, 644, 2802, 13238, 67437, 368146, 2142108, 13222165,

    86217523, 591740360, 4260980454, 32099072715, 252336424728, 2065330186143,

    17564638082779]

                                       ""

                             "Class ", 732, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 0]]}

                             "Class ", 733, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1]}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 454, 1629, 6168, 24564, 102631, 449009, 2053838, 9808754,

    48842779, 253221093, 1364754026, 7634564623, 44259340375, 265487190171]

                                       ""

                             "Class ", 734, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 161, 636, 2744, 12819, 64391, 345705, 1973694, 11930131,

    76058595, 509728794, 3580448746, 26290859591, 201336518382, 1604627519113,

    13284062637917]

                                       ""

                             "Class ", 735, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 510, 1939, 7828, 33451, 150865, 716134, 3568495,

    18619173, 101475150, 576331173, 3403669770, 20859460386, 132411597351,

    869102782283]

                                       ""

                             "Class ", 736, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [0, 1, 1]]}

                             "Class ", 737, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[1, 4, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1]}],

    [[1, 3, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 4, 2, 3], {3}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 4, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[0, 0, 0, 0, 1], [0, 0, 1, 0, 0]}], [[2, 4, 3, 1],

    {1, 2, 3}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[3, 4, 1, 2], {}, {[0, 0, 0, 0, 1]}], [[3, 4, 2, 1], {1, 2, 3},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 1, 3, 4],

    {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 2, 4], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0]}], [

    [3, 5, 1, 4, 2], {1, 2}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0],

    [0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]}], [[3, 5, 2, 4, 1], {1, 2},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}],

    [[4, 5, 1, 2, 3], {4}, {[0, 0, 0, 0, 0, 1]}], [[4, 5, 1, 3, 2], {1, 2}, {

    [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0],

    [0, 1, 0, 0, 0, 0]}], [[4, 5, 2, 3, 1], {1, 2},

    {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 738, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 156, 619, 2713, 12969, 66951, 370484, 2184580, 13657975,

    90150612, 625915078, 4556556990, 34682753209, 275338046690, 2274741463592,

    19518523261934]

                                       ""

                             "Class ", 739, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {[1, 0, 0, 0]}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 145, 536, 2164, 9499, 45089, 230091, 1255274, 7284455,

    44764781, 290171218, 1977237154, 14120078693, 105396684978, 820336890047,

    6643610995883]

                                       ""

                             "Class ", 740, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 133, 442, 1537, 5583, 21165, 83707, 345324, 1485687, 6663354,

    31134078, 151408319, 765462514, 4017644518, 21860398111, 123120413119]

                                       ""

                             "Class ", 741, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 133, 442, 1537, 5583, 21165, 83707, 345324, 1485687, 6663354,

    31134078, 151408319, 765462514, 4017644518, 21860398111, 123120413119]

                                       ""

                             "Class ", 742, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 455, 1642, 6273, 25256, 106756, 472352, 2182249,

    10503282, 52554409, 272841606, 1467117830, 8158027910, 46843387855,

    277385156386]

                                       ""

                             "Class ", 743, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 744, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 745, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 3, 1, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 746, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {1, 2}, {}],

    [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 154, 592, 2470, 11076, 52978, 268701, 1438223, 8091438,

    47683520, 293457391, 1881070291, 12529426668, 86540675041, 618678639767,

    4570249994025]

                                       ""

                             "Class ", 747, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 498, 1838, 7091, 28448, 118192, 506838, 2237195,

    10141364, 47119768, 224027278, 1088336186, 5395624880, 27268034894,

    140336351644]

                                       ""

                             "Class ", 748, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}],

    [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3}, {}],

    [[2, 3, 1, 4, 5], {1, 2}, {}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2}, {}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2}, {}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {2, 3}, {}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {2, 3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 133, 441, 1523, 5456, 20209, 77186, 303296, 1223725, 5061257,

    21426477, 92724984, 409727159, 1846696836, 8481930786, 39666656131]

                                       ""

                             "Class ", 749, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {[0, 1, 0, 0]}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {3, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 133, 441, 1523, 5456, 20209, 77186, 303296, 1223725, 5061257,

    21426477, 92724984, 409727159, 1846696836, 8481930786, 39666656131]

                                       ""

                             "Class ", 750, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]}

                {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 511, 1950, 7903, 33848, 152529, 720466, 3555715,

    18285538, 97752779, 542107657, 3112916651, 18477588573, 113203102619,

    714836382820]

                                       ""

                             "Class ", 751, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 0, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 0, 1]]}

                             "Class ", 752, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140,

    3703963, 11921353, 38467475, 124409280, 403183707, 1309058762]

                                       ""

                             "Class ", 753, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 4, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {}, {[0, 0, 0, 1], [0, 1, 0, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 0, 1], [0, 1, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 4, 2, 1], {3, 4},

    {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 123, 375, 1157, 3603, 11304, 35683, 113219, 360805, 1154140,

    3703963, 11921353, 38467475, 124409280, 403183707, 1309058762]

                                       ""

                             "Class ", 754, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 155, 608, 2630, 12419, 63440, 347924, 2035709, 12640790,

    82933310, 572697965, 4148875634, 31440426440, 248594609411, 2046230418476,

    17498226615170]

                                       ""

                             "Class ", 755, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 756, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[2, 3, 1, 4], {}, {}],

    [[2, 3, 4, 1], {1}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {}, {}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4, 5], {1, 2}, {}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2}, {}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2}, {}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2, 5], {4}, {}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {2, 3}, {}], [[3, 5, 1, 2, 4], {4}, {}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {2, 3}, {}], [[4, 5, 1, 2, 3], {4}, {}],

    [[4, 5, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 5, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 145, 535, 2143, 9244, 42654, 209390, 1088545, 5968952,

    34403476, 207797159, 1311736943, 8633552562, 59121001805, 420406302358,

    3098963682147]

                                       ""

                             "Class ", 757, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {[1, 0, 0, 0]}], [[1, 2, 3, 4], {2}, {}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {}, {[1, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1}, {[1, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {}, {[1, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[2, 3, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3, 5], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 3, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 4, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 5, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 758, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {}],

    [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 155, 608, 2630, 12419, 63440, 347924, 2035709, 12640790,

    82933310, 572697965, 4148875634, 31440426440, 248594609411, 2046230418476,

    17498226615170]

                                       ""

