Av(1243, 1342, 1432, 2314, 2413, 3142, 3241, 3412, 4132)

Permutation examples

length 2: 12, 21

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

length 4: 1234, 1324, 1423, 2134, 2143, 2341, 2431, 3124, 3214, 3421, 4123, 4213, 4231, 4312, 4321

length 5: 12345, 13245, 14235, 15234, 21345, 21435, 21534, 23451, 25341, 31245, 32145, 32154, 34521, 35421, 41235, 42135, 43125, 43215, 45321, 51234, 52134, 52341, 53124, 53214, 53421, 54123, 54213, 54231, 54312, 54321

Conjectured Struct Cover

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

Legend

$\mathcal{/}$ = Av(21)

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

$\mathcal{A}$ = Av(1243, 1342, 1432, 2314, 2413, 3142, 3241, 3412, 4132)

$\mathcal{B}$ = Av(213, 1243, 1342, 1432, 3412, 4132)

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

Recurrence relation

$a_{0} = 1,~a_{1} = 1,~a_{2} = 2,~a_{3} = 6$

$a_{n} = b_{n-1}+\sum_{i=0}^{n-2}c_{n-i-2}\binom{n-j-1}{1}+\sum_{i=0}^{n-3}\binom{n-i-2}{1}$