Av(14325, 14352, 14532, 41325, 41352, 41532, 43125, 43152, 43512, 45132, 45312)
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1, 1, 2, 6, 24, 109, 522, 2574, 12964, 66426, 345300, 1816976, 9660732, 51825093, 280168474, ...
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This specification was found using the strategy pack "Row And Col Placements Tracked Fusion" and has 19 rules.

Found on January 23, 2022.

Finding the specification took 66 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{18}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\ F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{5}\! \left(x , y\right)\\ F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y , 1\right)\\ F_{6}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right) F_{7}\! \left(x , y , z\right)\\ F_{7}\! \left(x , y , z\right) &= \frac{y F_{8}\! \left(x , y , 1\right)-z F_{8}\! \left(x , y , \frac{z}{y}\right)}{-z +y}\\ F_{8}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y , z\right)+F_{9}\! \left(x , y , z\right)\\ F_{9}\! \left(x , y , z\right) &= F_{6}\! \left(x , y , y z \right)\\ F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , z\right) F_{13}\! \left(x , z\right) F_{8}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y\right) &= y x\\ F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{13}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{18}\! \left(x \right)\\ F_{17}\! \left(x , y\right) &= \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}\\ F_{18}\! \left(x \right) &= x\\ \end{align*}\)

This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 20 rules.

Found on January 22, 2022.

Finding the specification took 6 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{19}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\ F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{5}\! \left(x , y\right)\\ F_{5}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{6}\! \left(x , y\right)\\ F_{6}\! \left(x , y\right) &= \frac{y F_{7}\! \left(x , y , 1\right)-F_{7}\! \left(x , y , \frac{1}{y}\right)}{-1+y}\\ F_{7}\! \left(x , y , z\right) &= F_{8}\! \left(x , y , y z \right)\\ F_{8}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{9}\! \left(x , y , z\right)\\ F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , z\right) F_{11}\! \left(x , y\right)\\ F_{10}\! \left(x , y , z\right) &= \frac{y F_{7}\! \left(x , y , 1\right)-z F_{7}\! \left(x , y , \frac{z}{y}\right)}{-z +y}\\ F_{11}\! \left(x , y\right) &= y x\\ F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right)\\ F_{13}\! \left(x , y , z\right) &= F_{11}\! \left(x , z\right) F_{14}\! \left(x , z\right) F_{8}\! \left(x , y , z\right)\\ F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{19}\! \left(x \right)\\ F_{18}\! \left(x , y\right) &= -\frac{-y F_{4}\! \left(x , y\right)+F_{4}\! \left(x , 1\right)}{-1+y}\\ F_{19}\! \left(x \right) &= x\\ \end{align*}\)