Av(1243, 1324, 1342, 1432, 2341, 2413, 2431, 3142, 3241, 3421, 4132)

Permutation examples

length 2: 12, 21

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

length 4: 1234, 1423, 2134, 2143, 2314, 3124, 3214, 3412, 4123, 4213, 4231, 4312, 4321

length 5: 12345, 15234, 21345, 21534, 23145, 31245, 32145, 32154, 34125, 41235, 42135, 42315, 43125, 43215, 45123, 51234, 52134, 52314, 53124, 53214, 53412, 54123, 54213, 54231, 54312, 54321

Conjectured Struct Cover

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

Legend

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

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

$\mathcal{A}$ = Av(1243, 1324, 1342, 1432, 2341, 2413, 2431, 3142, 3241, 3421, 4132)

Recurrence relation

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

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