Av(12)
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Generating Function
\(\displaystyle -\frac{1}{x -1}\)
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Counting Sequence
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(x -1\right) F \! \left(x \right)+1 = 0\)
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Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(n \right) = 1, \quad n \geq 1\)
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Explicit Closed Form
\(\displaystyle 1\)
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This specification was found using the strategy pack "Point Placements" and has 5 rules.

Found on January 21, 2022.

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