Av(1243, 1342, 1423, 1432, 2143, 2314, 2431, 3142, 3241, 4123)

Permutation examples

length 2: 12, 21

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

length 4: 1234, 1324, 2134, 2341, 2413, 3124, 3214, 3412, 3421, 4132, 4213, 4231, 4312, 4321

length 5: 12345, 13245, 21345, 23451, 31245, 32145, 34512, 34521, 35214, 41325, 42135, 43125, 43215, 45132, 45213, 45231, 45312, 45321, 52413, 53214, 53412, 53421, 54132, 54213, 54231, 54312, 54321

Conjectured Struct Cover

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

Legend

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

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

$\mathcal{A}$ = Av(1243, 1342, 1423, 1432, 2143, 2314, 2431, 3142, 3241, 4123)

$\mathcal{B}$ = Av(231, 1243, 1423, 1432, 2143, 4123)

$\mathcal{C}$ = Av(132, 213, 4123)

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

Recurrence relation

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

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