                             "Class ", 759, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 760, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 144, 522, 2033, 8452, 37308, 174052, 854817, 4404425,

    23736623, 133447201, 780795623, 4744473101, 29884038824, 194781951096,

    1311723379979]

                                       ""

                             "Class ", 761, " is:"

{{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[2, 1, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {2}, {[0, 0, 0, 1]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 762, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 161, 633, 2699, 12355, 60292, 311747, 1699855, 9735104,

    58356537, 365063420, 2377074442, 16073677895, 112642033105, 816596108398,

    6113991289112]

                                       ""

                             "Class ", 763, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 150, 552, 2166, 9014, 39537, 181989, 875697, 4391273,

    22888126, 123722075, 692247191, 4002344544, 23875376720, 146750398409,

    928259219578]

                                       ""

                             "Class ", 764, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 1, 0]]}

                             "Class ", 765, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 0]]}

                             "Class ", 766, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 767, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[0, 0, 1, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 768, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2, 3}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 142, 499, 1850, 7193, 29186, 123109, 538078, 2430355,

    11317646, 54229907, 266906858, 1347262321, 6965034370, 36833528197,

    199037675054]

                                       ""

                             "Class ", 769, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 3, 2], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 2, 3], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[0, 0, 1, 0]}],

    [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 2, 4], {3}, {[0, 0, 1, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 770, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 191, 777, 3401, 15889, 78693, 410897, 2252010, 12908554,

    77148545, 479484267, 3091830200, 20642874392, 142448382345, 1014335180040,

    7442456143905]

                                       ""

                             "Class ", 771, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 0]]}

                             "Class ", 772, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645,

    19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775,

    173164232965]

                                       ""

                             "Class ", 773, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 4, 2, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 1, 3, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {2}, {[0, 1, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645,

    19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775,

    173164232965]

                                       ""

                             "Class ", 774, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 1, 2], {1, 2}, {}],

    [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 171, 707, 3204, 15749, 83300, 470984, 2831087, 18008327,

    120738071, 850305354, 6271355886, 48311807740, 387817605178, 3237192774831,

    28044776158699]

                                       ""

                             "Class ", 775, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 154, 595, 2521, 11630, 58020, 311073, 1782318, 10858328,

    70026479, 476185265, 3402488499, 25467789370, 199148357099, 1622927709427,

    13753569800555]

                                       ""

                             "Class ", 776, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 0]]}

                             "Class ", 777, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 1, 0, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 778, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 3, 1], {2}, {}],

    [[4, 3, 1, 2], {2}, {}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 154, 594, 2504, 11448, 56369, 297135, 1668073, 9927928,

    62397542, 412700501, 2863716410, 20790695332, 157541135556, 1243237147450,

    10197415552495]

                                       ""

                             "Class ", 779, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 0, 1, 0]}], [[3, 1, 2, 4], {1, 3}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 510, 1939, 7828, 33451, 150865, 716134, 3568495,

    18619173, 101475150, 576331173, 3403669770, 20859460386, 132411597351,

    869102782283]

                                       ""

                             "Class ", 780, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [0, 1, 1]]}

                             "Class ", 781, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 4, 2], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 1, 3], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[2, 4, 3, 1], [1, 1, 1]]}

                             "Class ", 782, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 3}, {}],

    [[4, 1, 2, 3], {1, 3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 157, 625, 2724, 12882, 65661, 358184, 2078824, 12777884,

    82855953, 564792174, 4034813818, 30127613130, 234572156578, 1900326225474,

    15987537001596]

                                       ""

                             "Class ", 783, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}],

    [[3, 1, 2], {1}, {[1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 456, 1659, 6445, 26625, 116340, 534978, 2578019,

    12975819, 68031029, 370675556, 2094558286, 12251312062, 74049468472,

    461787381911]

                                       ""

                             "Class ", 784, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 455, 1642, 6273, 25256, 106756, 472352, 2182249,

    10503282, 52554409, 272841606, 1467117830, 8158027910, 46843387855,

    277385156386]

                                       ""

                             "Class ", 785, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [0, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 0]]}

                             "Class ", 786, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 455, 1642, 6273, 25256, 106756, 472352, 2182249,

    10503282, 52554409, 272841606, 1467117830, 8158027910, 46843387855,

    277385156386]

                                       ""

                             "Class ", 787, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {[1, 0, 0, 0]}],

    [[3, 2, 1], {2}, {}], [[3, 1, 2, 4], {1, 3}, {[1, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 788, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 4, 1], {1, 2}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 455, 1642, 6273, 25256, 106756, 472352, 2182249,

    10503282, 52554409, 272841606, 1467117830, 8158027910, 46843387855,

    277385156386]

                                       ""

                             "Class ", 789, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]}

                {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 3, 2, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[3, 2, 1], {1}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 790, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 173, 727, 3359, 16865, 91189, 527205, 3240296, 21070229,

    144365844, 1038606834, 7821848646, 61500766220, 503661435228, 4287151240403,

    37857251495725]

                                       ""

                             "Class ", 791, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 164, 665, 2962, 14345, 74896, 418637, 2490834, 15699317,

    104388608, 729649641, 5344595010, 40913476697, 326524095080, 2710940084725,

    23368683690690]

                                       ""

                             "Class ", 792, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}],

    [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {3}, {}], [[3, 2, 1, 4, 5], {4}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3, 5], {4}, {}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}],

    [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 2, 4, 1], {3, 4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 144, 523, 2048, 8597, 38486, 182905, 919146, 4866871,

    27068420, 157693007, 959873708, 6091057009, 40213034874, 275699950381,

    1959625294310]

                                       ""

                             "Class ", 793, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 144, 523, 2048, 8597, 38486, 182905, 919146, 4866871,

    27068420, 157693007, 959873708, 6091057009, 40213034874, 275699950381,

    1959625294310]

                                       ""

                             "Class ", 794, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 44, 153, 579, 2356, 10224, 47037, 228317, 1164422, 6217150,

    34644804, 200954104, 1210498098, 7557073290, 48806078579, 325546568953,

    2239382613122]

                                       ""

                             "Class ", 795, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[3, 1, 2, 4], {1, 3}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 143, 508, 1907, 7512, 30918, 132566, 590736, 2730485,

    13069804, 64700829, 330889385, 1746483684, 9505268809, 53298432595,

    307655418493]

                                       ""

                             "Class ", 796, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {}, {}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {2}, {}],

