Av(132, 1234, 2341, 3241, 4123, 4213)

Permutation examples

length 2: 12, 21

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

length 4: 2134, 2314, 3124, 3214, 3412, 3421, 4231, 4312, 4321

length 5: 32145, 34125, 34215, 42315, 43125, 43215, 45231, 45312, 45321, 53412, 53421, 54231, 54312, 54321

ATRAP tree (size 5, depth 3)

Legend

$\mathcal{A}$ = Av(132, 1234, 2341, 3241, 4123, 4213)

$\mathcal{B}$ = Av(123, 132, 3241, 4213)

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

$\mathcal{D}$ = Av(12, 21)

Generating function

$A(x) = \frac{- x^{6} - 2 x^{5} + 2 x^{3} - x + 1}{x^{3} - 2 x + 1}$

Coefficients

1, 1, 2, 5, 9, 14, 22, 35, 56, 90, 145, ...

System of equations

$\operatorname{F_{4}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{3}}{\left (x \right )}$

$\operatorname{F_{0}}{\left (x \right )} = 1$

$\operatorname{F_{3}}{\left (x \right )} = \operatorname{F_{1}}{\left (x \right )} + \operatorname{F_{2}}{\left (x \right )}$

$\operatorname{F_{1}}{\left (x \right )} = \frac{x \left(- x^{5} - x^{4} + x^{3} - x + 1\right)}{x^{3} - 2 x + 1}$

$\operatorname{F_{2}}{\left (x \right )} = - \frac{x^{2} \left(x + 1\right)^{2}}{x^{2} + x - 1}$