The set of forbidden pattern is
 
                           {[1, 2, 3, 4], [2, 1, 3]}
 
                         This is the (RIGOROUS) scheme
 
Warning, new definition for Chi
[{[2, 1], [1, 2, 3], [2, 3, 1], [1, 3, 2]}, {[], [1], [1, 2]}, table([
 
    [2, 3, 1] = 2
 
    [2, 1] = 1
 
    [1, 3, 2] = 2
 
    [1, 2, 3] = 3
 
    ]), table([
 
    [1, 2] = {[1, 2, 3], [2, 3, 1], [1, 3, 2]}
 
    [] = {[1]}
 
    [1] = {[2, 1], [1, 2]}
 
    ]), table([
 
    [1, 2] = {}
 
    [] = {}
 
    [2, 3, 1] = {2, 3}
 
    [2, 1] = {2}
 
    [1, 3, 2] = {3}
 
    [1, 2, 3] = {3}
 
    [1] = {}
 
    ])]
 
                              This is the sequence
 
[1, 1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418,
 
    514229, 1346269, 3524578, 9227465, 24157817, 63245986, 165580141, 433494437,
 
    1134903170, 2971215073, 7778742049]
 
                    This is the (Semi-Rigorous) Recurrence
 
                                             2
                                  1 - 3 N + N