    [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {3}, {}], [[3, 1, 2, 4, 5], {4}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4, 5], {4}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {3}, {}], [[3, 2, 5, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {2}, {}], [[4, 2, 5, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3}, {}],

    [[4, 3, 5, 1, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {4}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 797, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 4, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {2}, {[0, 1, 0, 0]}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 1, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[3, 1, 2, 4, 5], {4}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {1, 2, 3}, {[0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440,

    9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420]

                                       ""

                             "Class ", 798, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2}, {}], [[4, 2, 1, 3], {1, 2}, {}],

    [[4, 3, 1, 2], {1, 2}, {}], [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 46, 174, 734, 3397, 17073, 92383, 534394, 3285735, 21371815,

    146464768, 1053892172, 7938081093, 62421809790, 511252570435, 4352109113678,

    38433400907722]

                                       ""

                             "Class ", 799, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {1}, {}],

    [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 146, 551, 2304, 10583, 52876, 284825, 1641964, 10069157,

    65358030, 447156673, 3213073762, 24173358055, 189903097662, 1554056709979,

    13219541120092]

                                       ""

                             "Class ", 800, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4], {}, {}],

    [[3, 2, 4, 1], {3}, {}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 2, 1, 3], {}, {}],

    [[4, 2, 3, 1], {3}, {}], [[4, 3, 1, 2], {}, {}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 2, 1, 4, 5], {4}, {}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3, 5], {4}, {}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2, 5], {4}, {}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {3, 4}, {}], [[5, 2, 1, 3, 4], {4}, {}],

    [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 1, 2, 4], {4}, {}],

    [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 2, 4, 1], {3, 4}, {}], [[5, 4, 1, 2, 3], {4}, {}],

    [[5, 4, 1, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 4, 2, 3, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 146, 549, 2270, 10223, 49730, 259513, 1444286, 8529363,

    53221394, 349592237, 2409622142, 17378786743, 130822808258, 1025576436321,

    8356012921118]

                                       ""

                             "Class ", 801, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {3}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4], {}, {[1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {3}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {}, {[1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {3}, {[1, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4, 5], {4}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3, 5], {4}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 2, 1, 3, 4], {4}, {[1, 0, 0, 0, 0, 0]}],

    [[5, 2, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 1, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 3, 2, 4, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 802, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {}], [[3, 1, 2, 4], {1, 3}, {}], [[3, 2, 1, 4], {1, 2}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2}, {}], [[4, 2, 3, 1], {2}, {}], [[4, 3, 1, 2], {2}, {}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 45, 164, 665, 2958, 14289, 74368, 414261, 2456058, 15424837,

    102200804, 711883185, 5196888790, 39652937145, 315466293736, 2611171493069,

    22442744833362]

                                       ""

                             "Class ", 803, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {1}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}], [[3, 1, 2, 4], {1, 3}, {}],

    [[4, 1, 2, 3], {3}, {}], [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3}, {[1, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 42, 134, 455, 1642, 6273, 25256, 106756, 472352, 2182249,

    10503282, 52554409, 272841606, 1467117830, 8158027910, 46843387855,

    277385156386]

                                       ""

                             "Class ", 804, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]}

                {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {[0, 0, 1]}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 0]}], [[3, 1, 2], {}, {[0, 0, 0, 1]}],

    [[3, 2, 1], {3}, {[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0]}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {3}, {[0, 0, 0, 0, 1]}],

    [[4, 1, 3, 2], {1, 2}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0]}],

    [[4, 2, 3, 1], {}, {[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[5, 2, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[5, 2, 4, 1, 3],

    {3, 4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0]}], [

    [5, 3, 4, 1, 2], {4}, {[0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0],

    [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}],

    [[5, 3, 4, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 43, 145, 534, 2126, 9064, 41089, 196982, 994225, 5263225,

    29128902, 168072937, 1008616244, 6281797211, 40527230987, 270380255580,

    1862517747679]

                                       ""

                             "Class ", 805, " is:"

{{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [0, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [0, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 0]], [[1, 2, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 0]], [[4, 3, 2, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 1, 3], {}, {}], [[2, 3, 1], {1}, {}], [[3, 1, 2], {}, {}],

    [[3, 2, 1], {}, {[1, 0, 0, 0]}], [[2, 1, 3, 4], {3}, {}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4], {}, {}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4], {}, {[1, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {}, {[1, 0, 0, 0, 0]}], [[4, 1, 2, 3], {3}, {}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {2}, {[1, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2}, {[1, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[3, 1, 2, 4, 5], {4}, {}],

    [[3, 1, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 1, 4, 5], {4}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 1, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1, 5], {3}, {[1, 0, 0, 0, 0, 0]}],

    [[3, 2, 5, 1, 4], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 1, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 1, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 2, 3, 5, 1], {2}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 2, 5, 1, 3], {1, 2}, {[1, 0, 0, 0, 0, 0]}],

    [[4, 3, 1, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 2, 5, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 1, 2], {4}, {[0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0]}],

    [[4, 3, 5, 2, 1], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 14, 41, 122, 365, 1094, 3281, 9842, 29525, 88574, 265721, 797162,

    2391485, 7174454, 21523361, 64570082, 193710245, 581130734]

                                       ""

                             "Class ", 806, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 807, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 808, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 809, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 2], [0, 1, 0]}],

    [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 810, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 811, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 812, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 813, " is:"

{{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1, 2}, {[0, 0, 2], [0, 1, 0]}],

    [[2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 814, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 310, 947, 2950, 9337, 29945, 97110, 317917, 1049314,

    3488022, 11666966, 39239988, 132626379, 450235112, 1534504202]

                                       ""

                             "Class ", 815, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2, 3}, {[0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 816, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 817, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}],

    [[2, 1], {1}, {[0, 0, 2]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 818, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}

                             "Class ", 819, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}

                {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {[0, 0, 1, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 820, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 821, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}],

    [[2, 1], {1}, {[0, 0, 2]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 822, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662,

    4038909, 13728369, 46919812, 161143157, 555857157, 1924956954]

                                       ""

                             "Class ", 823, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 824, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 1, 0]]}

                             "Class ", 825, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 826, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662,

    4038909, 13728369, 46919812, 161143157, 555857157, 1924956954]

                                       ""

                             "Class ", 827, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 828, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {2}, {}], [[1, 3, 2], {2}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 829, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 830, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 831, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 832, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [

    [2, 3, 1, 4], {1, 2, 3},

    {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 833, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 834, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {1, 2}, {[0, 0, 1, 0]}]

    }

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 835, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[1, 2, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[1, 3, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 3, 1, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 3, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 836, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[3, 1, 2, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 837, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 0, 1], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 838, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}

                             "Class ", 839, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}],

    [[2, 1], {1}, {[0, 1, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 840, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}

                             "Class ", 841, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]}

                {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {[0, 0, 1]}],

    [[1, 2, 3], {1}, {[0, 1, 0, 0]}], [[1, 3, 2], {2}, {[0, 0, 0, 1]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 842, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}

                             "Class ", 843, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 844, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 845, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}

                             "Class ", 846, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 82, 202, 497, 1224, 3017, 7439, 18343, 45228, 111514, 274945,

    677894, 1671393, 4120937, 10160465, 25051354]

                                       ""

                             "Class ", 847, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}

                             "Class ", 848, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 849, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}

                             "Class ", 850, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 82, 202, 497, 1224, 3017, 7439, 18343, 45228, 111514, 274945,

    677894, 1671393, 4120937, 10160465, 25051354]

                                       ""

                             "Class ", 851, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 318, 990, 3147, 10170, 33312, 110349, 369043, 1244332,

    4225451, 14437860, 49603122, 171248961, 593796453, 2067041691]

                                       ""

                             "Class ", 852, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 853, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 854, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 855, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 0]]}

                {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 0, 1]]}

                             "Class ", 856, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 0, 1]]}

                {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 0, 1]]}

                             "Class ", 857, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}],

    [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[2, 1, 4, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 1, 4, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 2, 4, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 858, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 318, 990, 3147, 10170, 33312, 110349, 369043, 1244332,

    4225451, 14437860, 49603122, 171248961, 593796453, 2067041691]

                                       ""

                             "Class ", 859, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 860, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 861, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 862, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 318, 990, 3147, 10170, 33312, 110349, 369043, 1244332,

    4225451, 14437860, 49603122, 171248961, 593796453, 2067041691]

                                       ""

                             "Class ", 863, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 864, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 865, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 4, 3], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 1, 2], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 866, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 867, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 868, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 869, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 870, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 871, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 872, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}],

    [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {3}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 873, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 874, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 311, 955, 2995, 9553, 30896, 101082, 333946, 1112496,

    3732955, 12605029, 42800317, 146046819, 500555447, 1722402303]

                                       ""

                             "Class ", 875, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 1, 0]]}

                             "Class ", 876, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}],

    [[2, 1], {1}, {[0, 2, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 877, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 878, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 879, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {2, 3}, {[0, 0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 880, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 37, 111, 346, 1109, 3631, 12090, 40809, 139317, 480178, 1668597,

    5839492, 20563032, 72806578, 259036908, 925631892, 3320565922]

                                       ""

                             "Class ", 881, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 882, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 0]]}

                             "Class ", 883, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 884, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 885, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 886, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]}

                {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 1, 0]]}}, " the pattern set ",

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[1, 1, 0]}],

    [[2, 1], {1}, {[0, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 887, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 105, 317, 982, 3105, 9981, 32520, 107157, 356481, 1195662,

    4038909, 13728369, 46919812, 161143157, 555857157, 1924956954]

                                       ""

                             "Class ", 888, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 90, 243, 671, 1893, 5442, 15896, 47055, 140856, 425644,

    1296651, 3977669, 12276601, 38093996, 118768897, 371875733]

                                       ""

                             "Class ", 889, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 890, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 891, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 892, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 893, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {}], [[3, 1, 2, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 2, 3], {2}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 1, 3, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[4, 2, 3, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 894, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 3, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 2, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 2, 3, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0], [1, 0, 0, 0]}], [[3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 895, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 310, 947, 2950, 9337, 29945, 97110, 317917, 1049314,

    3488022, 11666966, 39239988, 132626379, 450235112, 1534504202]

                                       ""

                             "Class ", 896, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 897, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 898, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 899, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {2}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 97, 275, 794, 2327, 6905, 20705, 62642, 190987, 586219,

    1810011, 5617914, 17518463, 54857506, 172431935, 543861219]

                                       ""

                             "Class ", 900, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {2}, {[0, 1, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 901, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}], [[4, 3, 2, 1], {3}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 902, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {1, 2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 36, 104, 309, 939, 2905, 9118, 28964, 92940, 300808, 980864,

    3219205, 10626023, 35252867, 117485454, 393133485, 1320357501]

                                       ""

                             "Class ", 903, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {1, 2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 83, 209, 531, 1365, 3552, 9349, 24859, 66693, 180326, 490897,

    1344363, 3701141, 10237522, 28436805, 79288823]

                                       ""

                             "Class ", 904, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 905, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 31, 66, 127, 225, 373, 586, 881, 1277, 1795, 2458, 3291, 4321,

    5577, 7090, 8893, 11021]

                                       ""

                             "Class ", 906, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4],

    {1, 2, 3}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 2, 1, 3], {2, 3}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {2, 3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 35, 96, 267, 750, 2123, 6046, 17303, 49721, 143365, 414584,

    1201917, 3492117, 10165779, 29643870, 86574831, 253188111]

                                       ""

                             "Class ", 907, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 0, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 0, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 74, 163, 347, 722, 1480, 3005, 6065, 12196, 24470, 49031,

    98167, 196454, 393044, 786241, 1572653]

                                       ""

                             "Class ", 908, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [0, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [0, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 0]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 0]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {}, {}],

    [[3, 2, 1, 4], {1, 4}, {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}]

    , [[4, 2, 1, 3], {1, 4}, {[0, 0, 1, 0, 0], [0, 1, 0, 0, 0]}],

    [[4, 3, 1, 2], {3}, {[0, 1, 0, 0, 0]}],

    [[4, 3, 2, 1], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

                             "Class ", 909, " is:"

{{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[4, 3, 2, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {3}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1, 2}, {[1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 31, 66, 127, 225, 373, 586, 881, 1277, 1795, 2458, 3291, 4321,

    5577, 7090, 8893, 11021]

                                       ""

                             "Class ", 910, " is:"

