Av(1234, 1243, 1432, 2314, 2413, 4123, 4132)

Permutation examples

length 2: 12, 21

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

length 4: 1324, 1342, 1423, 2134, 2143, 2341, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4213, 4231, 4312, 4321

length 5: 14523, 21435, 21453, 21534, 24351, 24531, 25341, 31452, 32145, 32154, 32451, 32541, 34512, 34521, 35412, 35421, 42135, 42153, 42351, 42531, 43125, 43152, 43215, 43251, 43512, 43521, 45213, 45231, 45312, 45321, 53214, 53241, 53412, 53421, 54213, 54231, 54312, 54321

Conjectured Struct Cover

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

Legend

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

$\mathcal{A}$ = Av(1234, 1243, 1432, 2314, 2413, 4123, 4132)

Recurrence relation

$a_{0} = 1,~a_{1} = 1,~a_{2} = 2,~a_{3} = 6,~a_{4} = 17,~a_{5} = 38$

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