###### Av(132, 213, 231)
Generating Function
$$\displaystyle \frac{x^{2}-x +1}{\left(x -1\right)^{2}}$$
Counting Sequence
1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ...
Implicit Equation for the Generating Function
$$\displaystyle \left(x -1\right)^{2} F \! \left(x \right)-x^{2}+x -1 = 0$$
Recurrence
$$\displaystyle a \! \left(0\right) = 1$$
$$\displaystyle a \! \left(1\right) = 1$$
$$\displaystyle a \! \left(2\right) = 2$$
$$\displaystyle a \! \left(n \right) = n, \quad n \geq 3$$
Explicit Closed Form
$$\displaystyle \left\{\begin{array}{cc}1 & n =0 \\ n & \text{otherwise} \end{array}\right.$$

### This specification was found using the strategy pack "Point Placements" and has 10 rules.

Found on January 18, 2022.

Finding the specification took 0 seconds.

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\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{2}\! \left(x \right)\\ \end{align*}