Av(13542, 15342, 51342)
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Counting Sequence
1, 1, 2, 6, 24, 117, 652, 3983, 25970, 177635, 1260031, 9195735, 68658450, 522286247, 4035341246, ...
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This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 85 rules.

Finding the specification took 46781 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_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= x^{3} F_{6} \left(x \right)^{2}+3 x^{2} F_{6} \left(x \right)^{2}+8 x^{2} F_{6}\! \left(x \right)+3 x F_{6} \left(x \right)^{2}-20 x F_{6}\! \left(x \right)+F_{6} \left(x \right)^{2}+16 x\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\ F_{11}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)\\ F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{2}\! \left(x \right)\\ F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)\\ F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)\\ F_{16}\! \left(x , y_{0}\right) &= -\frac{y_{0} \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}\\ F_{17}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{18}\! \left(x , y_{0}\right)\\ F_{18}\! \left(x , y_{0}\right) &= x^{3} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+2 x^{3} F_{18}\! \left(x , y_{0}\right) y_{0}^{3}+x^{3} y_{0}^{3}+3 x^{2} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+14 x^{2} F_{18}\! \left(x , y_{0}\right) y_{0}^{2}+11 y_{0}^{2} x^{2}+3 x F_{18}\! \left(x , y_{0}\right)^{2} y_{0}-14 x F_{18}\! \left(x , y_{0}\right) y_{0}-y_{0} x +F_{18}\! \left(x , y_{0}\right)^{2}+2 F_{18}\! \left(x , y_{0}\right)\\ F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)\\ F_{20}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)\\ F_{22}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)\\ F_{23}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}\right)\\ F_{24}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right)\\ F_{25}\! \left(x , y_{0}\right) &= F_{26}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)\\ F_{27}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)\\ F_{28}\! \left(x , y_{0}\right) &= F_{29}\! \left(x , y_{0}\right)\\ F_{29}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right)^{2} F_{31}\! \left(x , y_{0}\right)\\ F_{30}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)\\ F_{31}\! \left(x , y_{0}\right) &= y_{0} x\\ F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right)\\ F_{33}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)\\ F_{34}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)\\ F_{35}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)\\ F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}, 1\right)\\ F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}, y_{0} y_{1}\right)\\ F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}, y_{1}, 1\right)\\ F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{40}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x , y_{0}\right)\\ F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{77}\! \left(x , y_{0}, y_{1} y_{2}\right)\\ F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x , y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{0}, y_{0} y_{1}\right)\\ F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, 1, y_{1}\right)\\ F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{48}\! \left(x , y_{0} y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{48}\! \left(x , y_{0}\right) &= x^{3} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{48}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{48}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{48}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{48}\! \left(x , y_{0}\right)^{2}\\ F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{50}\! \left(x , y_{1}, y_{0}, y_{2}\right)\\ F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{52}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{53}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\ F_{53}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)\\ F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x , y_{0} y_{1}, y_{0} y_{2}\right)\\ F_{57}\! \left(x , y_{0}, y_{1}\right) &= F_{58}\! \left(x , 1, y_{0}, y_{1}\right)\\ F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{40}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\ F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{60}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{63}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{63}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\ F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{64}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right) F_{65}\! \left(x , y_{0}\right)\\ F_{65}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)\\ F_{66}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)\\ F_{67}\! \left(x , y_{0}\right) &= F_{68}\! \left(x , y_{0}\right)\\ F_{68}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)\\ F_{69}\! \left(x , y_{0}\right) &= F_{70}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)\\ F_{70}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)\\ F_{71}\! \left(x , y_{0}\right) &= F_{72}\! \left(x , 1, y_{0}\right)\\ F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{73}\! \left(x , y_{0} y_{1}, y_{1}\right)\\ F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{74}\! \left(x , y_{0}, y_{1}, 1\right)\\ F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{75}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{65}\! \left(x , y_{0}\right)\\ F_{77}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right) F_{48}\! \left(x , y_{0}\right)\\ F_{78}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{79}\! \left(x , y_{0}\right)\\ F_{79}\! \left(x , y_{0}\right) &= F_{80}\! \left(x , 1, y_{0}\right)\\ F_{80}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{81}\! \left(x , 1, y_{1}\right)-F_{81}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}\\ F_{81}\! \left(x , y_{0}, y_{1}\right) &= F_{82}\! \left(x , y_{0} y_{1}, y_{1}\right)\\ F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{82}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{1}\right)\\ F_{84}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}\right)\\ F_{84}\! \left(x , y_{0}\right) &= F_{66}\! \left(x , y_{0}\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 85 rules.

