Av(1234, 1342, 1432, 3241)
Generating Function
\(\displaystyle -\frac{\left(x +1\right) \left(2 x^{8}-x^{7}+2 x^{6}+4 x^{5}+9 x^{4}-2 x^{3}+3 x^{2}-3 x +1\right)}{\left(x -1\right) \left(2 x^{4}+2 x^{3}+x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right)}\)
Counting Sequence
1, 1, 2, 6, 20, 61, 161, 402, 974, 2291, 5269, 11940, 26746, 59349, 130721, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(x -1\right) \left(2 x^{4}+2 x^{3}+x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) F \! \left(x \right)+\left(x +1\right) \left(2 x^{8}-x^{7}+2 x^{6}+4 x^{5}+9 x^{4}-2 x^{3}+3 x^{2}-3 x +1\right) = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 20\)
\(\displaystyle a \! \left(5\right) = 61\)
\(\displaystyle a \! \left(6\right) = 161\)
\(\displaystyle a \! \left(7\right) = 402\)
\(\displaystyle a \! \left(8\right) = 974\)
\(\displaystyle a \! \left(9\right) = 2291\)
\(\displaystyle a \! \left(n +7\right) = -2 a \! \left(n \right)-4 a \! \left(n +1\right)-5 a \! \left(n +2\right)-2 a \! \left(n +3\right)+a \! \left(n +4\right)+a \! \left(n +5\right)+2 a \! \left(n +6\right)+30, \quad n \geq 10\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 20\)
\(\displaystyle a \! \left(5\right) = 61\)
\(\displaystyle a \! \left(6\right) = 161\)
\(\displaystyle a \! \left(7\right) = 402\)
\(\displaystyle a \! \left(8\right) = 974\)
\(\displaystyle a \! \left(9\right) = 2291\)
\(\displaystyle a \! \left(n +7\right) = -2 a \! \left(n \right)-4 a \! \left(n +1\right)-5 a \! \left(n +2\right)-2 a \! \left(n +3\right)+a \! \left(n +4\right)+a \! \left(n +5\right)+2 a \! \left(n +6\right)+30, \quad n \geq 10\)
Explicit Closed Form
\(\displaystyle \frac{773997 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n +6}\right)}{32065}+\frac{3526892 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n +5}\right)}{96195}+\frac{1210879 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n +4}\right)}{38478}-\frac{1834484 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n +3}\right)}{96195}-\frac{397568 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n +2}\right)}{8745}-\frac{135957 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{1-n}\right)}{5830}-\frac{2368801 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n}\right)}{96195}+\frac{2232328 \left(\underset{\alpha =\mathit{RootOf} \left(2 Z^{8}+2 Z^{7}+Z^{6}-3 Z^{5}-3 Z^{4}-Z^{2}+3 Z -1\right)}{\textcolor{gray}{\sum}}\! \alpha^{-n -1}\right)}{96195}-\left(\left\{\begin{array}{cc}-\frac{1}{2} & n =0 \\ 1 & n =1 \\ 0 & \text{otherwise} \end{array}\right.\right)\)
This specification was found using the strategy pack "Point Placements" and has 712 rules.
