Av(1342, 3412)

Permutation examples

length 2: 12, 21

length 3: 123, 132, 213, 231, 312, 321

length 4: 1234, 1243, 1324, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3421, 4123, 4132, 4213, 4231, 4312, 4321

length 5: 12345, 12354, 12435, 12534, 12543, 13245, 13254, 14235, 14325, 15234, 15243, 15324, 15423, 15432, 21345, 21354, 21435, 21534, 21543, 23145, 23154, 23415, 23451, 23514, 23541, 24135, 24315, 24351, 25134, 25143, 25314, 25341, 25413, 25431, 31245, 31254, 31425, 31524, 31542, 32145, 32154, 32415, 32451, 32514, 32541, 34215, 34251, 34521, 35214, 35241, 35421, 41235, 41253, 41325, 41532, 42135, 42153, 42315, 42351, 42531, 43125, 43152, 43215, 43251, 43521, 45321, 51234, 51243, 51324, 51423, 51432, 52134, 52143, 52314, 52341, 52413, 52431, 53124, 53142, 53214, 53241, 53421, 54123, 54132, 54213, 54231, 54312, 54321

ATRAP tree (size 30, depth 11)

Note

The tree displayed is for a class symmetrical to Av(1342, 3412).

Legend

$\mathcal{A}$ = Av(2314, 3412)

$\mathcal{B}$ = Av(231)

$\mathcal{C}$ = Av(12)

$\mathcal{D}$ = Av(123, 3412)

Coefficients

1, 1, 2, 6, 22, 88, 366, 1556, 6720, 29396, 129996, ...