Av(13524, 13542, 31524, 31542, 35124, 35142)
View Raw Data
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3296, 18896, 111080, 665200, 4041016, 24831040, 154014376, 962753936, ...
Search on OEIS Search on PermPAL

This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 61 rules.

Found on January 23, 2022.

Finding the specification took 115 seconds.

Copy to clipboard:

View tree on standalone page.

+ Expand

Copy 61 equations to clipboard:
\(\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_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{0}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= x\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{20}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right) F_{58}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{21} \left(x \right)^{2} F_{11}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{11}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x , 1\right)\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{43}\! \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_{37}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{39}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)^{2} F_{42}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= y x\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}\\ F_{46}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x \right)+F_{53}\! \left(x , y\right)\\ F_{48}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{48}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\ F_{57}\! \left(x \right) &= F_{53}\! \left(x , 1\right)\\ F_{58}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{59}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{11}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 65 rules.

Found on January 23, 2022.

Finding the specification took 144 seconds.

Copy to clipboard:

View tree on standalone page.

+ Expand

Copy 65 equations to clipboard:
\(\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_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{0}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= x\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{20}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{11}\! \left(x \right) F_{62}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{11}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{21} \left(x \right)^{2} F_{11}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{11}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x , 1\right)\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{49}\! \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_{37}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\ F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , 1, y\right)\\ F_{40}\! \left(x , y , z\right) &= F_{41}\! \left(x , y z , z\right)\\ F_{41}\! \left(x , y , z\right) &= F_{42}\! \left(x , y\right)+F_{46}\! \left(x , y , z\right)\\ F_{42}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)^{2} F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= y x\\ F_{46}\! \left(x , y , z\right) &= F_{47}\! \left(x , y , z\right)\\ F_{47}\! \left(x , y , z\right) &= F_{42}\! \left(x , y\right) F_{45}\! \left(x , z\right) F_{48}\! \left(x , y , z\right)\\ F_{48}\! \left(x , y , z\right) &= -\frac{z F_{40}\! \left(x , 1, z\right)-y F_{40}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\ F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{51}\! \left(x , y\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_{34}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{53}\! \left(x , y\right) &= F_{54}\! \left(x \right)+F_{59}\! \left(x , y\right)\\ F_{54}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{11}\! \left(x \right)}\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{22}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{45}\! \left(x , y\right) F_{54}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{59}\! \left(x , 1\right)\\ F_{62}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{63}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{11}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\ \end{align*}\)