Found on January 18, 2022.Finding the specification took 61 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_{20}\! \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_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{298}\! \left(x \right)\\
F_{22}\! \left(x \right) &= 0\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \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_{4}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{129}\! \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_{52}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{54}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{4}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{4}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{4}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{61}\! \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_{57}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{4}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{4}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{75}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{4}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{4}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{95}\! \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_{88}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \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_{103}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{106}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \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_{122}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
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_{126}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{129}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{130}\! \left(x \right)+F_{253}\! \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_{140}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{133}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{134}\! \left(x \right)+F_{138}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{227}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{152}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{163}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{159}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{202}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{173}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{180}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{186}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{186}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{204}\! \left(x \right)+F_{225}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{210}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{216}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{215}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{211}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{220}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{207}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \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_{207}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{176}\! \left(x \right)\\
F_{227}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{228}\! \left(x \right)+F_{249}\! \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_{234}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{240}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{239}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{231}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)+F_{248}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{231}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{245}\! \left(x \right)\\
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_{252}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{176}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{203}\! \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_{282}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \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_{261}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{249}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{273}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{260}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{268}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{277}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{279}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{280}\! \left(x \right)+F_{281}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{278}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{225}\! \left(x \right)+F_{284}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{286}\! \left(x \right)+F_{288}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)+F_{293}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{287}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)+F_{297}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{287}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{294}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{300}\! \left(x \right)+F_{610}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{301}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{302}\! \left(x \right)+F_{362}\! \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_{309}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{305}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{306}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{307}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{308}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{310}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{253}\! \left(x \right)+F_{311}\! \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_{315}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{305}\! \left(x \right)+F_{314}\! \left(x \right)\\
F_{314}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{134}\! \left(x \right)+F_{138}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{342}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{317}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{318}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{321}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{305}\! \left(x \right)+F_{320}\! \left(x \right)\\
F_{320}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{321}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{322}\! \left(x \right)\\
F_{322}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{173}\! \left(x \right)+F_{323}\! \left(x \right)\\
F_{323}\! \left(x \right) &= F_{324}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{327}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{333}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{329}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{330}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{331}\! \left(x \right)+F_{332}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{320}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{328}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{334}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{336}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{326}\! \left(x \right)\\
F_{337}\! \left(x \right) &= F_{338}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{339}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{340}\! \left(x \right)+F_{341}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{326}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{338}\! \left(x \right)\\
F_{342}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{249}\! \left(x \right)+F_{343}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{344}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{344}\! \left(x \right) &= F_{345}\! \left(x \right)+F_{347}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{346}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{353}\! \left(x \right)\\
F_{348}\! \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_{314}\! \left(x \right)\\
F_{352}\! \left(x \right) &= F_{348}\! \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_{357}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{346}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{358}\! \left(x \right)\\
F_{358}\! \left(x \right) &= F_{359}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{359}\! \left(x \right) &= F_{360}\! \left(x \right)+F_{361}\! \left(x \right)\\
F_{360}\! \left(x \right) &= F_{346}\! \left(x \right)\\
F_{361}\! \left(x \right) &= F_{358}\! \left(x \right)\\
F_{362}\! \left(x \right) &= F_{363}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{363}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{364}\! \left(x \right)\\
