Av(12345, 12435)
Counting Sequence
1, 1, 2, 6, 24, 118, 672, 4258, 29241, 213865, 1645677, 13204357, 109723588, 939262476, 8247972113, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 50 rules.
Finding the specification took 14115 seconds.
Copy 50 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , 1, y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{1}, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{17}\! \left(x , y_{0}, 1\right) y_{0}-F_{17}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{1}, y_{0}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{49}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{21}\! \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_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{26}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{39}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)+F_{44}\! \left(x , y_{2}, y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{3}, y_{0}, y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{3}\! \left(x \right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{26}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0} y_{1}-F_{26}\! \left(x , \frac{1}{y_{1}}, y_{1}, y_{2}, y_{3}\right)}{y_{0} y_{1}-1}\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{30}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}, y_{3}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{34}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)+F_{36}\! \left(x , y_{2}, y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{3}, y_{0}, y_{1}, y_{2}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{21}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{0}-F_{21}\! \left(x , y_{1}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{3}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{35}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{F_{26}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right) y_{1}-F_{26}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}, y_{3}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{37}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{19}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{19}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{31}\! \left(x , y_{1}, y_{2}, y_{3}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{40}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}-F_{41}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{3}}{-y_{3}+y_{2}}\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{42}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{42}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{43}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{46}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-y_{1} y_{2} F_{47}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{3}}, y_{3}\right)+y_{3} F_{47}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}, y_{3}\right)}{y_{1} y_{2}-y_{3}}\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{20}\! \left(x , y_{0} y_{1}, y_{1} y_{2}, y_{3}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{26}\! \left(x , y_{1}, y_{2}, y_{3}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 51 rules.
Finding the specification took 18550 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{4}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= -\frac{-F_{6}\! \left(x , y_{0}\right) y_{0}+F_{6}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , 1, y_{0}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}, y_{0}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{13}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{13}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{17}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{18}\! \left(x , y_{0}, 1\right) y_{0}-F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{1}, y_{0}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{1}, y_{0}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{50}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{22}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{27}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{40}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)+F_{45}\! \left(x , y_{2}, y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{3}, y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{4}\! \left(x \right)\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{27}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0} y_{1}-F_{27}\! \left(x , \frac{1}{y_{1}}, y_{1}, y_{2}, y_{3}\right)}{y_{0} y_{1}-1}\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{31}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}, y_{3}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{35}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)+F_{37}\! \left(x , y_{2}, y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{3}, y_{0}, y_{1}, y_{2}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{22}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{0}-F_{22}\! \left(x , y_{1}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{34}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{4}\! \left(x \right)\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0}+F_{32}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{10}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{F_{27}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right) y_{1}-F_{27}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}, y_{3}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
F_{38}\! \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_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{10}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{1}, y_{2}, y_{3}, y_{0}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{10}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}-F_{42}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{3}}{-y_{3}+y_{2}}\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{43}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{43}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{44}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{47}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-y_{1} y_{2} F_{48}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{3}}, y_{3}\right)+y_{3} F_{48}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}, y_{3}\right)}{y_{1} y_{2}-y_{3}}\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{21}\! \left(x , y_{0} y_{1}, y_{1} y_{2}, y_{3}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{10}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{1}, y_{2}, y_{3}, y_{0}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
\end{align*}\)