Av(12345, 12354, 13245, 13254, 13524)
Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3514, 21117, 131604, 843518, 5527609, 36874144, 249604634, 1710291967, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 130 rules.
Finding the specification took 43685 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_{23}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{128}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{23}\! \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_{1}\! \left(x \right)+F_{126}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{9}\! \left(x , y_{0}, 1\right)\\
F_{9}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{1}\right)+F_{80}\! \left(x , y_{0}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}, y_{1}\right) F_{12}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right) F_{23}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{78}\! \left(x , y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}, 1\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{9}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{9}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right) F_{23}\! \left(x \right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{21}\! \left(x , y_{0}\right) y_{0}-F_{21}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{21}\! \left(x , y_{0}\right) &= -\frac{-F_{22}\! \left(x , y_{0}\right) y_{0}+F_{22}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{22}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}, 1\right)\\
F_{23}\! \left(x \right) &= x\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{25}\! \left(x , y_{0}, y_{1}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{27}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{29}\! \left(x , y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{9}\! \left(x , y_{0}, 1\right) y_{0}-F_{9}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{2}\right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{33}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{33}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{34}\! \left(x , 1, y_{1}\right) y_{1}-F_{34}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x \right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x \right) F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{38}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{1}, y_{2}\right)+F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{42}\! \left(x , y_{0}, 1\right) y_{0}-F_{42}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{1}\right)+F_{47}\! \left(x , y_{1}\right)+F_{87}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)\\
F_{46}\! \left(x , y_{0}\right) &= F_{42}\! \left(x , y_{0}, 1\right)\\
F_{47}\! \left(x , y_{0}\right) &= F_{23}\! \left(x \right) F_{48}\! \left(x , y_{0}\right)\\
F_{48}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= F_{50}\! \left(x , y_{0}, 1\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{52}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{53}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{1}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{1}, y_{2}\right)+F_{56}\! \left(x , y_{1}, y_{2}\right)+F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{1}\right) F_{33}\! \left(x , y_{0}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{57}\! \left(x , y_{0}, y_{1}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{58}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{58}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{58}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{0}, y_{1}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{60}\! \left(x , y_{0}, y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{61}\! \left(x , y_{0}\right) y_{0}-F_{61}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{61}\! \left(x , y_{0}\right) &= -\frac{-F_{62}\! \left(x , y_{0}\right) y_{0}+F_{62}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{62}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{45}\! \left(x , y_{0}\right)+F_{47}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)\\
F_{63}\! \left(x , y_{0}\right) &= F_{23}\! \left(x \right) F_{61}\! \left(x , y_{0}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x \right) F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{66}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{66}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{67}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{67}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{45}\! \left(x , y_{1}\right)+F_{68}\! \left(x , y_{0}, y_{1}\right)+F_{69}\! \left(x , y_{0}, y_{1}\right)+F_{80}\! \left(x , y_{0}, y_{1}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{67}\! \left(x , y_{0}, y_{1}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{1}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)+F_{72}\! \left(x , y_{0}, y_{1}\right)+F_{78}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{73}\! \left(x , y_{0}, 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) &= -\frac{-F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{75}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{50}\! \left(x , y_{1}, y_{2}\right)+F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x \right) F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{79}\! \left(x , y_{0}, y_{1}\right)\\
F_{79}\! \left(x , y_{0}, y_{1}\right) &= F_{37}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{80}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{81}\! \left(x , y_{0}, y_{1}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{82}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{23}\! \left(x \right)\\
F_{83}\! \left(x , y_{0}\right) &= F_{23}\! \left(x \right) F_{84}\! \left(x , y_{0}\right)\\
F_{84}\! \left(x , y_{0}\right) &= F_{57}\! \left(x , y_{0}, 1\right)\\
F_{85}\! \left(x , y_{0}\right) &= F_{23}\! \left(x \right) F_{86}\! \left(x , y_{0}\right)\\
F_{86}\! \left(x , y_{0}\right) &= -\frac{-F_{61}\! \left(x , y_{0}\right) y_{0}+F_{61}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{87}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x \right) F_{66}\! \left(x , y_{0}, y_{1}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{2}\right) F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{89}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{90}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{90}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{91}\! \left(x , 1, y_{1}\right) y_{1}-F_{91}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{91}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x \right) F_{93}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{93}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{102}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{106}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{108}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{124}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{94}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{95}\! \left(x , y_{1}, y_{2}\right)\\
F_{94}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{93}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{95}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{97}\! \left(x , y_{0}, 1\right) y_{0}-F_{97}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{97}\! \left(x , y_{0}, y_{1}\right) &= F_{98}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{1}\right)+F_{82}\! \left(x , y_{1}\right)+F_{83}\! \left(x , y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{99}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{98}\! \left(x , y_{0}, y_{1}\right)\\
F_{100}\! \left(x , y_{0}, y_{1}\right) &= F_{101}\! \left(x , y_{0}, y_{1}\right) F_{23}\! \left(x \right)\\
F_{101}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{66}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{66}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{102}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{103}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{12}\! \left(x , y_{2}\right)\\
F_{103}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{104}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{104}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{104}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{105}\! \left(x , 1, y_{1}\right) y_{1}-F_{105}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{105}\! \left(x , y_{0}, y_{1}\right) &= F_{98}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{106}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{107}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{23}\! \left(x \right)\\
F_{107}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{20}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{108}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{109}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{23}\! \left(x \right)\\
F_{109}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{110}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right)\\
F_{110}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-F_{111}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{3}+F_{111}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right)}{-1+y_{3}}\\
F_{111}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{1}\! \left(x \right)+F_{112}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{113}\! \left(x , y_{1}, y_{2}, y_{3}\right)+F_{115}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{119}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{121}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{122}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{112}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{111}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{12}\! \left(x , y_{0}\right)\\
F_{113}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{12}\! \left(x , y_{0}\right)\\
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{52}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{52}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{116}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{12}\! \left(x , y_{2}\right)\\
F_{116}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{117}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{0}-F_{117}\! \left(x , y_{1}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{F_{118}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{118}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{118}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{53}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{119}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{12}\! \left(x , y_{3}\right) F_{120}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{120}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{32}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{0}-F_{32}\! \left(x , y_{1}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{121}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{110}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{23}\! \left(x \right)\\
F_{122}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{123}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{23}\! \left(x \right)\\
F_{123}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}-F_{37}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{3}}{-y_{3}+y_{2}}\\
F_{124}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{23}\! \left(x \right)\\
F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{37}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{126}\! \left(x , y_{0}\right) &= F_{127}\! \left(x , y_{0}\right) F_{23}\! \left(x \right)\\
F_{127}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{6}\! \left(x , y_{0}\right)+F_{6}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{62}\! \left(x , 1\right)\\
\end{align*}\)