F_{364}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{365}\! \left(x \right)+F_{609}\! \left(x \right)\\
F_{365}\! \left(x \right) &= F_{366}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{366}\! \left(x \right) &= F_{367}\! \left(x \right)+F_{379}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{368}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{368}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{369}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{369}\! \left(x \right) &= F_{370}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{370}\! \left(x \right) &= F_{371}\! \left(x \right)+F_{374}\! \left(x \right)\\
F_{371}\! \left(x \right) &= F_{372}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{372}\! \left(x \right) &= F_{373}\! \left(x \right)\\
F_{373}\! \left(x \right) &= x^{2}\\
F_{374}\! \left(x \right) &= F_{308}\! \left(x \right)+F_{375}\! \left(x \right)\\
F_{375}\! \left(x \right) &= F_{376}\! \left(x \right)\\
F_{376}\! \left(x \right) &= F_{377}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{377}\! \left(x \right) &= F_{372}\! \left(x \right)\\
F_{378}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{379}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{440}\! \left(x \right)\\
F_{380}\! \left(x \right) &= F_{381}\! \left(x \right)\\
F_{381}\! \left(x \right) &= F_{382}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)+F_{389}\! \left(x \right)\\
F_{383}\! \left(x \right) &= F_{384}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{384}\! \left(x \right) &= F_{385}\! \left(x \right)\\
F_{385}\! \left(x \right) &= F_{386}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{386}\! \left(x \right) &= F_{387}\! \left(x \right)+F_{388}\! \left(x \right)\\
F_{387}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{308}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{390}\! \left(x \right)\\
F_{390}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{391}\! \left(x \right)+F_{412}\! \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_{397}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{384}\! \left(x \right)+F_{394}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{395}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{396}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{396}\! \left(x \right) &= F_{388}\! \left(x \right)\\
F_{397}\! \left(x \right) &= F_{398}\! \left(x \right)+F_{403}\! \left(x \right)\\
F_{398}\! \left(x \right) &= F_{399}\! \left(x \right)\\
F_{399}\! \left(x \right) &= F_{4}\! \left(x \right) F_{400}\! \left(x \right)\\
F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)+F_{402}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{384}\! \left(x \right)\\
F_{402}\! \left(x \right) &= F_{398}\! \left(x \right)\\
F_{403}\! \left(x \right) &= F_{404}\! \left(x \right)\\
F_{404}\! \left(x \right) &= F_{4}\! \left(x \right) F_{405}\! \left(x \right)\\
F_{405}\! \left(x \right) &= F_{406}\! \left(x \right)+F_{407}\! \left(x \right)\\
F_{406}\! \left(x \right) &= F_{394}\! \left(x \right)\\
F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\
F_{408}\! \left(x \right) &= F_{4}\! \left(x \right) F_{409}\! \left(x \right)\\
F_{409}\! \left(x \right) &= F_{410}\! \left(x \right)+F_{411}\! \left(x \right)\\
F_{410}\! \left(x \right) &= F_{394}\! \left(x \right)\\
F_{411}\! \left(x \right) &= F_{408}\! \left(x \right)\\
F_{412}\! \left(x \right) &= F_{4}\! \left(x \right) F_{413}\! \left(x \right)\\
F_{413}\! \left(x \right) &= F_{414}\! \left(x \right)+F_{415}\! \left(x \right)\\
F_{414}\! \left(x \right) &= F_{380}\! \left(x \right)\\
F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)\\
F_{416}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{417}\! \left(x \right)+F_{438}\! \left(x \right)\\
F_{417}\! \left(x \right) &= F_{4}\! \left(x \right) F_{418}\! \left(x \right)\\
F_{418}\! \left(x \right) &= F_{419}\! \left(x \right)+F_{423}\! \left(x \right)\\
F_{419}\! \left(x \right) &= F_{308}\! \left(x \right)+F_{420}\! \left(x \right)\\
F_{420}\! \left(x \right) &= F_{421}\! \left(x \right)\\
F_{421}\! \left(x \right) &= F_{4}\! \left(x \right) F_{422}\! \left(x \right)\\
F_{422}\! \left(x \right) &= F_{308}\! \left(x \right)\\
F_{423}\! \left(x \right) &= F_{424}\! \left(x \right)+F_{429}\! \left(x \right)\\
F_{424}\! \left(x \right) &= F_{425}\! \left(x \right)\\
F_{425}\! \left(x \right) &= F_{4}\! \left(x \right) F_{426}\! \left(x \right)\\
