length 2: 12, 21
length 3: 213, 231, 312, 321
length 4: 3214, 3241, 3421, 4213, 4231, 4312, 4321
length 5: 43215, 43251, 43521, 45321, 53214, 53241, 53421, 54213, 54231, 54312, 54321
$\mathcal{A}$ = Av(123, 132, 3412)
$\operatorname{F_{4}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{3}}{\left (x \right )}$
$\operatorname{F_{0}}{\left (x \right )} = 1$
$\operatorname{F_{3}}{\left (x \right )} = \operatorname{F_{1}}{\left (x \right )} + \operatorname{F_{2}}{\left (x \right )}$
$\operatorname{F_{1}}{\left (x \right )} = x \operatorname{F_{4}}{\left (x \right )}$
$\operatorname{F_{2}}{\left (x \right )} = \frac{x^{2}}{\left(x - 1\right)^{2}}$