length 2: 12, 21
length 3: 213, 231, 312, 321
length 4: 3214, 3241, 3412, 3421, 4213, 4231, 4312, 4321
length 5: 43215, 43251, 43512, 43521, 45213, 45231, 45312, 45321, 53214, 53241, 53412, 53421, 54213, 54231, 54312, 54321
$\operatorname{F_{2}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{1}}{\left (x \right )}$
$\operatorname{F_{0}}{\left (x \right )} = 1$
$\operatorname{F_{1}}{\left (x \right )} = - \frac{x \operatorname{F_{2}}{\left (x \right )}}{x - 1}$