F_{426}\! \left(x \right) &= F_{427}\! \left(x \right)+F_{428}\! \left(x \right)\\
F_{427}\! \left(x \right) &= F_{308}\! \left(x \right)\\
F_{428}\! \left(x \right) &= F_{424}\! \left(x \right)\\
F_{429}\! \left(x \right) &= F_{430}\! \left(x \right)\\
F_{430}\! \left(x \right) &= F_{4}\! \left(x \right) F_{431}\! \left(x \right)\\
F_{431}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{433}\! \left(x \right)\\
F_{432}\! \left(x \right) &= F_{420}\! \left(x \right)\\
F_{433}\! \left(x \right) &= F_{434}\! \left(x \right)\\
F_{434}\! \left(x \right) &= F_{4}\! \left(x \right) F_{435}\! \left(x \right)\\
F_{435}\! \left(x \right) &= F_{436}\! \left(x \right)+F_{437}\! \left(x \right)\\
F_{436}\! \left(x \right) &= F_{420}\! \left(x \right)\\
F_{437}\! \left(x \right) &= F_{434}\! \left(x \right)\\
F_{438}\! \left(x \right) &= F_{4}\! \left(x \right) F_{439}\! \left(x \right)\\
F_{439}\! \left(x \right) &= F_{380}\! \left(x \right)\\
F_{440}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{441}\! \left(x \right)+F_{564}\! \left(x \right)\\
F_{441}\! \left(x \right) &= F_{4}\! \left(x \right) F_{442}\! \left(x \right)\\
F_{442}\! \left(x \right) &= F_{443}\! \left(x \right)+F_{451}\! \left(x \right)\\
F_{443}\! \left(x \right) &= F_{368}\! \left(x \right)+F_{444}\! \left(x \right)\\
F_{444}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{445}\! \left(x \right)+F_{449}\! \left(x \right)\\
F_{445}\! \left(x \right) &= F_{4}\! \left(x \right) F_{446}\! \left(x \right)\\
F_{446}\! \left(x \right) &= F_{447}\! \left(x \right)+F_{448}\! \left(x \right)\\
F_{447}\! \left(x \right) &= F_{372}\! \left(x \right)\\
F_{448}\! \left(x \right) &= F_{375}\! \left(x \right)\\
F_{449}\! \left(x \right) &= F_{4}\! \left(x \right) F_{450}\! \left(x \right)\\
F_{450}\! \left(x \right) &= F_{374}\! \left(x \right)\\
F_{451}\! \left(x \right) &= F_{452}\! \left(x \right)+F_{538}\! \left(x \right)\\
F_{452}\! \left(x \right) &= F_{453}\! \left(x \right)\\
F_{453}\! \left(x \right) &= F_{4}\! \left(x \right) F_{454}\! \left(x \right)\\
F_{454}\! \left(x \right) &= F_{455}\! \left(x \right)+F_{461}\! \left(x \right)\\
F_{455}\! \left(x \right) &= F_{368}\! \left(x \right)+F_{456}\! \left(x \right)\\
F_{456}\! \left(x \right) &= F_{457}\! \left(x \right)\\
F_{457}\! \left(x \right) &= F_{4}\! \left(x \right) F_{458}\! \left(x \right)\\
F_{458}\! \left(x \right) &= F_{459}\! \left(x \right)+F_{460}\! \left(x \right)\\
F_{459}\! \left(x \right) &= F_{372}\! \left(x \right)\\
F_{460}\! \left(x \right) &= F_{375}\! \left(x \right)\\
F_{461}\! \left(x \right) &= F_{452}\! \left(x \right)+F_{462}\! \left(x \right)\\
F_{462}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{463}\! \left(x \right)+F_{484}\! \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_{469}\! \left(x \right)\\
F_{465}\! \left(x \right) &= F_{456}\! \left(x \right)+F_{466}\! \left(x \right)\\
F_{466}\! \left(x \right) &= F_{467}\! \left(x \right)\\
F_{467}\! \left(x \right) &= F_{4}\! \left(x \right) F_{468}\! \left(x \right)\\
F_{468}\! \left(x \right) &= F_{460}\! \left(x \right)\\
F_{469}\! \left(x \right) &= F_{470}\! \left(x \right)+F_{475}\! \left(x \right)\\
F_{470}\! \left(x \right) &= F_{471}\! \left(x \right)\\
F_{471}\! \left(x \right) &= F_{4}\! \left(x \right) F_{472}\! \left(x \right)\\
F_{472}\! \left(x \right) &= F_{473}\! \left(x \right)+F_{474}\! \left(x \right)\\
F_{473}\! \left(x \right) &= F_{456}\! \left(x \right)\\
F_{474}\! \left(x \right) &= F_{470}\! \left(x \right)\\
F_{475}\! \left(x \right) &= F_{476}\! \left(x \right)\\
F_{476}\! \left(x \right) &= F_{4}\! \left(x \right) F_{477}\! \left(x \right)\\
F_{477}\! \left(x \right) &= F_{478}\! \left(x \right)+F_{479}\! \left(x \right)\\
F_{478}\! \left(x \right) &= F_{466}\! \left(x \right)\\
F_{479}\! \left(x \right) &= F_{480}\! \left(x \right)\\
F_{480}\! \left(x \right) &= F_{4}\! \left(x \right) F_{481}\! \left(x \right)\\
F_{481}\! \left(x \right) &= F_{482}\! \left(x \right)+F_{483}\! \left(x \right)\\
F_{482}\! \left(x \right) &= F_{466}\! \left(x \right)\\
F_{483}\! \left(x \right) &= F_{480}\! \left(x \right)\\
F_{484}\! \left(x \right) &= F_{4}\! \left(x \right) F_{485}\! \left(x \right)\\
F_{485}\! \left(x \right) &= F_{486}\! \left(x \right)+F_{513}\! \left(x \right)\\
