###### Av(12)

Generating Function

\(\displaystyle -\frac{1}{x -1}\)

Counting Sequence

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

Implicit Equation for the Generating Function

\(\displaystyle \left(x -1\right) F \! \left(x \right)+1 = 0\)

Recurrence

\(\displaystyle a \! \left(0\right) = 1\)

\(\displaystyle a \! \left(n \right) = 1, \quad n \geq 1\)

\(\displaystyle a \! \left(n \right) = 1, \quad n \geq 1\)

Explicit Closed Form

\(\displaystyle 1\)

### This specification was found using the strategy pack "Point Placements" and has 5 rules.

Found on January 21, 2022.Finding the specification took 0 seconds.

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