#This file begins by enumerating 11 of the 369 different equivalence classes for the case of 1 pattern of length 4 and 1 pattern of length 5.
#At line 4520, begin samples of attempting to find enumeration schemes for random sets of patterns (1 length four and 1 length five).

> SipurF([4,5],4,2,10,20,n,N,x,3,2);
    There all together, 369, different equivalence classes 
For the equivalence class of patterns, {

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
  {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], 

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

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

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

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

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

    [[3, 4, 2, 1], {}, {3}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 496, 2566, 13869, 77420, 442966]
For the equivalence class of patterns, {

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
   {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], 

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

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

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

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

     [[3, 4, 1, 2], {}, {1, 2}], [[3, 4, 2, 1], {}, {3}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 496, 2568, 13908, 77898, 447724]
For the equivalence class of patterns, {

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
  {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], 

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

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

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

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

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

    [[3, 4, 2, 1], {}, {3}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 496, 2566, 13869, 77420, 442966]
For the equivalence class of patterns, {

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

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

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

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

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

  [[4, 1, 3, 2], {}, {1}], [[4, 2, 3, 1], {}, {1}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 491, 2475, 12822, 67609, 360929]
For the equivalence class of patterns, {

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

  [[4, 3, 1, 2], {}, {1}], [[4, 3, 2, 1], {}, {1}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 496, 2566, 13869, 77420, 442966]
For the equivalence class of patterns, {

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

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

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

  [[4, 2, 3, 1], {}, {1}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 496, 2566, 13869, 77420, 442966]
For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
   {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], 

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

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

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

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

     [[3, 4, 1, 2], {}, {1, 2}], [[3, 4, 2, 1], {}, {3}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 496, 2569, 13931, 78219, 451279]
For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

  [3, 1, 4, 2], 

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

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

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

  }
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 491, 2475, 12820, 67564, 360330]
For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

           has a scheme of depth , 3
                          here it is: 
        {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], 

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

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

          [[2, 3, 1], {[0, 0, 2, 0]}, {1}]}
         Using  the scheme, the first, , 21, terms are 
[1, 1, 2, 6, 23, 102, 495, 2549, 13682, 75714, 428882, 2474573, 

  14492346, 85926361, 514763279, 3111119358, 18946375767, 

  116147683902, 716179441293, 4438862153246, 27638747494178]
For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
   {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], 

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

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

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

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

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

     [[3, 4, 2, 1], {}, {3}]}
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 495, 2549, 13682, 75714, 428882]
For the equivalence class of patterns, {

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

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

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

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

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

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

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

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

           has a scheme of depth , 4
                          here it is: 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

  }
         Using  the scheme, the first, , 11, terms are 
     [1, 1, 2, 6, 23, 102, 495, 2548, 13660, 75416, 425661]
                Out of a total of , 369, cases 
             11, were successful and , 358, failed 
                     Success Rate: , 0.0298
                     Here are the failures 
{{{[1, 2, 3, 4], [1, 4, 3, 2, 5]}, {[4, 3, 2, 1], [5, 2, 3, 4, 1]}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  }}

###############################################################################################################################
###############################################################################################################################
>VatterR4S5(1,1,100,4,2);
VatterR4S5(1,1,10,5,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5



            The computation took, 291.864, seconds.



      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5



            The computation took, 446.701, seconds.

>VatterR4S5(1,1,100,4,2);
VatterR4S5(1,1,30,5,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5


                           Theorem, 1
        The enumeration scheme of permutations avoiding
                {[1, 4, 3, 2], [5, 1, 4, 2, 3]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

  }


            The computation took, 282.783, seconds.



      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5


                           Theorem, 1
        The enumeration scheme of permutations avoiding
                {[4, 1, 3, 2], [1, 5, 4, 2, 3]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

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

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

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

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

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


            The computation took, 1021.833, seconds.

>VatterR4S5(1,1,100,4,2);
VatterR4S5(1,1,30,5,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5


                           Theorem, 1
        The enumeration scheme of permutations avoiding
                {[1, 4, 3, 2], [5, 1, 4, 2, 3]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

  }


            The computation took, 284.255, seconds.



      ENUMERATIO SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5



            The computation took, 932.215, seconds.

>VatterR4S5(1,1,100,4,2);
VatterR4S5(1,1,30,5,2);


      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5



            The computation took, 281.676, seconds.



      ENUMERATION SCHEMES OF PERMUTATIONS AVOIDING, 1, 

        PATTERNS OF LENGTH 4 AND, 1, PATTERNS OF LENGTH 5


                           Theorem, 1
        The enumeration scheme of permutations avoiding
                {[3, 4, 2, 1], [5, 4, 3, 2, 1]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

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

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

  }

                           Theorem, 2
        The enumeration scheme of permutations avoiding
                {[4, 1, 3, 2], [1, 5, 4, 2, 3]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

                           Theorem, 3
        The enumeration scheme of permutations avoiding
                {[4, 3, 1, 2], [3, 4, 5, 2, 1]}
                              is 
{[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {}, {}], 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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