F_{486}\! \left(x \right) &= F_{487}\! \left(x \right)\\
F_{487}\! \left(x \right) &= F_{488}\! \left(x \right)\\
F_{488}\! \left(x \right) &= F_{4}\! \left(x \right) F_{489}\! \left(x \right)\\
F_{489}\! \left(x \right) &= F_{490}\! \left(x \right)+F_{492}\! \left(x \right)\\
F_{490}\! \left(x \right) &= F_{372}\! \left(x \right)+F_{491}\! \left(x \right)\\
F_{491}\! \left(x \right) &= F_{457}\! \left(x \right)\\
F_{492}\! \left(x \right) &= F_{487}\! \left(x \right)+F_{493}\! \left(x \right)\\
F_{493}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{484}\! \left(x \right)+F_{494}\! \left(x \right)\\
F_{494}\! \left(x \right) &= F_{4}\! \left(x \right) F_{495}\! \left(x \right)\\
F_{495}\! \left(x \right) &= F_{496}\! \left(x \right)+F_{498}\! \left(x \right)\\
F_{496}\! \left(x \right) &= F_{491}\! \left(x \right)+F_{497}\! \left(x \right)\\
F_{497}\! \left(x \right) &= F_{467}\! \left(x \right)\\
F_{498}\! \left(x \right) &= F_{499}\! \left(x \right)+F_{504}\! \left(x \right)\\
F_{499}\! \left(x \right) &= F_{500}\! \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_{491}\! \left(x \right)\\
F_{503}\! \left(x \right) &= F_{499}\! \left(x \right)\\
F_{504}\! \left(x \right) &= F_{505}\! \left(x \right)\\
F_{505}\! \left(x \right) &= F_{4}\! \left(x \right) F_{506}\! \left(x \right)\\
F_{506}\! \left(x \right) &= F_{507}\! \left(x \right)+F_{508}\! \left(x \right)\\
F_{507}\! \left(x \right) &= F_{497}\! \left(x \right)\\
F_{508}\! \left(x \right) &= F_{509}\! \left(x \right)\\
F_{509}\! \left(x \right) &= F_{4}\! \left(x \right) F_{510}\! \left(x \right)\\
F_{510}\! \left(x \right) &= F_{511}\! \left(x \right)+F_{512}\! \left(x \right)\\
F_{511}\! \left(x \right) &= F_{497}\! \left(x \right)\\
F_{512}\! \left(x \right) &= F_{509}\! \left(x \right)\\
F_{513}\! \left(x \right) &= F_{514}\! \left(x \right)\\
F_{514}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{515}\! \left(x \right)+F_{536}\! \left(x \right)\\
F_{515}\! \left(x \right) &= F_{4}\! \left(x \right) F_{516}\! \left(x \right)\\
F_{516}\! \left(x \right) &= F_{517}\! \left(x \right)+F_{521}\! \left(x \right)\\
F_{517}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{518}\! \left(x \right)\\
F_{518}\! \left(x \right) &= F_{519}\! \left(x \right)\\
F_{519}\! \left(x \right) &= F_{4}\! \left(x \right) F_{520}\! \left(x \right)\\
F_{520}\! \left(x \right) &= F_{375}\! \left(x \right)\\
F_{521}\! \left(x \right) &= F_{522}\! \left(x \right)+F_{527}\! \left(x \right)\\
F_{522}\! \left(x \right) &= F_{523}\! \left(x \right)\\
F_{523}\! \left(x \right) &= F_{4}\! \left(x \right) F_{524}\! \left(x \right)\\
F_{524}\! \left(x \right) &= F_{525}\! \left(x \right)+F_{526}\! \left(x \right)\\
F_{525}\! \left(x \right) &= F_{375}\! \left(x \right)\\
F_{526}\! \left(x \right) &= F_{522}\! \left(x \right)\\
F_{527}\! \left(x \right) &= F_{528}\! \left(x \right)\\
F_{528}\! \left(x \right) &= F_{4}\! \left(x \right) F_{529}\! \left(x \right)\\
F_{529}\! \left(x \right) &= F_{530}\! \left(x \right)+F_{531}\! \left(x \right)\\
F_{530}\! \left(x \right) &= F_{518}\! \left(x \right)\\
F_{531}\! \left(x \right) &= F_{532}\! \left(x \right)\\
F_{532}\! \left(x \right) &= F_{4}\! \left(x \right) F_{533}\! \left(x \right)\\
F_{533}\! \left(x \right) &= F_{534}\! \left(x \right)+F_{535}\! \left(x \right)\\
F_{534}\! \left(x \right) &= F_{518}\! \left(x \right)\\
F_{535}\! \left(x \right) &= F_{532}\! \left(x \right)\\
F_{536}\! \left(x \right) &= F_{4}\! \left(x \right) F_{537}\! \left(x \right)\\
F_{537}\! \left(x \right) &= F_{487}\! \left(x \right)\\
F_{538}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{539}\! \left(x \right)+F_{560}\! \left(x \right)\\
F_{539}\! \left(x \right) &= F_{4}\! \left(x \right) F_{540}\! \left(x \right)\\
F_{540}\! \left(x \right) &= F_{541}\! \left(x \right)+F_{545}\! \left(x \right)\\
F_{541}\! \left(x \right) &= F_{444}\! \left(x \right)+F_{542}\! \left(x \right)\\
F_{542}\! \left(x \right) &= F_{543}\! \left(x \right)\\
F_{543}\! \left(x \right) &= F_{4}\! \left(x \right) F_{544}\! \left(x \right)\\
F_{544}\! \left(x \right) &= F_{448}\! \left(x \right)\\
F_{545}\! \left(x \right) &= F_{546}\! \left(x \right)+F_{551}\! \left(x \right)\\
F_{546}\! \left(x \right) &= F_{547}\! \left(x \right)\\
F_{547}\! \left(x \right) &= F_{4}\! \left(x \right) F_{548}\! \left(x \right)\\
