Av(1243, 1432, 2143, 2314, 3142, 3214, 4123, 4132)

Permutation examples

length 2: 12, 21

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

length 4: 1234, 1324, 1342, 1423, 2134, 2341, 2413, 2431, 3124, 3241, 3412, 3421, 4213, 4231, 4312, 4321

length 5: 12345, 13245, 13452, 14235, 14523, 21345, 23451, 24351, 24513, 24531, 25341, 31245, 32451, 34512, 34521, 35241, 35412, 35421, 42351, 43512, 43521, 45213, 45231, 45312, 45321, 53241, 53412, 53421, 54213, 54231, 54312, 54321

Conjectured Struct Cover

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

Legend

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

$\mathcal{A}$ = Av(1243, 1432, 2143, 2314, 3142, 3214, 4123, 4132)

$\mathcal{B}$ = Av(132, 231, 321, 4123)

Recurrence relation

$a_{0} = 1,~a_{1} = 1,~a_{2} = 2,~a_{3} = 6,~a_{4} = 16,~a_{5} = 32$

$a_{n} = a_{n-2}+b_{n-3}+a_{n-1}+a_{n-3}+5$