The set of forbidden pattern is
 
                                 {[1, 2, 4, 3]}
 
                         This is the (RIGOROUS) scheme
 
Warning, new definition for Chi
[{[2, 1], [1, 2, 3], [1, 3, 2], [3, 1, 2], [2, 3, 1, 4], [2, 4, 1, 3],
 
    [3, 4, 1, 2], [3, 4, 2, 1]}, {[], [1], [1, 2], [2, 3, 1]}, table([
 
    [1, 2, 3] = 3
 
    [2, 1] = 1
 
    [1, 3, 2] = 2
 
    [2, 3, 1, 4] = 4
 
    [3, 4, 1, 2] = 1
 
    [2, 4, 1, 3] = 1
 
    [3, 4, 2, 1] = 3
 
    [3, 1, 2] = 1
 
    ]), table([
 
    [1, 2] = {[1, 2, 3], [2, 3, 1], [1, 3, 2]}
 
    [] = {[1]}
 
    [1] = {[2, 1], [1, 2]}
 
    [2, 3, 1] = {[2, 3, 1, 4], [2, 4, 1, 3], [3, 4, 1, 2], [3, 4, 2, 1]}
 
    ]), table([
 
    [1, 2] = {}
 
    [1, 2, 3] = {2}
 
    [] = {}
 
    [2, 1] = {}
 
    [1, 3, 2] = {}
 
    [2, 3, 1, 4] = {3}
 
    [3, 4, 1, 2] = {}
 
    [2, 4, 1, 3] = {}
 
    [1] = {}
 
    [3, 4, 2, 1] = {}
 
    [2, 3, 1] = {}
 
    [3, 1, 2] = {}
 
    ])]
 
                              This is the sequence
 
[1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705,
 
    167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718,
 
    21937062144834, 162958355218089, 1221225517285209, 9225729232653663,
 
    70209849031116183, 537935616492552297, 4147342550996290153,
 
    32159907636432567578, 250717538500344886206, 1964347085978431234383,
 
    15462159345628498316319, 122238900487877503161969]
 
                    This is the (Semi-Rigorous) Recurrence
 
                2                      2        2        2    2  2
             9 n  - 9 N - 22 n N - 10 n  N + 9 N  + 6 n N  + n  N