Av(12435, 12453, 14235, 14253, 21435, 21453)
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Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3298, 18944, 111774, 673104, 4119464, 25544388, 160127770, 1012992140, ...
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This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 58 rules.

Finding the specification took 1706 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_{31}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\ F_{5}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\ F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{7}\! \left(x , y\right) &= x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 F_{7}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{31}\! \left(x \right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= x^{2} F_{16}\! \left(x , y\right)^{2} y^{2}-2 y x F_{16}\! \left(x , y\right)^{2}+x F_{16}\! \left(x , y\right) y +2 F_{16}\! \left(x , y\right)-1\\ F_{18}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\ F_{20}\! \left(x , y\right) &= y x\\ F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{31}\! \left(x \right)\\ F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x \right)+F_{32}\! \left(x , y\right)\\ F_{28}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{31}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{31}\! \left(x \right) &= x\\ F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)\\ F_{33}\! \left(x , y\right) &= F_{31}\! \left(x \right) F_{34}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= -\frac{y \left(F_{35}\! \left(x , 1\right)-F_{35}\! \left(x , y\right)\right)}{-1+y}\\ F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{38}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y , 1\right)\\ F_{39}\! \left(x , y , z\right) &= F_{40}\! \left(x , y , y z \right)\\ F_{41}\! \left(x , y , z\right) &= -\frac{-z F_{40}\! \left(x , y , z\right)+F_{40}\! \left(x , y , 1\right)}{-1+z}\\ F_{42}\! \left(x , y , z\right) &= F_{31}\! \left(x \right) F_{41}\! \left(x , y , z\right)\\ F_{42}\! \left(x , y , z\right) &= F_{43}\! \left(x , y , z\right)\\ F_{43}\! \left(x , y , z\right) &= F_{27}\! \left(x , z\right)+F_{44}\! \left(x , y , z\right)\\ F_{44}\! \left(x , y , z\right) &= F_{45}\! \left(x , y , z\right)\\ F_{45}\! \left(x , y , z\right) &= F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{46}\! \left(x , z\right)\\ F_{47}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{46}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{50}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{5}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{5}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{31}\! \left(x \right)\\ F_{57}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 82 rules.

Finding the specification took 5857 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_{38}\! \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\right) &= F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{7}\! \left(x , y\right) &= x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 F_{7}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{38}\! \left(x \right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{7}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= y x\\ F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{23}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{23}\! \left(x , y\right)\\ F_{31}\! \left(x , y\right) &= x^{2} F_{31}\! \left(x , y\right)^{2} y^{2}-2 x F_{31}\! \left(x , y\right)^{2} y +x F_{31}\! \left(x , y\right) y +2 F_{31}\! \left(x , y\right)-1\\ F_{33}\! \left(x , y\right) &= F_{32}\! \left(x , y\right) F_{38}\! \left(x \right)\\ F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x \right)+F_{60}\! \left(x , y\right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{38}\! \left(x \right) &= x\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{38}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{47}\! \left(x \right) &= 0\\ F_{48}\! \left(x \right) &= F_{38}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{38}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{55}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= -F_{59}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= \frac{F_{58}\! \left(x \right)}{F_{38}\! \left(x \right)}\\ F_{58}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{38}\! \left(x \right) F_{62}\! \left(x , y\right)\\ F_{62}\! \left(x , y\right) &= -\frac{y \left(F_{63}\! \left(x , 1\right)-F_{63}\! \left(x , y\right)\right)}{-1+y}\\ F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\ F_{64}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)+F_{65}\! \left(x , y\right)\\ F_{65}\! \left(x , y\right) &= F_{66}\! \left(x , y\right)\\ F_{66}\! \left(x , y\right) &= F_{38}\! \left(x \right) F_{67}\! \left(x , y\right)\\ F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\ F_{68}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{69}\! \left(x \right)\\ F_{70}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)+F_{69}\! \left(x \right)\\ F_{71}\! \left(x , y\right) &= F_{38}\! \left(x \right) F_{70}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)\\ F_{72}\! \left(x , y\right) &= F_{73}\! \left(x \right)+F_{80}\! \left(x , y\right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{75}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= -F_{79}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= \frac{F_{78}\! \left(x \right)}{F_{38}\! \left(x \right)}\\ F_{78}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{63}\! \left(x , 1\right)\\ F_{80}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 82 rules.

Finding the specification took 3540 seconds.

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