Av(1234, 4231)
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Generating Function
\(\displaystyle -\frac{2 x^{11}-20 x^{10}+83 x^{9}-217 x^{8}+413 x^{7}-554 x^{6}+519 x^{5}-357 x^{4}+172 x^{3}-56 x^{2}+11 x -1}{\left(x -1\right)^{12}}\)
Counting Sequence
1, 1, 2, 6, 22, 86, 332, 1217, 4140, 12934, 37088, 98115, 241269, 555881, 1208988, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(x -1\right)^{12} F \! \left(x \right)+2 x^{11}-20 x^{10}+83 x^{9}-217 x^{8}+413 x^{7}-554 x^{6}+519 x^{5}-357 x^{4}+172 x^{3}-56 x^{2}+11 x -1 = 0\)
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 22\)
\(\displaystyle a \! \left(5\right) = 86\)
\(\displaystyle a \! \left(6\right) = 332\)
\(\displaystyle a \! \left(7\right) = 1217\)
\(\displaystyle a \! \left(8\right) = 4140\)
\(\displaystyle a \! \left(9\right) = 12934\)
\(\displaystyle a \! \left(10\right) = 37088\)
\(\displaystyle a \! \left(11\right) = 98115\)
\(\displaystyle a \! \left(n \right) = 1-\frac{1251}{3080} n +\frac{2629}{5600} n^{2}-\frac{1}{8064} n^{8}+\frac{527}{241920} n^{7}-\frac{17}{2400} n^{6}+\frac{9301}{725760} n^{5}+\frac{913}{24192} n^{4}-\frac{6581}{60480} n^{3}-\frac{1}{80640} n^{9}+\frac{1}{302400} n^{10}+\frac{1}{7983360} n^{11}, \quad n \geq 12\)
Explicit Closed Form
\(\displaystyle 1-\frac{1251}{3080} n +\frac{2629}{5600} n^{2}-\frac{1}{8064} n^{8}+\frac{527}{241920} n^{7}-\frac{17}{2400} n^{6}+\frac{9301}{725760} n^{5}+\frac{913}{24192} n^{4}-\frac{6581}{60480} n^{3}-\frac{1}{80640} n^{9}+\frac{1}{302400} n^{10}+\frac{1}{7983360} n^{11}\)

To create this heatmap, we sampled 1,000,000 permutations of length 300 uniformly at random. The color of the point \((i, j)\) represents how many permutations have value \(j\) at index \(i\) (darker = more).

This specification was found using the strategy pack "Regular Insertion Encoding Bottom" and has 421 rules.

Found on April 28, 2021.

Finding the specification took 12 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_{17}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{17}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{17}\! \left(x \right) &= x\\ F_{18}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{17}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{17}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{17}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{17}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{36}\! \left(x \right) &= 0\\ F_{37}\! \left(x \right) &= F_{17}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{17}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{17}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{17}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{17}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{53}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{17}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{53}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{17}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{17}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{306}\! \left(x \right)+F_{36}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{17}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{65}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{17}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{17}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{17}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{76}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{17}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{17}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{17}\! \left(x \right) F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{17}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{17}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{9}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{40}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{17}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{17}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{99}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{120}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{109}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{124}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{125}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{127}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{125}\! \left(x \right)+F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{130}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{131}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{132}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{141}\! \left(x \right)\\ F_{140}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{132}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{141}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{142}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{144}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{142}\! \left(x \right)+F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{139}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{202}\! \left(x \right)+F_{263}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{153}\! \left(x \right)+F_{177}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{160}\! \left(x \right)\\ F_{164}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{165}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{155}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{17}\! \left(x \right) F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{17}\! \left(x \right) F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{17}\! \left(x \right) F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{183}\! \left(x \right)+F_{185}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{17}\! \left(x \right) F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{17}\! \left(x \right) F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{17}\! \left(x \right) F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{17}\! \left(x \right) F_{190}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{17}\! \left(x \right) F_{193}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{187}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{17}\! \left(x \right) F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{17}\! \left(x \right) F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{197}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{17}\! \left(x \right) F_{203}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{227}\! \left(x \right)\\ F_{205}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{206}\! \left(x \right)+F_{215}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{17}\! \left(x \right) F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{208}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{206}\! \left(x \right)+F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{17}\! \left(x \right) F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{17}\! \left(x \right) F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{17}\! \left(x \right) F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{219}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{220}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{17}\! \left(x \right) F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{222}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{220}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{17}\! \left(x \right) F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{17}\! \left(x \right) F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{227}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{228}\! \left(x \right)+F_{245}\! \left(x \right)+F_{247}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{17}\! \left(x \right) F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{230}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{228}\! \left(x \right)+F_{231}\! \left(x \right)+F_{233}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{17}\! \left(x \right) F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{155}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{17}\! \left(x \right) F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{236}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{237}\! \left(x \right)+F_{239}\! \left(x \right)+F_{241}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{17}\! \left(x \right) F_{238}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{17}\! \left(x \right) F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{173}\! \left(x \right)\\ F_{241}\! \left(x \right) &= 0\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{17}\! \left(x \right) F_{244}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{235}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{17}\! \left(x \right) F_{246}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{204}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{17}\! \left(x \right) F_{248}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{255}\! \left(x \right)\\ F_{250}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{237}\! \left(x \right)+F_{251}\! \left(x \right)+F_{254}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{17}\! \left(x \right) F_{252}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{254}\! \left(x \right) &= 0\\ F_{255}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{256}\! \left(x \right)+F_{261}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{17}\! \left(x \right) F_{257}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{258}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{256}\! \left(x \right)+F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{17}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{235}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{17}\! \left(x \right) F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{249}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{17}\! \left(x \right) F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{267}\! \left(x \right)+F_{270}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{17}\! \left(x \right) F_{268}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{253}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{17}\! \left(x \right) F_{271}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{274}\! \left(x \right)+F_{279}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{17}\! \left(x \right) F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{276}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{274}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{17}\! \left(x \right) F_{278}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{187}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{17}\! \left(x \right) F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{272}\! \left(x \right)\\ F_{281}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{282}\! \left(x \right)+F_{294}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{17}\! \left(x \right) F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{284}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{282}\! \left(x \right)+F_{285}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{17}\! \left(x \right) F_{286}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{287}\! \left(x \right)\\ F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{291}\! \left(x \right)\\ F_{288}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{277}\! \left(x \right)+F_{289}\! \left(x \right)\\ F_{289}\! \left(x \right) &= F_{17}\! \left(x \right) F_{290}\! \left(x \right)\\ F_{290}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{288}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{17}\! \left(x \right) F_{293}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{287}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{17}\! \left(x \right) F_{295}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{296}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{298}\! \left(x \right)\\ F_{297}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{279}\! \left(x \right)+F_{289}\! \left(x \right)\\ F_{298}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{299}\! \left(x \right)+F_{304}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{17}\! \left(x \right) F_{300}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{299}\! \left(x \right)+F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= F_{17}\! \left(x \right) F_{303}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{287}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{17}\! \left(x \right) F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{296}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{17}\! \left(x \right) F_{307}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{308}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)+F_{312}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)+F_{36}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{17}\! \left(x \right) F_{311}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{269}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{312}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{313}\! \left(x \right)+F_{392}\! \left(x \right)\\ F_{313}\! \left(x \right) &= F_{17}\! \left(x \right) F_{314}\! \left(x \right)\\ F_{314}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{335}\! \left(x \right)\\ F_{315}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{316}\! \left(x \right)\\ F_{316}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{317}\! \left(x \right)+F_{325}\! \left(x \right)\\ F_{317}\! \left(x \right) &= F_{17}\! \left(x \right) F_{318}\! \left(x \right)\\ F_{318}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{319}\! \left(x \right)\\ F_{319}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{320}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{321}\! \left(x \right)+F_{323}\! \left(x \right)\\ F_{321}\! \left(x \right) &= F_{17}\! \left(x \right) F_{322}\! \left(x \right)\\ F_{322}\! \left(x \right) &= F_{319}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{17}\! \left(x \right) F_{324}\! \left(x \right)\\ F_{324}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{325}\! \left(x \right) &= F_{17}\! \left(x \right) F_{326}\! \left(x \right)\\ F_{326}\! \left(x \right) &= F_{327}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{332}\! \left(x \right)\\ F_{328}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{329}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{329}\! \left(x \right) &= F_{17}\! \left(x \right) F_{330}\! \left(x \right)\\ F_{330}\! \left(x \right) &= F_{331}\! \left(x \right)\\ F_{331}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{328}\! \left(x \right)\\ F_{332}\! \left(x \right) &= F_{333}\! \left(x \right)\\ F_{333}\! \left(x \right) &= F_{17}\! \left(x \right) F_{334}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{327}\! \left(x \right)\\ F_{335}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{336}\! \left(x \right)\\ F_{336}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{337}\! \left(x \right)+F_{360}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{337}\! \left(x \right) &= F_{17}\! \left(x \right) F_{338}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{339}\! \left(x \right)\\ F_{339}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{337}\! \left(x \right)+F_{340}\! \left(x \right)+F_{348}\! \left(x \right)\\ F_{340}\! \left(x \right) &= F_{17}\! \left(x \right) F_{341}\! \left(x \right)\\ F_{341}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{342}\! \left(x \right)\\ F_{342}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{343}\! \left(x \right)\\ F_{343}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{344}\! \left(x \right)+F_{346}\! \left(x \right)\\ F_{344}\! \left(x \right) &= F_{17}\! \left(x \right) F_{345}\! \left(x \right)\\ F_{345}\! \left(x \right) &= F_{342}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{17}\! \left(x \right) F_{347}\! \left(x \right)\\ F_{347}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{348}\! \left(x \right) &= F_{17}\! \left(x \right) F_{349}\! \left(x \right)\\ F_{349}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{350}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{351}\! \left(x \right)+F_{357}\! \left(x \right)\\ F_{351}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{352}\! \left(x \right)+F_{354}\! \left(x \right)+F_{355}\! \left(x \right)\\ F_{352}\! \left(x \right) &= F_{17}\! \left(x \right) F_{353}\! \left(x \right)\\ F_{353}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{351}\! \left(x \right)\\ F_{354}\! \left(x \right) &= 0\\ F_{355}\! \left(x \right) &= F_{17}\! \left(x \right) F_{356}\! \left(x \right)\\ F_{356}\! \left(x \right) &= F_{187}\! \left(x \right)\\ F_{357}\! \left(x \right) &= F_{358}\! \left(x \right)\\ F_{358}\! \left(x \right) &= F_{17}\! \left(x \right) F_{359}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{350}\! \left(x \right)\\ F_{360}\! \left(x \right) &= F_{17}\! \left(x \right) F_{361}\! \left(x \right)\\ F_{361}\! \left(x \right) &= F_{335}\! \left(x \right)+F_{362}\! \left(x \right)\\ F_{362}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{363}\! \left(x \right)\\ F_{363}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{364}\! \left(x \right)+F_{371}\! \left(x \right)+F_{373}\! \left(x \right)\\ F_{364}\! \left(x \right) &= F_{17}\! \left(x \right) F_{365}\! \left(x \right)\\ F_{365}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{366}\! \left(x \right)\\ F_{366}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{364}\! \left(x \right)+F_{367}\! \left(x \right)+F_{369}\! \left(x \right)\\ F_{367}\! \left(x \right) &= F_{17}\! \left(x \right) F_{368}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{342}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{17}\! \left(x \right) F_{370}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{235}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{17}\! \left(x \right) F_{372}\! \left(x \right)\\ F_{372}\! \left(x \right) &= F_{362}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{17}\! \left(x \right) F_{374}\! \left(x \right)\\ F_{374}\! \left(x \right) &= F_{249}\! \left(x \right)\\ F_{375}\! \left(x \right) &= F_{17}\! \left(x \right) F_{376}\! \left(x \right)\\ F_{376}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{377}\! \left(x \right)\\ F_{377}\! \left(x \right) &= F_{378}\! \left(x \right)+F_{384}\! \left(x \right)\\ F_{378}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{352}\! \left(x \right)+F_{379}\! \left(x \right)+F_{382}\! \left(x \right)\\ F_{379}\! \left(x \right) &= F_{17}\! \left(x \right) F_{380}\! \left(x \right)\\ F_{380}\! \left(x \right) &= F_{381}\! \left(x \right)\\ F_{381}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{378}\! \left(x \right)\\ F_{382}\! \left(x \right) &= F_{17}\! \left(x \right) F_{383}\! \left(x \right)\\ F_{383}\! \left(x \right) &= F_{272}\! \left(x \right)\\ F_{384}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{385}\! \left(x \right)+F_{390}\! \left(x \right)\\ F_{385}\! \left(x \right) &= F_{17}\! \left(x \right) F_{386}\! \left(x \right)\\ F_{386}\! \left(x \right) &= F_{332}\! \left(x \right)+F_{387}\! \left(x \right)\\ F_{387}\! \left(x \right) &= 4 F_{36}\! \left(x \right)+F_{385}\! \left(x \right)+F_{388}\! \left(x \right)\\ F_{388}\! \left(x \right) &= F_{17}\! \left(x \right) F_{389}\! \left(x \right)\\ F_{389}\! \left(x \right) &= F_{350}\! \left(x \right)\\ F_{390}\! \left(x \right) &= F_{17}\! \left(x \right) F_{391}\! \left(x \right)\\ F_{391}\! \left(x \right) &= F_{377}\! \left(x \right)\\ F_{392}\! \left(x \right) &= F_{17}\! \left(x \right) F_{393}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{308}\! \left(x \right)+F_{394}\! \left(x \right)\\ F_{394}\! \left(x \right) &= F_{395}\! \left(x \right)+F_{398}\! \left(x \right)\\ F_{395}\! \left(x \right) &= 2 F_{36}\! \left(x \right)+F_{396}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{396}\! \left(x \right) &= F_{17}\! \left(x \right) F_{397}\! \left(x \right)\\ F_{397}\! \left(x \right) &= F_{331}\! \left(x \right)+F_{381}\! \left(x \right)\\ F_{398}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{399}\! \left(x \right)+F_{419}\! \left(x \right)\\ F_{399}\! \left(x \right) &= F_{17}\! \left(x \right) F_{400}\! \left(x \right)\\ F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)+F_{407}\! \left(x \right)\\ F_{401}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{402}\! \left(x \right)\\ F_{402}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{403}\! \left(x \right)+F_{405}\! \left(x \right)\\ F_{403}\! \left(x \right) &= F_{17}\! \left(x \right) F_{404}\! \left(x \right)\\ F_{404}\! \left(x \right) &= F_{401}\! \left(x \right)\\ F_{405}\! \left(x \right) &= F_{17}\! \left(x \right) F_{406}\! \left(x \right)\\ F_{406}\! \left(x \right) &= F_{327}\! \left(x \right)\\ F_{407}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{408}\! \left(x \right)\\ F_{408}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{409}\! \left(x \right)+F_{415}\! \left(x \right)+F_{417}\! \left(x \right)\\ F_{409}\! \left(x \right) &= F_{17}\! \left(x \right) F_{410}\! \left(x \right)\\ F_{410}\! \left(x \right) &= F_{402}\! \left(x \right)+F_{411}\! \left(x \right)\\ F_{411}\! \left(x \right) &= 3 F_{36}\! \left(x \right)+F_{409}\! \left(x \right)+F_{412}\! \left(x \right)+F_{413}\! \left(x \right)\\ F_{412}\! \left(x \right) &= 0\\ F_{413}\! \left(x \right) &= F_{17}\! \left(x \right) F_{414}\! \left(x \right)\\ F_{414}\! \left(x \right) &= F_{350}\! \left(x \right)\\ F_{415}\! \left(x \right) &= F_{17}\! \left(x \right) F_{416}\! \left(x \right)\\ F_{416}\! \left(x \right) &= F_{407}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{17}\! \left(x \right) F_{418}\! \left(x \right)\\ F_{418}\! \left(x \right) &= F_{377}\! \left(x \right)\\ F_{419}\! \left(x \right) &= F_{17}\! \left(x \right) F_{420}\! \left(x \right)\\ F_{420}\! \left(x \right) &= F_{394}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements" and has 557 rules.

Found on January 18, 2022.

Finding the specification took 55 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{24}\! \left(x \right) &= 0\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{48}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{4}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{452}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{4}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{7}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{4}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{51}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{4}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{4}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{130}\! \left(x \right)+F_{24}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{4}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{4}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{100}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{4}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{102}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{100}\! \left(x \right)+F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{110}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{114}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{115}\! \left(x \right)+F_{116}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{115}\! \left(x \right) &= 0\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{121}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{119}\! \left(x \right)+F_{122}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{122}\! \left(x \right) &= 0\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{133}\! \left(x \right)+F_{136}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{140}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{141}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{144}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{145}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{148}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{149}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{151}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{149}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{158}\! \left(x \right)\\ F_{153}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{154}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{157}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{158}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{159}\! \left(x \right)+F_{163}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{167}\! \left(x \right)+F_{170}\! \left(x \right)+F_{173}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{173}\! \left(x \right) &= 0\\ F_{174}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{176}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{175}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{200}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{183}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{184}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{190}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{188}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{151}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{151}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{215}\! \left(x \right)\\ F_{201}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{202}\! \left(x \right)+F_{211}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)+F_{210}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)+F_{214}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{201}\! \left(x \right)\\ F_{215}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{216}\! \left(x \right)+F_{237}\! \left(x \right)+F_{241}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{219}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{221}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{224}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{226}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{225}\! \left(x \right)+F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{231}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{240}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{215}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{241}\! \left(x \right)+F_{244}\! \left(x \right)+F_{248}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{247}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{248}\! \left(x \right) &= 0\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{275}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{252}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{253}\! \left(x \right)+F_{257}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{256}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{252}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{259}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{257}\! \left(x \right)+F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{261}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{274}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{268}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{270}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{315}\! \left(x \right)\\ F_{276}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{277}\! \left(x \right)+F_{292}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{278}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{283}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)+F_{286}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{281}\! \left(x \right)+F_{287}\! \left(x \right)\\ F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\ F_{288}\! \left(x \right) &= F_{289}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{289}\! \left(x \right) &= F_{290}\! \left(x \right)+F_{291}\! \left(x \right)\\ F_{290}\! \left(x \right) &= F_{285}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{287}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{293}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)+F_{300}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{297}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)+F_{299}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{295}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{302}\! \left(x \right)+F_{311}\! \left(x \right)\\ F_{302}\! \left(x \right) &= F_{303}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{304}\! \left(x \right)+F_{305}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{306}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{307}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{308}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)+F_{310}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{306}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{312}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{312}\! \left(x \right) &= F_{313}\! \left(x \right)+F_{314}\! \left(x \right)\\ F_{313}\! \left(x \right) &= F_{295}\! \left(x \right)\\ F_{314}\! \left(x \right) &= F_{301}\! \left(x \right)\\ F_{315}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{316}\! \left(x \right)+F_{364}\! \left(x \right)+F_{441}\! \left(x \right)\\ F_{316}\! \left(x \right) &= F_{317}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{317}\! \left(x \right) &= F_{318}\! \left(x \right)+F_{319}\! \left(x \right)\\ F_{318}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{319}\! \left(x \right) &= F_{220}\! \left(x \right)+F_{320}\! \left(x \right)\\ F_{320}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{321}\! \left(x \right)+F_{346}\! \left(x \right)\\ F_{321}\! \left(x \right) &= F_{322}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{328}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{324}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{325}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{325}\! \left(x \right) &= F_{326}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{326}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{327}\! \left(x \right)\\ F_{327}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{103}\! \left(x \right)+F_{325}\! \left(x \right)\\ F_{328}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{329}\! \left(x \right)\\ F_{329}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{330}\! \left(x \right)+F_{334}\! \left(x \right)\\ F_{330}\! \left(x \right) &= F_{331}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)+F_{333}\! \left(x \right)\\ F_{332}\! \left(x \right) &= F_{324}\! \left(x \right)\\ F_{333}\! \left(x \right) &= F_{329}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{335}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{335}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{336}\! \left(x \right)\\ F_{336}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{334}\! \left(x \right)+F_{337}\! \left(x \right)\\ F_{337}\! \left(x \right) &= F_{338}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)+F_{340}\! \left(x \right)\\ F_{339}\! \left(x \right) &= F_{327}\! \left(x \right)\\ F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)\\ F_{341}\! \left(x \right) &= F_{342}\! \left(x \right)\\ F_{342}\! \left(x \right) &= F_{343}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{343}\! \left(x \right) &= F_{344}\! \left(x \right)+F_{345}\! \left(x \right)\\ F_{344}\! \left(x \right) &= F_{327}\! \left(x \right)\\ F_{345}\! \left(x \right) &= F_{341}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{347}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{347}\! \left(x \right) &= F_{281}\! \left(x \right)+F_{348}\! \left(x \right)\\ F_{348}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{346}\! \left(x \right)+F_{349}\! \left(x \right)\\ F_{349}\! \left(x \right) &= F_{350}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{351}\! \left(x \right)+F_{352}\! \left(x \right)\\ F_{351}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{327}\! \left(x \right)\\ F_{352}\! \left(x \right) &= F_{341}\! \left(x \right)+F_{353}\! \left(x \right)\\ F_{353}\! \left(x \right) &= F_{354}\! \left(x \right)\\ F_{354}\! \left(x \right) &= F_{355}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{355}\! \left(x \right) &= F_{356}\! \left(x \right)+F_{358}\! \left(x \right)\\ F_{356}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{357}\! \left(x \right)\\ F_{357}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{358}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{360}\! \left(x \right)\\ F_{360}\! \left(x \right) &= F_{361}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{361}\! \left(x \right) &= F_{362}\! \left(x \right)+F_{363}\! \left(x \right)\\ F_{362}\! \left(x \right) &= F_{357}\! \left(x \right)\\ F_{363}\! \left(x \right) &= F_{359}\! \left(x \right)\\ F_{364}\! \left(x \right) &= F_{365}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{365}\! \left(x \right) &= F_{366}\! \left(x \right)+F_{384}\! \left(x \right)\\ F_{366}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{367}\! \left(x \right)\\ F_{367}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{368}\! \left(x \right)+F_{372}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{369}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{370}\! \left(x \right)+F_{371}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{367}\! \left(x \right)\\ F_{372}\! \left(x \right) &= F_{373}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{374}\! \left(x \right)\\ F_{374}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{372}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{375}\! \left(x \right) &= F_{376}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{376}\! \left(x \right) &= F_{377}\! \left(x \right)+F_{378}\! \left(x \right)\\ F_{377}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{378}\! \left(x \right) &= F_{379}\! \left(x \right)\\ F_{379}\! \left(x \right) &= F_{380}\! \left(x \right)\\ F_{380}\! \left(x \right) &= F_{381}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{381}\! \left(x \right) &= F_{382}\! \left(x \right)+F_{383}\! \left(x \right)\\ F_{382}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{383}\! \left(x \right) &= F_{379}\! \left(x \right)\\ F_{384}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{385}\! \left(x \right)\\ F_{385}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{386}\! \left(x \right)+F_{407}\! \left(x \right)+F_{411}\! \left(x \right)\\ F_{386}\! \left(x \right) &= F_{387}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{387}\! \left(x \right) &= F_{388}\! \left(x \right)+F_{389}\! \left(x \right)\\ F_{388}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{389}\! \left(x \right) &= F_{390}\! \left(x \right)\\ F_{390}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{391}\! \left(x \right)+F_{395}\! \left(x \right)\\ F_{391}\! \left(x \right) &= F_{392}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{392}\! \left(x \right) &= F_{393}\! \left(x \right)+F_{394}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{394}\! \left(x \right) &= F_{390}\! \left(x \right)\\ F_{395}\! \left(x \right) &= F_{396}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{396}\! \left(x \right) &= F_{306}\! \left(x \right)+F_{397}\! \left(x \right)\\ F_{397}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{395}\! \left(x \right)+F_{398}\! \left(x \right)\\ F_{398}\! \left(x \right) &= F_{399}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{399}\! \left(x \right) &= F_{400}\! \left(x \right)+F_{401}\! \left(x \right)\\ F_{400}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{401}\! \left(x \right) &= F_{402}\! \left(x \right)\\ F_{402}\! \left(x \right) &= F_{403}\! \left(x \right)\\ F_{403}\! \left(x \right) &= F_{4}\! \left(x \right) F_{404}\! \left(x \right)\\ F_{404}\! \left(x \right) &= F_{405}\! \left(x \right)+F_{406}\! \left(x \right)\\ F_{405}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{406}\! \left(x \right) &= F_{402}\! \left(x \right)\\ F_{407}\! \left(x \right) &= F_{4}\! \left(x \right) F_{408}\! \left(x \right)\\ F_{408}\! \left(x \right) &= F_{409}\! \left(x \right)+F_{410}\! \left(x \right)\\ F_{409}\! \left(x \right) &= F_{367}\! \left(x \right)\\ F_{410}\! \left(x \right) &= F_{385}\! \left(x \right)\\ F_{411}\! \left(x \right) &= F_{4}\! \left(x \right) F_{412}\! \left(x \right)\\ F_{412}\! \left(x \right) &= F_{301}\! \left(x \right)+F_{413}\! \left(x \right)\\ F_{413}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{411}\! \left(x \right)+F_{414}\! \left(x \right)+F_{418}\! \left(x \right)\\ F_{414}\! \left(x \right) &= F_{4}\! \left(x \right) F_{415}\! \left(x \right)\\ F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{417}\! \left(x \right)\\ F_{416}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{402}\! \left(x \right)\\ F_{418}\! \left(x \right) &= F_{4}\! \left(x \right) F_{419}\! \left(x \right)\\ F_{419}\! \left(x \right) &= F_{420}\! \left(x \right)+F_{426}\! \left(x \right)\\ F_{420}\! \left(x \right) &= F_{421}\! \left(x \right)\\ F_{421}\! \left(x \right) &= F_{422}\! \left(x \right)\\ F_{422}\! \left(x \right) &= F_{4}\! \left(x \right) F_{423}\! \left(x \right)\\ F_{423}\! \left(x \right) &= F_{424}\! \left(x \right)+F_{425}\! \left(x \right)\\ F_{424}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{425}\! \left(x \right) &= F_{421}\! \left(x \right)\\ F_{426}\! \left(x \right) &= F_{427}\! \left(x \right)\\ F_{427}\! \left(x \right) &= 4 F_{24}\! \left(x \right)+F_{428}\! \left(x \right)+F_{437}\! \left(x \right)\\ F_{428}\! \left(x \right) &= F_{4}\! \left(x \right) F_{429}\! \left(x \right)\\ F_{429}\! \left(x \right) &= F_{430}\! \left(x \right)+F_{431}\! \left(x \right)\\ F_{430}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{431}\! \left(x \right) &= F_{432}\! \left(x \right)\\ F_{432}\! \left(x \right) &= F_{433}\! \left(x \right)\\ F_{433}\! \left(x \right) &= F_{4}\! \left(x \right) F_{434}\! \left(x \right)\\ F_{434}\! \left(x \right) &= F_{435}\! \left(x \right)+F_{436}\! \left(x \right)\\ F_{435}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{436}\! \left(x \right) &= F_{432}\! \left(x \right)\\ F_{437}\! \left(x \right) &= F_{4}\! \left(x \right) F_{438}\! \left(x \right)\\ F_{438}\! \left(x \right) &= F_{439}\! \left(x \right)+F_{440}\! \left(x \right)\\ F_{439}\! \left(x \right) &= F_{421}\! \left(x \right)\\ F_{440}\! \left(x \right) &= F_{427}\! \left(x \right)\\ F_{441}\! \left(x \right) &= F_{4}\! \left(x \right) F_{442}\! \left(x \right)\\ F_{442}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{443}\! \left(x \right)\\ F_{443}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{441}\! \left(x \right)+F_{444}\! \left(x \right)+F_{448}\! \left(x \right)\\ F_{444}\! \left(x \right) &= F_{4}\! \left(x \right) F_{445}\! \left(x \right)\\ F_{445}\! \left(x \right) &= F_{446}\! \left(x \right)+F_{447}\! \left(x \right)\\ F_{446}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{447}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{353}\! \left(x \right)\\ F_{448}\! \left(x \right) &= F_{4}\! \left(x \right) F_{449}\! \left(x \right)\\ F_{449}\! \left(x \right) &= F_{450}\! \left(x \right)+F_{451}\! \left(x \right)\\ F_{450}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{421}\! \left(x \right)\\ F_{451}\! \left(x \right) &= F_{301}\! \left(x \right)+F_{427}\! \left(x \right)\\ F_{452}\! \left(x \right) &= F_{4}\! \left(x \right) F_{453}\! \left(x \right)\\ F_{453}\! \left(x \right) &= F_{454}\! \left(x \right)+F_{472}\! \left(x \right)\\ F_{454}\! \left(x \right) &= F_{455}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{455}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{456}\! \left(x \right)+F_{460}\! \left(x \right)\\ F_{456}\! \left(x \right) &= F_{4}\! \left(x \right) F_{457}\! \left(x \right)\\ F_{457}\! \left(x \right) &= F_{458}\! \left(x \right)+F_{459}\! \left(x \right)\\ F_{458}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{459}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{455}\! \left(x \right)\\ F_{460}\! \left(x \right) &= F_{4}\! \left(x \right) F_{461}\! \left(x \right)\\ F_{461}\! \left(x \right) &= F_{462}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{462}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{460}\! \left(x \right)+F_{463}\! \left(x \right)\\ F_{463}\! \left(x \right) &= F_{4}\! \left(x \right) F_{464}\! \left(x \right)\\ F_{464}\! \left(x \right) &= F_{465}\! \left(x \right)+F_{466}\! \left(x \right)\\ F_{465}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{466}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{467}\! \left(x \right)\\ F_{467}\! \left(x \right) &= F_{468}\! \left(x \right)\\ F_{468}\! \left(x \right) &= F_{4}\! \left(x \right) F_{469}\! \left(x \right)\\ F_{469}\! \left(x \right) &= F_{470}\! \left(x \right)+F_{471}\! \left(x \right)\\ F_{470}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{471}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{467}\! \left(x \right)\\ F_{472}\! \left(x \right) &= F_{473}\! \left(x \right)+F_{491}\! \left(x \right)\\ F_{473}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{474}\! \left(x \right)+F_{478}\! \left(x \right)\\ F_{474}\! \left(x \right) &= F_{4}\! \left(x \right) F_{475}\! \left(x \right)\\ F_{475}\! \left(x \right) &= F_{476}\! \left(x \right)+F_{477}\! \left(x \right)\\ F_{476}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{477}\! \left(x \right) &= F_{281}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{478}\! \left(x \right) &= F_{4}\! \left(x \right) F_{479}\! \left(x \right)\\ F_{479}\! \left(x \right) &= F_{480}\! \left(x \right)+F_{481}\! \left(x \right)\\ F_{480}\! \left(x \right) &= F_{467}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{481}\! \left(x \right) &= F_{473}\! \left(x \right)+F_{482}\! \left(x \right)\\ F_{482}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{483}\! \left(x \right)+F_{487}\! \left(x \right)\\ F_{483}\! \left(x \right) &= F_{4}\! \left(x \right) F_{484}\! \left(x \right)\\ F_{484}\! \left(x \right) &= F_{485}\! \left(x \right)+F_{486}\! \left(x \right)\\ F_{485}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{486}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{306}\! \left(x \right)\\ F_{487}\! \left(x \right) &= F_{4}\! \left(x \right) F_{488}\! \left(x \right)\\ F_{488}\! \left(x \right) &= F_{489}\! \left(x \right)+F_{490}\! \left(x \right)\\ F_{489}\! \left(x \right) &= F_{467}\! \left(x \right)\\ F_{490}\! \left(x \right) &= F_{482}\! \left(x \right)\\ F_{491}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{492}\! \left(x \right)+F_{496}\! \left(x \right)+F_{546}\! \left(x \right)\\ F_{492}\! \left(x \right) &= F_{4}\! \left(x \right) F_{493}\! \left(x \right)\\ F_{493}\! \left(x \right) &= F_{494}\! \left(x \right)+F_{495}\! \left(x \right)\\ F_{494}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{495}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{320}\! \left(x \right)\\ F_{496}\! \left(x \right) &= F_{4}\! \left(x \right) F_{497}\! \left(x \right)\\ F_{497}\! \left(x \right) &= F_{498}\! \left(x \right)+F_{516}\! \left(x \right)\\ F_{498}\! \left(x \right) &= F_{455}\! \left(x \right)+F_{499}\! \left(x \right)\\ F_{499}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{500}\! \left(x \right)+F_{504}\! \left(x \right)\\ F_{500}\! \left(x \right) &= F_{4}\! \left(x \right) F_{501}\! \left(x \right)\\ F_{501}\! \left(x \right) &= F_{502}\! \left(x \right)+F_{503}\! \left(x \right)\\ F_{502}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{503}\! \left(x \right) &= F_{367}\! \left(x \right)+F_{499}\! \left(x \right)\\ F_{504}\! \left(x \right) &= F_{4}\! \left(x \right) F_{505}\! \left(x \right)\\ F_{505}\! \left(x \right) &= F_{467}\! \left(x \right)+F_{506}\! \left(x \right)\\ F_{506}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{504}\! \left(x \right)+F_{507}\! \left(x \right)\\ F_{507}\! \left(x \right) &= F_{4}\! \left(x \right) F_{508}\! \left(x \right)\\ F_{508}\! \left(x \right) &= F_{509}\! \left(x \right)+F_{510}\! \left(x \right)\\ F_{509}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{510}\! \left(x \right) &= F_{379}\! \left(x \right)+F_{511}\! \left(x \right)\\ F_{511}\! \left(x \right) &= F_{512}\! \left(x \right)\\ F_{512}\! \left(x \right) &= F_{4}\! \left(x \right) F_{513}\! \left(x \right)\\ F_{513}\! \left(x \right) &= F_{514}\! \left(x \right)+F_{515}\! \left(x \right)\\ F_{514}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{515}\! \left(x \right) &= F_{421}\! \left(x \right)+F_{511}\! \left(x \right)\\ F_{516}\! \left(x \right) &= F_{491}\! \left(x \right)+F_{517}\! \left(x \right)\\ F_{517}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{518}\! \left(x \right)+F_{522}\! \left(x \right)+F_{526}\! \left(x \right)\\ F_{518}\! \left(x \right) &= F_{4}\! \left(x \right) F_{519}\! \left(x \right)\\ F_{519}\! \left(x \right) &= F_{520}\! \left(x \right)+F_{521}\! \left(x \right)\\ F_{520}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{521}\! \left(x \right) &= F_{367}\! \left(x \right)+F_{390}\! \left(x \right)\\ F_{522}\! \left(x \right) &= F_{4}\! \left(x \right) F_{523}\! \left(x \right)\\ F_{523}\! \left(x \right) &= F_{524}\! \left(x \right)+F_{525}\! \left(x \right)\\ F_{524}\! \left(x \right) &= F_{499}\! \left(x \right)\\ F_{525}\! \left(x \right) &= F_{517}\! \left(x \right)\\ F_{526}\! \left(x \right) &= F_{4}\! \left(x \right) F_{527}\! \left(x \right)\\ F_{527}\! \left(x \right) &= F_{482}\! \left(x \right)+F_{528}\! \left(x \right)\\ F_{528}\! \left(x \right) &= 2 F_{24}\! \left(x \right)+F_{526}\! \left(x \right)+F_{529}\! \left(x \right)+F_{533}\! \left(x \right)\\ F_{529}\! \left(x \right) &= F_{4}\! \left(x \right) F_{530}\! \left(x \right)\\ F_{530}\! \left(x \right) &= F_{531}\! \left(x \right)+F_{532}\! \left(x \right)\\ F_{531}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{532}\! \left(x \right) &= F_{379}\! \left(x \right)+F_{402}\! \left(x \right)\\ F_{533}\! \left(x \right) &= F_{4}\! \left(x \right) F_{534}\! \left(x \right)\\ F_{534}\! \left(x \right) &= F_{535}\! \left(x \right)+F_{536}\! \left(x \right)\\ F_{535}\! \left(x \right) &= F_{511}\! \left(x \right)\\ F_{536}\! \left(x \right) &= F_{537}\! \left(x \right)\\ F_{537}\! \left(x \right) &= 3 F_{24}\! \left(x \right)+F_{538}\! \left(x \right)+F_{542}\! \left(x \right)\\ F_{538}\! \left(x \right) &= F_{4}\! \left(x \right) F_{539}\! \left(x \right)\\ F_{539}\! \left(x \right) &= F_{540}\! \left(x \right)+F_{541}\! \left(x \right)\\ F_{540}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{541}\! \left(x \right) &= F_{421}\! \left(x \right)+F_{432}\! \left(x \right)\\ F_{542}\! \left(x \right) &= F_{4}\! \left(x \right) F_{543}\! \left(x \right)\\ F_{543}\! \left(x \right) &= F_{544}\! \left(x \right)+F_{545}\! \left(x \right)\\ F_{544}\! \left(x \right) &= F_{511}\! \left(x \right)\\ F_{545}\! \left(x \right) &= F_{537}\! \left(x \right)\\ F_{546}\! \left(x \right) &= F_{4}\! \left(x \right) F_{547}\! \left(x \right)\\ F_{547}\! \left(x \right) &= F_{473}\! \left(x \right)+F_{548}\! \left(x \right)\\ F_{548}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{546}\! \left(x \right)+F_{549}\! \left(x \right)+F_{553}\! \left(x \right)\\ F_{549}\! \left(x \right) &= F_{4}\! \left(x \right) F_{550}\! \left(x \right)\\ F_{550}\! \left(x \right) &= F_{551}\! \left(x \right)+F_{552}\! \left(x \right)\\ F_{551}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{552}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{353}\! \left(x \right)\\ F_{553}\! \left(x \right) &= F_{4}\! \left(x \right) F_{554}\! \left(x \right)\\ F_{554}\! \left(x \right) &= F_{555}\! \left(x \right)+F_{556}\! \left(x \right)\\ F_{555}\! \left(x \right) &= F_{467}\! \left(x \right)+F_{511}\! \left(x \right)\\ F_{556}\! \left(x \right) &= F_{482}\! \left(x \right)+F_{537}\! \left(x \right)\\ \end{align*}\)