Av(1234, 1243, 1342, 2143, 2314, 2341, 2431, 3214, 4213)

Permutation examples

length 2: 12, 21

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

length 4: 1324, 1423, 1432, 2134, 2413, 3124, 3142, 3241, 3412, 3421, 4123, 4132, 4231, 4312, 4321

length 5: 15423, 15432, 25134, 35124, 41523, 41532, 43512, 43521, 45123, 45132, 45231, 45312, 45321, 51423, 51432, 53412, 53421, 54123, 54132, 54231, 54312, 54321

Conjectured Struct Cover

$\mathcal{A}$
$=$
$\bigsqcup$
$\bullet$
$\bullet$ $\bullet$
$\bullet$
$\bigsqcup$
$\bullet$
$\bullet$
$\bullet$
$\bullet$
$\bigsqcup$
$\bullet$
$\bullet$
$\bullet$
$\bullet$
$\bigsqcup$
$\mathcal{B}$
$\mathcal{C}$
$\bullet$
$\bigsqcup$
$\bullet$
$\bullet$
$\mathcal{C}$
$\bullet$
$\bigsqcup$
$\bullet$
$\bullet$
$\bullet$ $\bullet$
$\bullet$

Legend

$\mathcal{A}$ = Av(1234, 1243, 1342, 2143, 2314, 2341, 2431, 3214, 4213)

$\mathcal{B}$ = Av(123, 132, 3214, 4213)

$\mathcal{C}$ = Av(123, 132, 213, 231)

Recurrence relation

$a_{0} = 1,~a_{1} = 1,~a_{2} = 2,~a_{3} = 6,~a_{4} = 15,~a_{5} = 22$

$a_{n} = \sum_{i=0}^{n-1}b_{i}c_{n-i-1}+c_{n-3}$