Av(12345, 12354, 12435, 12453, 12534, 12543, 13425, 13452, 13524, 13542, 14523, 14532, 23415, 23514, 24513)
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Counting Sequence
1, 1, 2, 6, 24, 105, 474, 2160, 9869, 45118, 206266, 942828, 4308667, 19685861, 89922650, ...

This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 62 rules.

Found on January 23, 2022.

Finding the specification took 292 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_{14}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{14}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{57}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x \right)+F_{57}\! \left(x \right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= y x\\ F_{11}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{9}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)\\ F_{13}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\ F_{14}\! \left(x \right) &= x\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{14}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{3}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{21}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{22}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\ F_{23}\! \left(x \right) &= F_{14}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{14}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{14}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{22}\! \left(x , 1\right)\\ F_{28}\! \left(x \right) &= F_{14}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x , 1\right)\\ F_{30}\! \left(x , y\right) &= -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}\\ F_{31}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\ F_{33}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{30}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}\\ F_{36}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{44}\! \left(x \right)+F_{54}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{38}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{41}\! \left(x \right)\\ F_{39}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}\\ F_{41}\! \left(x \right) &= F_{14}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{43}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{14}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{14}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{14}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{14}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{35}\! \left(x , 1\right)\\ F_{49}\! \left(x \right) &= F_{14}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x , 1\right)\\ F_{51}\! \left(x , y\right) &= -\frac{-y F_{52}\! \left(x , y\right)+F_{52}\! \left(x , 1\right)}{-1+y}\\ F_{52}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{53}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{35}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{51}\! \left(x , y\right)\\ F_{56}\! \left(x \right) &= F_{14}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{14}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{36}\! \left(x , 1\right)\\ F_{59}\! \left(x \right) &= F_{14}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{44}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{14}\! \left(x \right) F_{58}\! \left(x \right)\\ \end{align*}\)