{{%2, [[2, 4, 3, 1], [1, 1, 1]]}, {%2, [[3, 2, 4, 1], [1, 1, 1]]},

    {%2, [[4, 1, 3, 2], [1, 1, 1]]}, {%2, [[4, 2, 1, 3], [1, 1, 1]]},

    {%1, [[1, 3, 4, 2], [1, 1, 1]]}, {%1, [[1, 4, 2, 3], [1, 1, 1]]},

    {%1, [[2, 3, 1, 4], [1, 1, 1]]}, {%1, [[3, 1, 2, 4], [1, 1, 1]]}}

%1 := [[3, 2, 1], [1, 1]]

%2 := [[1, 2, 3], [1, 1]]

                {[[1, 2, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 1]]}

                {[[1, 2, 3], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}

"For the class ", {{%1, [[2, 4, 3, 1], [1, 1, 1]]},

    {%1, [[3, 2, 4, 1], [1, 1, 1]]}, {%1, [[4, 1, 3, 2], [1, 1, 1]]},

    {%1, [[4, 2, 1, 3], [1, 1, 1]]}, {%2, [[1, 3, 4, 2], [1, 1, 1]]},

    {%2, [[1, 4, 2, 3], [1, 1, 1]]}, {%2, [[2, 3, 1, 4], [1, 1, 1]]},

    {%2, [[3, 1, 2, 4], [1, 1, 1]]}}, " the pattern set ",

    {%1, [[3, 2, 4, 1], [1, 1, 1]]}, " has scheme:"

%1 := [[1, 2, 3], [1, 1]]

%2 := [[3, 2, 1], [1, 1]]

{[[], {}, {}], [[1], {}, {}], [[1, 2], {2}, {[0, 0, 1]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 3}, {[0, 0, 0, 1], [1, 0, 0, 0]}],

    [[3, 1, 2], {1, 3}, {[0, 0, 0, 1], [0, 0, 1, 0]}],

    [[3, 2, 1], {1}, {[0, 1, 0, 1]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 32, 74, 163, 347, 722, 1480, 3005, 6065, 12196, 24470, 49031,

    98167, 196454, 393044, 786241, 1572653]

                                       ""

                             "Class ", 911, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 0, 1], [0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 912, " is:"

{{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 4, 3, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[3, 2, 1, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[2, 3, 4, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}], [[2, 3, 1], {}, {[0, 0, 1, 0]}], [

    [2, 3, 1, 4], {1, 2, 3},

    {[0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [1, 0, 0, 0, 0]}],

    [[2, 4, 1, 3], {1, 2, 3, 4}, {[0, 0, 0, 0, 0]}],

    [[3, 4, 1, 2], {1, 2}, {[0, 0, 0, 1, 0], [0, 1, 0, 0, 0]}],

    [[3, 4, 2, 1], {3}, {[0, 0, 0, 1, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 913, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[4, 2, 1, 3], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[2, 4, 3, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 1, 3, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 4, 2, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[3, 1, 2, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 3, 4, 2], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 3, 1, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 2, 4, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {[0, 1, 0]}], [[2, 1], {}, {}],

    [[2, 1, 3], {1, 2}, {[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0]}],

    [[3, 1, 2], {2}, {[0, 1, 0, 0]}], [[3, 2, 1], {1}, {}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418, 514229,

    1346269, 3524578, 9227465, 24157817, 63245986]

                                       ""

                             "Class ", 914, " is:"

{{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}}

                {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}

"For the class ", {{[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[1, 3, 2], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]},

    {[[2, 1, 3], [1, 1]], [[4, 3, 1, 2], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[2, 3, 1], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[1, 2, 4, 3], [1, 1, 1]]},

    {[[3, 1, 2], [1, 1]], [[2, 1, 3, 4], [1, 1, 1]]}}, " the pattern set ",

    {[[1, 3, 2], [1, 1]], [[3, 4, 2, 1], [1, 1, 1]]}, " has scheme:"

{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {[0, 1, 0]}], [[2, 1], {1}, {}],

    [[1, 2, 3], {1}, {[0, 0, 1, 0], [0, 1, 0, 0]}],

    [[1, 3, 2], {1, 2, 3}, {[0, 0, 0, 0]}],

    [[2, 3, 1], {1, 2}, {[0, 0, 1, 0], [1, 0, 0, 0]}]}

            "The first ", 20, " terms of the counting sequence are:"

[1, 2, 5, 13, 33, 81, 193, 449, 1025, 2305, 5121, 11265, 24577, 53249, 114689,

    245761, 524289, 1114113, 2359297, 4980737]

                                       ""

"Out of the ", 914, " equivalence classes ", 639, "(or ", 69.91247265,

    " %) classes have enumeration schemes."

275, "(or ", 30.08752735,

    " %) classes do not have enumeration schemes of depth <=", 5,

    ", with gap vectors of weight <=", 2

                        "The classes that failed are: "

