length 2: 12, 21
length 3: 231, 312, 321
length 4: 4231, 4312, 4321
length 5: 54231, 54312, 54321
$\mathcal{A}$ = Av(123, 132, 213, 3412, 3421)
$\mathcal{C}$ = Av(123, 132, 213, 231)
$\operatorname{F_{4}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{3}}{\left (x \right )}$
$\operatorname{F_{0}}{\left (x \right )} = 1$
$\operatorname{F_{3}}{\left (x \right )} = \operatorname{F_{1}}{\left (x \right )} + \operatorname{F_{2}}{\left (x \right )}$
$\operatorname{F_{1}}{\left (x \right )} = \frac{x \left(- x^{2} - 1\right)}{x - 1}$
$\operatorname{F_{2}}{\left (x \right )} = - \frac{x^{2}}{x - 1}$