Av(12435, 12453, 21435, 21453, 24135, 24153)
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Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3292, 18806, 109834, 651436, 3907526, 23640140, 143982570, 881673958, ...
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This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 126 rules.

Finding the specification took 1819 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_{33}\! \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}+x F_{7}\! \left(x , y\right)^{4} y +2 x^{2} F_{7}\! \left(x , y\right) y^{2}+3 x F_{7}\! \left(x , y\right)^{3} y +y^{2} x^{2}+x F_{7}\! \left(x , y\right)^{2} y -x F_{7}\! \left(x , y\right) y -F_{7}\! \left(x , y\right)^{3}+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_{19}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{121}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{8}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{15}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= y x\\ F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{2}\! \left(x \right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)^{2} F_{19}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x \right)+F_{34}\! \left(x , y\right)\\ F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{32}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{33}\! \left(x \right) &= x\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{119}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{40}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= F_{31}\! \left(x \right)+F_{43}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{46}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= -\frac{y \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)\right)}{-1+y}\\ F_{47}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{51}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{53}\! \left(x \right)\\ F_{54}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)+F_{53}\! \left(x \right)\\ F_{55}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{54}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{59}\! \left(x \right) &= -F_{107}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{66}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{67}\! \left(x \right) &= x F_{67} \left(x \right)^{4}+x^{2} F_{67} \left(x \right)^{2}+3 x F_{67} \left(x \right)^{3}+2 x^{2} F_{67}\! \left(x \right)+x F_{67} \left(x \right)^{2}-F_{67} \left(x \right)^{3}+x^{2}-F_{67}\! \left(x \right) x +F_{67}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{33}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= \frac{F_{74}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{74}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{77}\! \left(x \right) x +F_{77} \left(x \right)^{2}+x\\ F_{78}\! \left(x \right) &= F_{67}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{33}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{79}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= -F_{106}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{102}\! \left(x \right)}\\ F_{85}\! \left(x \right) &= -F_{91}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= -F_{90}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{90}\! \left(x \right) x +F_{90} \left(x \right)^{2}-2 F_{90}\! \left(x \right)+2\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{33}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{33}\! \left(x \right)}\\ F_{97}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{67}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{105}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{106}\! \left(x \right) &= x F_{106} \left(x \right)^{4}+x^{2} F_{106} \left(x \right)^{2}-F_{106} \left(x \right)^{3} x -2 x F_{106} \left(x \right)^{2}-F_{106} \left(x \right)^{3}+2 F_{106}\! \left(x \right) x +3 F_{106} \left(x \right)^{2}-2 F_{106}\! \left(x \right)+1\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{67}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{110}\! \left(x \right) &= x^{4} F_{110}\! \left(x \right)+x^{3} F_{110} \left(x \right)^{2}-6 x^{3} F_{110}\! \left(x \right)-3 x^{2} F_{110} \left(x \right)^{2}+x^{3}+10 x^{2} F_{110}\! \left(x \right)+3 x F_{110} \left(x \right)^{2}-x^{2}-6 F_{110}\! \left(x \right) x -F_{110} \left(x \right)^{2}+2 F_{110}\! \left(x \right)\\ F_{111}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= -F_{113}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{49}\! \left(x , 1\right)\\ F_{117}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{119}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{43}\! \left(x , y\right)\\ F_{120}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{26}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)\\ F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{33}\! \left(x \right)\\ F_{124}\! \left(x , y\right) &= F_{123}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\ F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)\\ F_{125}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 80 rules.

Finding the specification took 891 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_{32}\! \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_{7}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{10}\! \left(x , y\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) &= x^{2} F_{11}\! \left(x , y\right)^{2} y^{2}+y x F_{11}\! \left(x , y\right)^{4}-x F_{11}\! \left(x , y\right)^{3} y -2 x F_{11}\! \left(x , y\right)^{2} y +2 x F_{11}\! \left(x , y\right) y -F_{11}\! \left(x , y\right)^{3}+3 F_{11}\! \left(x , y\right)^{2}-2 F_{11}\! \left(x , y\right)+1\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= y x\\ F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{32}\! \left(x \right)\\ F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\ F_{25}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{32}\! \left(x \right)\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{30}\! \left(x \right)+F_{33}\! \left(x , y\right)\\ F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{32}\! \left(x \right)}\\ F_{31}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{32}\! \left(x \right) &= x\\ F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\ F_{39}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{39}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{30}\! \left(x \right)+F_{42}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{32}\! \left(x \right) F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= -\frac{y \left(F_{46}\! \left(x , 1\right)-F_{46}\! \left(x , y\right)\right)}{-1+y}\\ F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y , 1\right)\\ F_{50}\! \left(x , y , z\right) &= F_{51}\! \left(x , y , y z \right)\\ F_{52}\! \left(x , y , z\right) &= -\frac{-F_{51}\! \left(x , y , z\right) z +F_{51}\! \left(x , y , 1\right)}{-1+z}\\ F_{53}\! \left(x , y , z\right) &= F_{32}\! \left(x \right) F_{52}\! \left(x , y , z\right)\\ F_{53}\! \left(x , y , z\right) &= F_{54}\! \left(x , y , z\right)\\ F_{54}\! \left(x , y , z\right) &= F_{55}\! \left(x , z\right)+F_{57}\! \left(x , y , z\right)\\ F_{55}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{57}\! \left(x , y , z\right) &= F_{58}\! \left(x , y , z\right)\\ F_{58}\! \left(x , y , z\right) &= F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{59}\! \left(x , z\right)\\ F_{60}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{5}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\ F_{64}\! \left(x , y\right) &= F_{11}\! \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_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\ F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\ F_{68}\! \left(x , y\right) &= F_{32}\! \left(x \right) F_{69}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{69}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)\\ F_{72}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\ F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)\\ F_{73}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\ F_{76}\! \left(x , y\right) &= -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}\\ F_{77}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\ F_{79}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{15}\! \left(x , y\right)\\ \end{align*}\)