{{{%82, %57}}, {{%82, %54}}, {{%82, %45}}, {{%82, %44}}, {{%82, %41}},

    {{%82, %70}}, {{%82, %38}}, {{%82, %69}}, {{%82, %31}}, {{%82, %30}},

    {{%82, %29}}, {{%82, %64}}, {{%82, %61}}, {{%82, %58}},

    {{%82, [[4, 3, 2, 1], [1, 1, 1]]}}, {{%79, %69}}, {{%79, %31}},

    {{%79, %29}}, {{%79, %64}}, {{%79, %61}}, {{%82, %55}, {%82, %56}},

    {{%82, %13}, {%82, %14}}, {{%82, %11}, {%82, %12}},

    {{%82, %34}, {%82, %35}}, {{%82, %53}, {%82, %52}},

    {{%82, %15}, {%82, %16}}, {{%82, %42}, {%82, %43}},

    {{%82, %51}, {%82, %50}}, {{%82, %49}, {%82, %48}}, {{%82, %9}, {%82, %10}},

    {{%82, %7}, {%82, %8}}, {{%82, %77}, {%82, %78}}, {{%82, %47}, {%82, %46}},

    {{%82, %5}, {%82, %6}}, {{%82, %74}, {%82, %73}}, {{%82, %27}, {%82, %28}},

    {{%82, %72}, {%82, %71}}, {{%82, %39}, {%82, %40}}, {{%82, %1}, {%82, %3}},

    {{%82, %23}, {%82, %24}}, {{%82, %37}, {%82, %36}},

    {{%82, %21}, {%82, %22}}, {{%82, %33}, {%82, %32}},

    {{%82, %62}, {%82, %63}}, {{%82, %68}, {%82, %67}},

    {{%82, %25}, {%82, %26}}, {{%82, %66}, {%82, %65}},

    {{%82, %19}, {%82, %17}},

    {{%81, [[1, 2, 3, 4], [1, 1, 0]]}, {%80, [[1, 2, 3, 4], [0, 1, 1]]}},

    {{%81, %56}, {%80, %55}}, {{%81, %54}, {%80, %54}},

    {{%81, %34}, {%80, %35}}, {{%81, %53}, {%80, %52}},

    {{%81, %43}, {%80, %42}}, {{%81, %48}, {%80, %49}},

    {{%81, %27}, {%80, %28}}, {{%81, %41}, {%80, %41}},

    {{%81, %39}, {%80, %40}}, {{%81, %70}, {%80, %70}},

    {{%81, %38}, {%80, %38}}, {{%81, %1}, {%80, %3}}, {{%81, %14}, {%80, %13}},

    {{%81, %35}, {%80, %34}}, {{%81, %12}, {%80, %11}},

    {{%81, %52}, {%80, %53}}, {{%81, %69}, {%80, %69}},

    {{%81, %33}, {%80, %32}}, {{%81, %31}, {%80, %31}},

    {{%81, %32}, {%80, %33}}, {{%81, %30}, {%80, %30}}, {{%81, %10}, {%80, %9}},

    {{%81, %78}, {%80, %77}}, {{%81, %8}, {%80, %7}}, {{%81, %46}, {%80, %47}},

    {{%81, %62}, {%80, %63}}, {{%81, %25}, {%80, %26}},

    {{%81, %29}, {%80, %29}}, {{%81, %64}, {%80, %64}}, {{%81, %6}, {%80, %5}},

    {{%81, %28}, {%80, %27}}, {{%81, %73}, {%80, %74}},

    {{%81, %63}, {%80, %62}}, {{%81, %26}, {%80, %25}},

    {{%81, %67}, {%80, %68}}, {{%81, %3}, {%80, %1}}, {{%81, %36}, {%80, %37}},

    {{%81, %24}, {%80, %23}}, {{%81, %22}, {%80, %21}},

    {{%81, %61}, {%80, %61}}, {{%81, %19}, {%80, %17}},

    {{%81, %17}, {%80, %19}}, {{%81, %58}, {%80, %58}},

    {{%79, %62}, {%79, %63}},

    {{%76, [[1, 2, 3, 4], [0, 1, 1]]}, {%75, [[1, 2, 3, 4], [1, 1, 0]]}},

    {{%76, [[1, 2, 4, 3], [0, 1, 0]]}, {%75, [[2, 1, 3, 4], [0, 1, 0]]}},

    {{%76, [[1, 2, 4, 3], [1, 1, 0]]}, {%75, [[2, 1, 3, 4], [0, 1, 1]]}},

    {{%76, %57}, {%75, %57}}, {{%76, %55}, {%75, %56}},

    {{%76, %56}, {%75, %55}}, {{%76, %54}, {%75, %54}},

    {{%76, %13}, {%75, %14}}, {{%76, %11}, {%75, %12}},

    {{%76, %34}, {%75, %35}}, {{%76, %53}, {%75, %52}},

    {{%76, %15}, {%75, %16}}, {{%76, %42}, {%75, %43}},

    {{%76, %51}, {%75, %50}}, {{%76, %49}, {%75, %48}}, {{%76, %9}, {%75, %10}},

    {{%76, %7}, {%75, %8}}, {{%76, %77}, {%75, %78}}, {{%76, %47}, {%75, %46}},

    {{%76, %45}, {%75, %45}}, {{%76, %44}, {%75, %44}},

    {{%76, %16}, {%75, %15}}, {{%76, %50}, {%75, %51}},

    {{%76, %43}, {%75, %42}}, {{%76, %48}, {%75, %49}}, {{%76, %5}, {%75, %6}},

    {{%76, %74}, {%75, %73}}, {{%76, %27}, {%75, %28}},

    {{%76, %72}, {%75, %71}}, {{%76, %41}, {%75, %41}},

    {{%76, %39}, {%75, %40}}, {{%76, %70}, {%75, %70}},

    {{%76, %40}, {%75, %39}}, {{%76, %38}, {%75, %38}}, {{%76, %1}, {%75, %3}},

    {{%76, %23}, {%75, %24}}, {{%76, %37}, {%75, %36}},

    {{%76, %21}, {%75, %22}}, {{%76, %14}, {%75, %13}},

    {{%76, %35}, {%75, %34}}, {{%76, %12}, {%75, %11}},

    {{%76, %52}, {%75, %53}}, {{%76, %69}, {%75, %69}},

    {{%76, %33}, {%75, %32}}, {{%76, %31}, {%75, %31}},

    {{%76, %32}, {%75, %33}}, {{%76, %30}, {%75, %30}}, {{%76, %10}, {%75, %9}},

    {{%76, %78}, {%75, %77}}, {{%76, %8}, {%75, %7}}, {{%76, %46}, {%75, %47}},

    {{%76, %62}, {%75, %63}}, {{%76, %68}, {%75, %67}},

    {{%76, %25}, {%75, %26}}, {{%76, %66}, {%75, %65}},

    {{%76, %29}, {%75, %29}}, {{%76, %64}, {%75, %64}}, {{%76, %6}, {%75, %5}},

    {{%76, %28}, {%75, %27}}, {{%76, %73}, {%75, %74}},

    {{%76, %71}, {%75, %72}}, {{%76, %63}, {%75, %62}},

    {{%76, %26}, {%75, %25}}, {{%76, %67}, {%75, %68}},

    {{%76, %65}, {%75, %66}}, {{%76, %3}, {%75, %1}}, {{%76, %36}, {%75, %37}},

