length 2: 12, 21
length 3: 123, 312, 321
length 4: 1234, 4312
length 5: 12345
$\mathcal{A}$ = Av(132, 213, 231, 4123, 4321)
$\mathcal{C}$ = Av(123, 132, 213, 231, 321)
$\operatorname{F_{4}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{3}}{\left (x \right )}$
$\operatorname{F_{0}}{\left (x \right )} = 1$
$\operatorname{F_{3}}{\left (x \right )} = \operatorname{F_{1}}{\left (x \right )} + \operatorname{F_{2}}{\left (x \right )}$
$\operatorname{F_{1}}{\left (x \right )} = - \frac{x}{x - 1}$
$\operatorname{F_{2}}{\left (x \right )} = x^{2} \left(x + 1\right)^{2}$