Finding the specification took 46781 seconds.

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Copy 85 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= x^{3} F_{6} \left(x \right)^{2}+3 x^{2} F_{6} \left(x \right)^{2}+8 x^{2} F_{6}\! \left(x \right)+3 x F_{6} \left(x \right)^{2}-20 x F_{6}\! \left(x \right)+F_{6} \left(x \right)^{2}+16 x\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\ F_{11}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)\\ F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{2}\! \left(x \right)\\ F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)\\ F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)\\ F_{16}\! \left(x , y_{0}\right) &= -\frac{y_{0} \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}\\ F_{17}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{18}\! \left(x , y_{0}\right)\\ F_{18}\! \left(x , y_{0}\right) &= x^{3} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+2 x^{3} F_{18}\! \left(x , y_{0}\right) y_{0}^{3}+x^{3} y_{0}^{3}+3 x^{2} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+14 x^{2} F_{18}\! \left(x , y_{0}\right) y_{0}^{2}+11 y_{0}^{2} x^{2}+3 x F_{18}\! \left(x , y_{0}\right)^{2} y_{0}-14 x F_{18}\! \left(x , y_{0}\right) y_{0}-y_{0} x +F_{18}\! \left(x , y_{0}\right)^{2}+2 F_{18}\! \left(x , y_{0}\right)\\ F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)\\ F_{20}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)\\ F_{22}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)\\ F_{23}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}\right)\\ F_{24}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right)\\ F_{25}\! \left(x , y_{0}\right) &= F_{26}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\ F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)\\ F_{27}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)\\ F_{28}\! \left(x , y_{0}\right) &= F_{29}\! \left(x , y_{0}\right)\\ F_{29}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right)^{2} F_{31}\! \left(x , y_{0}\right)\\ F_{30}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)\\ F_{31}\! \left(x , y_{0}\right) &= y_{0} x\\ F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right)\\ F_{33}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)\\ F_{34}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)\\ F_{35}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)\\ F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}, 1\right)\\ F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}, y_{0} y_{1}\right)\\ F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}, y_{1}, 1\right)\\ F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{40}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x , y_{0}\right)\\ F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{77}\! \left(x , y_{0}, y_{1} y_{2}\right)\\ F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x , y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{0}, y_{0} y_{1}\right)\\ F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, 1, y_{1}\right)\\ F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{48}\! \left(x , y_{0} y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{48}\! \left(x , y_{0}\right) &= x^{3} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{48}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{48}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{48}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{48}\! \left(x , y_{0}\right)^{2}\\ F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{50}\! \left(x , y_{1}, y_{0}, y_{2}\right)\\ F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{52}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{53}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\ F_{53}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)\\ F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x , y_{0} y_{1}, y_{0} y_{2}\right)\\ F_{57}\! \left(x , y_{0}, y_{1}\right) &= F_{58}\! \left(x , 1, y_{0}, y_{1}\right)\\ F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{40}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\ F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{60}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{63}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{63}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\ F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{64}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right) F_{65}\! \left(x , y_{0}\right)\\ F_{65}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)\\ F_{66}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)\\ F_{67}\! \left(x , y_{0}\right) &= F_{68}\! \left(x , y_{0}\right)\\ F_{68}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)\\ F_{69}\! \left(x , y_{0}\right) &= F_{70}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)\\ F_{70}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)\\ F_{71}\! \left(x , y_{0}\right) &= F_{72}\! \left(x , 1, y_{0}\right)\\ F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{73}\! \left(x , y_{0} y_{1}, y_{1}\right)\\ F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{74}\! \left(x , y_{0}, y_{1}, 1\right)\\ F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{75}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\ F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\ F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{65}\! \left(x , y_{0}\right)\\ F_{77}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right) F_{48}\! \left(x , y_{0}\right)\\ F_{78}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{79}\! \left(x , y_{0}\right)\\ F_{79}\! \left(x , y_{0}\right) &= F_{80}\! \left(x , 1, y_{0}\right)\\ F_{80}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{81}\! \left(x , 1, y_{1}\right)-F_{81}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}\\ F_{81}\! \left(x , y_{0}, y_{1}\right) &= F_{82}\! \left(x , y_{0} y_{1}, y_{1}\right)\\ F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{82}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{1}\right)\\ F_{84}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}\right)\\ F_{84}\! \left(x , y_{0}\right) &= F_{66}\! \left(x , y_{0}\right)\\ \end{align*}\)