    {{%76, %24}, {%75, %23}}, {{%76, %22}, {%75, %21}},

    {{%76, %61}, {%75, %61}}, {{%76, %19}, {%75, %17}},

    {{%76, %17}, {%75, %19}}, {{%76, %58}, {%75, %58}},

    {{%60, [[2, 1, 3, 4], [1, 0, 0]]}, {%59, [[1, 2, 4, 3], [0, 0, 1]]}},

    {{%60, [[2, 1, 3, 4], [1, 0, 1]]}, {%59, [[1, 2, 4, 3], [1, 0, 1]]}},

    {{%60, %16}, {%59, %15}},

    {{%60, [[2, 3, 1, 4], [1, 0, 0]]}, {%59, [[1, 4, 2, 3], [0, 0, 1]]}},

    {{%60, [[2, 3, 1, 4], [1, 0, 1]]}, {%59, [[1, 4, 2, 3], [1, 0, 1]]}},

    {{%60, %43}, {%59, %42}}, {{%60, %48}, {%59, %49}}, {{%60, %5}, {%59, %6}},

    {{%60, %74}, {%59, %73}},

    {{%60, [[2, 3, 4, 1], [1, 0, 0]]}, {%59, [[4, 1, 2, 3], [0, 0, 1]]}},

    {{%60, [[2, 3, 4, 1], [1, 0, 1]]}, {%59, [[4, 1, 2, 3], [1, 0, 1]]}},

    {{%60, %27}, {%59, %28}}, {{%60, %72}, {%59, %71}},

    {{%60, [[2, 4, 1, 3], [1, 0, 0]]}, {%59, [[2, 4, 1, 3], [0, 0, 1]]}},

    {{%60, %70}, {%59, %70}}, {{%60, %40}, {%59, %39}},

    {{%60, %38}, {%59, %38}},

    {{%60, [[2, 4, 3, 1], [1, 0, 0]]}, {%59, [[4, 2, 1, 3], [0, 0, 1]]}},

    {{%60, [[2, 4, 3, 1], [1, 0, 1]]}, {%59, [[4, 2, 1, 3], [1, 0, 1]]}},

    {{%60, %37}, {%59, %36}}, {{%60, %21}, {%59, %22}},

    {{%60, %14}, {%59, %13}}, {{%60, %35}, {%59, %34}},

    {{%60, [[3, 1, 2, 4], [1, 0, 0]]}, {%59, [[1, 3, 4, 2], [0, 0, 1]]}},

    {{%60, [[3, 1, 2, 4], [1, 0, 1]]}, {%59, [[1, 3, 4, 2], [1, 0, 1]]}},

    {{%60, %12}, {%59, %11}}, {{%60, %52}, {%59, %53}},

    {{%60, %69}, {%59, %69}}, {{%60, %33}, {%59, %32}},

    {{%60, %32}, {%59, %33}}, {{%60, %30}, {%59, %30}}, {{%60, %10}, {%59, %9}},

    {{%60, [[3, 2, 1, 4], [1, 0, 0]]}, {%59, [[1, 4, 3, 2], [0, 0, 1]]}},

    {{%60, %8}, {%59, %7}}, {{%60, %62}, {%59, %63}}, {{%60, %68}, {%59, %67}},

    {{%60, [[3, 2, 4, 1], [1, 0, 0]]}, {%59, [[4, 1, 3, 2], [0, 0, 1]]}},

    {{%60, [[3, 2, 4, 1], [1, 0, 1]]}, {%59, [[4, 1, 3, 2], [1, 0, 1]]}},

    {{%60, %25}, {%59, %26}}, {{%60, %66}, {%59, %65}},

    {{%60, [[3, 4, 1, 2], [1, 0, 0]]}, {%59, [[3, 4, 1, 2], [0, 0, 1]]}},

    {{%60, %29}, {%59, %29}},

    {{%60, [[3, 4, 1, 2], [1, 1, 0]]}, {%59, [[3, 4, 1, 2], [0, 1, 1]]}},

    {{%60, %64}, {%59, %64}},

    {{%60, [[3, 4, 2, 1], [1, 0, 0]]}, {%59, [[4, 3, 1, 2], [0, 0, 1]]}},

    {{%60, [[3, 4, 2, 1], [1, 0, 1]]}, {%59, [[4, 3, 1, 2], [1, 0, 1]]}},

    {{%60, [[3, 4, 2, 1], [1, 1, 0]]}, {%59, [[4, 3, 1, 2], [0, 1, 1]]}},

    {{%60, [[3, 4, 2, 1], [1, 1, 1]]}, {%59, [[4, 3, 1, 2], [1, 1, 1]]}},

    {{%60, %6}, {%59, %5}}, {{%60, %28}, {%59, %27}}, {{%60, %63}, {%59, %62}},

    {{%60, %26}, {%59, %25}}, {{%60, %3}, {%59, %1}}, {{%60, %24}, {%59, %23}},

    {{%60, %61}, {%59, %61}}, {{%60, %19}, {%59, %17}},

    {{%60, %17}, {%59, %19}}, {{%60, %58}, {%59, %58}},

    {{%20, %57}, {%18, %57}}, {{%20, %55}, {%18, %56}},

    {{%20, %56}, {%18, %55}}, {{%20, %54}, {%18, %54}},

    {{%20, %11}, {%18, %12}}, {{%20, %53}, {%18, %52}},

    {{%20, %15}, {%18, %16}}, {{%20, %42}, {%18, %43}},

    {{%20, %51}, {%18, %50}}, {{%20, %49}, {%18, %48}}, {{%20, %7}, {%18, %8}},

    {{%20, %47}, {%18, %46}}, {{%20, %45}, {%18, %45}},

    {{%20, %44}, {%18, %44}}, {{%20, %16}, {%18, %15}},

    {{%20, %43}, {%18, %42}}, {{%20, %41}, {%18, %41}},

    {{%20, %39}, {%18, %40}}, {{%20, %40}, {%18, %39}},

    {{%20, %38}, {%18, %38}}, {{%20, %1}, {%18, %3}}, {{%20, %23}, {%18, %24}},

    {{%20, %37}, {%18, %36}}, {{%20, %21}, {%18, %22}},

    {{%20, %14}, {%18, %13}}, {{%20, %35}, {%18, %34}},

    {{%20, %33}, {%18, %32}}, {{%20, %31}, {%18, %31}},

    {{%20, %30}, {%18, %30}}, {{%20, %10}, {%18, %9}}, {{%20, %8}, {%18, %7}},

    {{%20, %29}, {%18, %29}}, {{%20, %6}, {%18, %5}}, {{%20, %28}, {%18, %27}},

    {{%20, %26}, {%18, %25}}, {{%20, %3}, {%18, %1}}, {{%20, %24}, {%18, %23}},

    {{%20, %22}, {%18, %21}}, {{%20, %19}, {%18, %17}},

    {{%4, [[2, 1, 3, 4], [1, 0, 0]]}, {%2, [[1, 2, 4, 3], [0, 0, 1]]}},

    {{%4, %16}, {%2, %15}}, {{%4, %14}, {%2, %13}},

    {{%4, [[3, 1, 2, 4], [1, 0, 0]]}, {%2, [[1, 3, 4, 2], [0, 0, 1]]}},

    {{%4, %12}, {%2, %11}}, {{%4, %10}, {%2, %9}},

    {{%4, [[3, 2, 1, 4], [1, 0, 0]]}, {%2, [[1, 4, 3, 2], [0, 0, 1]]}},

    {{%4, %8}, {%2, %7}},

    {{%4, [[3, 2, 4, 1], [1, 0, 0]]}, {%2, [[4, 1, 3, 2], [0, 0, 1]]}},

    {{%4, [[3, 2, 4, 1], [1, 0, 1]]}, {%2, [[4, 1, 3, 2], [1, 0, 1]]}},

    {{%4, %6}, {%2, %5}}, {{%4, %3}, {%2, %1}}}

%1 := [[2, 4, 3, 1], [0, 1, 0]]

