Av(1243, 2143, 2314, 2341, 3214, 3241, 4132)

Permutation examples

length 2: 12, 21

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

length 4: 1234, 1324, 1342, 1423, 1432, 2134, 2413, 2431, 3124, 3142, 3412, 3421, 4123, 4213, 4231, 4312, 4321

length 5: 12345, 13245, 14235, 14523, 14532, 15234, 15324, 15342, 15423, 15432, 21345, 25134, 25413, 25431, 31245, 35124, 35412, 35421, 41235, 41523, 45123, 45213, 45231, 45312, 45321, 51234, 52134, 53124, 53412, 53421, 54123, 54213, 54231, 54312, 54321

Conjectured Struct Cover

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

Legend

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

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

$\mathcal{A}$ = Av(1243, 2143, 2314, 2341, 3214, 3241, 4132)

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

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

Recurrence relation

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

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