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### Av(123, 132, 231, 3214)

#### Permutation examples

length 2: 12, 21

length 3: 213, 312, 321

length 4: 4213, 4312, 4321

length 5: 54213, 54312, 54321

#### Generating function

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

#### Coefficients

1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, ...

#### System of equations

$\operatorname{F_{2}}{\left (x \right )} = \operatorname{F_{0}}{\left (x \right )} + \operatorname{F_{1}}{\left (x \right )}$

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

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