Av(132, 2314, 3124, 3214, 3412, 3421, 4312, 4321)

Permutation examples

length 2: 12, 21

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

length 4: 1234, 2134, 2341, 3241, 4123, 4213, 4231

length 5: 12345, 21345, 23451, 32451, 51234, 52134, 52341

ATRAP tree (size 5, depth 3)

Legend

$\mathcal{A}$ = Av(132, 2314, 3124, 3214, 3412, 3421, 4312, 4321)

$\mathcal{B}$ = Av(132, 312, 321, 2314)

$\mathcal{C}$ = Av(132, 231, 312, 321)

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

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

Generating function

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

Coefficients

1, 1, 2, 5, 7, 7, 7, 7, 7, 7, 7, ...

System of equations

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

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

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

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

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