%2 := [[2, 1, 3], [1, 1]]

%3 := [[4, 2, 1, 3], [0, 1, 0]]

%4 := [[1, 3, 2], [1, 1]]

%5 := [[2, 3, 4, 1], [0, 1, 0]]

%6 := [[4, 1, 2, 3], [0, 1, 0]]

%7 := [[1, 4, 3, 2], [0, 1, 1]]

%8 := [[3, 2, 1, 4], [1, 1, 0]]

%9 := [[1, 4, 3, 2], [0, 1, 0]]

%10 := [[3, 2, 1, 4], [0, 1, 0]]

%11 := [[1, 3, 4, 2], [0, 1, 1]]

%12 := [[3, 1, 2, 4], [1, 1, 0]]

%13 := [[1, 3, 4, 2], [0, 1, 0]]

%14 := [[3, 1, 2, 4], [0, 1, 0]]

%15 := [[1, 4, 2, 3], [0, 1, 0]]

%16 := [[2, 3, 1, 4], [0, 1, 0]]

%17 := [[4, 2, 3, 1], [1, 1, 0]]

%18 := [[2, 1, 3], [0, 1]]

%19 := [[4, 2, 3, 1], [0, 1, 1]]

%20 := [[1, 3, 2], [1, 0]]

%21 := [[2, 4, 3, 1], [1, 1, 1]]

%22 := [[4, 2, 1, 3], [1, 1, 1]]

%23 := [[2, 4, 3, 1], [0, 1, 1]]

%24 := [[4, 2, 1, 3], [1, 1, 0]]

%25 := [[3, 2, 4, 1], [1, 1, 0]]

%26 := [[4, 1, 3, 2], [0, 1, 1]]

%27 := [[2, 3, 4, 1], [1, 1, 0]]

%28 := [[4, 1, 2, 3], [0, 1, 1]]

%29 := [[3, 4, 1, 2], [1, 0, 1]]

%30 := [[3, 1, 4, 2], [1, 1, 1]]

%31 := [[3, 1, 4, 2], [1, 0, 1]]

%32 := [[3, 1, 4, 2], [1, 1, 0]]

%33 := [[3, 1, 4, 2], [0, 1, 1]]

%34 := [[1, 3, 4, 2], [1, 1, 0]]

%35 := [[3, 1, 2, 4], [0, 1, 1]]

%36 := [[4, 2, 1, 3], [0, 1, 1]]

%37 := [[2, 4, 3, 1], [1, 1, 0]]

%38 := [[2, 4, 1, 3], [1, 1, 1]]

%39 := [[2, 4, 1, 3], [0, 1, 1]]

%40 := [[2, 4, 1, 3], [1, 1, 0]]

%41 := [[2, 4, 1, 3], [0, 1, 0]]

%42 := [[1, 4, 2, 3], [0, 1, 1]]

%43 := [[2, 3, 1, 4], [1, 1, 0]]

%44 := [[2, 1, 4, 3], [1, 1, 1]]

%45 := [[2, 1, 4, 3], [1, 0, 1]]

%46 := [[3, 2, 1, 4], [1, 1, 1]]

%47 := [[1, 4, 3, 2], [1, 1, 1]]

%48 := [[2, 3, 1, 4], [1, 1, 1]]

%49 := [[1, 4, 2, 3], [1, 1, 1]]

%50 := [[2, 3, 1, 4], [0, 1, 1]]

%51 := [[1, 4, 2, 3], [1, 1, 0]]

%52 := [[3, 1, 2, 4], [1, 1, 1]]

%53 := [[1, 3, 4, 2], [1, 1, 1]]

%54 := [[1, 3, 2, 4], [1, 1, 1]]

%55 := [[1, 3, 2, 4], [0, 1, 1]]

%56 := [[1, 3, 2, 4], [1, 1, 0]]

%57 := [[1, 3, 2, 4], [0, 1, 0]]

%58 := [[4, 2, 3, 1], [1, 1, 1]]

%59 := [[2, 1, 3], [1, 0]]

%60 := [[1, 3, 2], [0, 1]]

%61 := [[4, 2, 3, 1], [0, 1, 0]]

%62 := [[3, 2, 4, 1], [0, 1, 0]]

%63 := [[4, 1, 3, 2], [0, 1, 0]]

%64 := [[3, 4, 1, 2], [1, 1, 1]]

%65 := [[4, 1, 3, 2], [1, 1, 1]]

%66 := [[3, 2, 4, 1], [1, 1, 1]]

%67 := [[4, 1, 3, 2], [1, 1, 0]]

%68 := [[3, 2, 4, 1], [0, 1, 1]]

%69 := [[3, 1, 4, 2], [0, 1, 0]]

%70 := [[2, 4, 1, 3], [1, 0, 1]]

%71 := [[4, 1, 2, 3], [1, 1, 1]]

%72 := [[2, 3, 4, 1], [1, 1, 1]]

%73 := [[4, 1, 2, 3], [1, 1, 0]]

%74 := [[2, 3, 4, 1], [0, 1, 1]]

%75 := [[2, 1, 3], [0, 0]]

%76 := [[1, 3, 2], [0, 0]]

%77 := [[1, 4, 3, 2], [1, 1, 0]]

%78 := [[3, 2, 1, 4], [0, 1, 1]]

%79 := [[1, 2, 3], [1, 1]]

%80 := [[1, 2, 3], [1, 0]]

%81 := [[1, 2, 3], [0, 1]]

%82 := [[1, 2, 3], [0, 0]]