Av(14352, 41352, 43152, 43512)
Counting Sequence
1, 1, 2, 6, 24, 116, 634, 3766, 23742, 156498, 1067910, 7491666, 53758908, 393106896, 2920778054, ...
This specification was found using the strategy pack "Partial Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 60 rules.
Finding the specification took 8512 seconds.
Copy 60 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_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{6}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= x^{3} F_{6}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{6}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{6}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{6}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{6}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{6}\! \left(x , y_{0}\right)^{2}\\
F_{7}\! \left(x , y_{0}\right) &= F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{12}\! \left(x \right)\\
F_{11}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= y_{0} F_{15}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{12}\! \left(x \right) F_{17}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , 1, y_{0}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{19}\! \left(x , 1, y_{1}\right)-F_{19}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right)^{2} F_{23}\! \left(x , y_{0}\right)\\
F_{23}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{24}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{33}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{1}, y_{2}\right)+F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{6}\! \left(x , y_{1}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= y_{0} F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{1}, y_{2}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{39}\! \left(x , y_{0}\right) &= F_{40}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right)^{2} F_{12}\! \left(x \right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{1}, y_{2}\right) F_{43}\! \left(x , y_{0}, y_{2}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0}, y_{1}\right) F_{54}\! \left(x , y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{0}, y_{1}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}\right) &= F_{49}\! \left(x , y_{0}, y_{1}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{51}\! \left(y_{0} x , y_{1}\right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{12}\! \left(x \right) F_{51}\! \left(x , y_{0}\right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}\right) F_{54}\! \left(x , y_{1}\right)\\
F_{54}\! \left(x , y_{0}\right) &= x^{3} F_{54}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+2 x^{3} F_{54}\! \left(x , y_{0}\right) y_{0}^{3}+x^{3} y_{0}^{3}+3 x^{2} F_{54}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+14 x^{2} F_{54}\! \left(x , y_{0}\right) y_{0}^{2}+11 x^{2} y_{0}^{2}+3 x F_{54}\! \left(x , y_{0}\right)^{2} y_{0}-14 x F_{54}\! \left(x , y_{0}\right) y_{0}-y_{0} x +F_{54}\! \left(x , y_{0}\right)^{2}+2 F_{54}\! \left(x , y_{0}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}\right) F_{6}\! \left(x , y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}\right) &= F_{54}\! \left(x , y_{1}\right) F_{58}\! \left(x , y_{0}, y_{1}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{47}\! \left(x , y_{0}, y_{1}\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 51 rules.
Finding the specification took 11532 seconds.
Copy 51 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_{29}\! \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 , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{7}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= x^{3} F_{7}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+2 x^{3} F_{7}\! \left(x , y_{0}\right) y_{0}^{3}+x^{3} y_{0}^{3}+3 x^{2} F_{7}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+14 x^{2} F_{7}\! \left(x , y_{0}\right) y_{0}^{2}+11 y_{0}^{2} x^{2}+3 x F_{7}\! \left(x , y_{0}\right)^{2} y_{0}-14 x F_{7}\! \left(x , y_{0}\right) y_{0}-y_{0} x +F_{7}\! \left(x , y_{0}\right)^{2}+2 F_{7}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{29}\! \left(x \right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{12}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}\right) &= -\frac{y_{0} \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , 1, y_{0}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{18}\! \left(x , 1, y_{1}\right)-F_{18}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}, y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x , y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{25}\! \left(x , y_{0}\right) &= x^{3} F_{25}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{25}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{25}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{25}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{25}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{25}\! \left(x , y_{0}\right)^{2}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= y_{0} y_{1} F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{29}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{29}\! \left(x \right) &= x\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{32}\! \left(x , y_{1}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right)^{2} F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{35}\! \left(x , y_{2}\right) F_{38}\! \left(x , y_{1}, y_{2}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{1}\right) F_{38}\! \left(x , y_{0}, y_{1}\right) F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}\right) F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{1}\right) F_{48}\! \left(x , y_{0}, y_{1}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{1}\right) F_{48}\! \left(x , y_{0}, y_{1}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= F_{50}\! \left(x , y_{0}, y_{1}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{18}\! \left(x , 1, y_{1}\right)-F_{18}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}\\
\end{align*}\)