F_{548}\! \left(x \right) &= F_{549}\! \left(x \right)+F_{550}\! \left(x \right)\\
F_{549}\! \left(x \right) &= F_{444}\! \left(x \right)\\
F_{550}\! \left(x \right) &= F_{546}\! \left(x \right)\\
F_{551}\! \left(x \right) &= F_{552}\! \left(x \right)\\
F_{552}\! \left(x \right) &= F_{4}\! \left(x \right) F_{553}\! \left(x \right)\\
F_{553}\! \left(x \right) &= F_{554}\! \left(x \right)+F_{555}\! \left(x \right)\\
F_{554}\! \left(x \right) &= F_{542}\! \left(x \right)\\
F_{555}\! \left(x \right) &= F_{556}\! \left(x \right)\\
F_{556}\! \left(x \right) &= F_{4}\! \left(x \right) F_{557}\! \left(x \right)\\
F_{557}\! \left(x \right) &= F_{558}\! \left(x \right)+F_{559}\! \left(x \right)\\
F_{558}\! \left(x \right) &= F_{542}\! \left(x \right)\\
F_{559}\! \left(x \right) &= F_{556}\! \left(x \right)\\
F_{560}\! \left(x \right) &= F_{4}\! \left(x \right) F_{561}\! \left(x \right)\\
F_{561}\! \left(x \right) &= F_{562}\! \left(x \right)+F_{563}\! \left(x \right)\\
F_{562}\! \left(x \right) &= F_{487}\! \left(x \right)\\
F_{563}\! \left(x \right) &= F_{514}\! \left(x \right)\\
F_{564}\! \left(x \right) &= F_{4}\! \left(x \right) F_{565}\! \left(x \right)\\
F_{565}\! \left(x \right) &= F_{566}\! \left(x \right)+F_{593}\! \left(x \right)\\
F_{566}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{567}\! \left(x \right)\\
F_{567}\! \left(x \right) &= F_{568}\! \left(x \right)\\
F_{568}\! \left(x \right) &= F_{4}\! \left(x \right) F_{569}\! \left(x \right)\\
F_{569}\! \left(x \right) &= F_{570}\! \left(x \right)+F_{572}\! \left(x \right)\\
F_{570}\! \left(x \right) &= F_{372}\! \left(x \right)+F_{571}\! \left(x \right)\\
F_{571}\! \left(x \right) &= F_{445}\! \left(x \right)\\
F_{572}\! \left(x \right) &= F_{487}\! \left(x \right)+F_{573}\! \left(x \right)\\
F_{573}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{560}\! \left(x \right)+F_{574}\! \left(x \right)\\
F_{574}\! \left(x \right) &= F_{4}\! \left(x \right) F_{575}\! \left(x \right)\\
F_{575}\! \left(x \right) &= F_{576}\! \left(x \right)+F_{578}\! \left(x \right)\\
F_{576}\! \left(x \right) &= F_{571}\! \left(x \right)+F_{577}\! \left(x \right)\\
F_{577}\! \left(x \right) &= F_{543}\! \left(x \right)\\
F_{578}\! \left(x \right) &= F_{579}\! \left(x \right)+F_{584}\! \left(x \right)\\
F_{579}\! \left(x \right) &= F_{580}\! \left(x \right)\\
F_{580}\! \left(x \right) &= F_{4}\! \left(x \right) F_{581}\! \left(x \right)\\
F_{581}\! \left(x \right) &= F_{582}\! \left(x \right)+F_{583}\! \left(x \right)\\
F_{582}\! \left(x \right) &= F_{571}\! \left(x \right)\\
F_{583}\! \left(x \right) &= F_{579}\! \left(x \right)\\
F_{584}\! \left(x \right) &= F_{585}\! \left(x \right)\\
F_{585}\! \left(x \right) &= F_{4}\! \left(x \right) F_{586}\! \left(x \right)\\
F_{586}\! \left(x \right) &= F_{587}\! \left(x \right)+F_{588}\! \left(x \right)\\
F_{587}\! \left(x \right) &= F_{577}\! \left(x \right)\\
F_{588}\! \left(x \right) &= F_{589}\! \left(x \right)\\
F_{589}\! \left(x \right) &= F_{4}\! \left(x \right) F_{590}\! \left(x \right)\\
F_{590}\! \left(x \right) &= F_{591}\! \left(x \right)+F_{592}\! \left(x \right)\\
F_{591}\! \left(x \right) &= F_{577}\! \left(x \right)\\
F_{592}\! \left(x \right) &= F_{589}\! \left(x \right)\\
F_{593}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{594}\! \left(x \right)\\
F_{594}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{536}\! \left(x \right)+F_{595}\! \left(x \right)\\
F_{595}\! \left(x \right) &= F_{4}\! \left(x \right) F_{596}\! \left(x \right)\\
F_{596}\! \left(x \right) &= F_{597}\! \left(x \right)+F_{599}\! \left(x \right)\\
F_{597}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{598}\! \left(x \right)\\
F_{598}\! \left(x \right) &= F_{519}\! \left(x \right)\\
F_{599}\! \left(x \right) &= F_{522}\! \left(x \right)+F_{600}\! \left(x \right)\\
F_{600}\! \left(x \right) &= F_{601}\! \left(x \right)\\
F_{601}\! \left(x \right) &= F_{4}\! \left(x \right) F_{602}\! \left(x \right)\\
F_{602}\! \left(x \right) &= F_{603}\! \left(x \right)+F_{604}\! \left(x \right)\\
F_{603}\! \left(x \right) &= F_{598}\! \left(x \right)\\
F_{604}\! \left(x \right) &= F_{605}\! \left(x \right)\\
F_{605}\! \left(x \right) &= F_{4}\! \left(x \right) F_{606}\! \left(x \right)\\
F_{606}\! \left(x \right) &= F_{607}\! \left(x \right)+F_{608}\! \left(x \right)\\
F_{607}\! \left(x \right) &= F_{598}\! \left(x \right)\\
F_{608}\! \left(x \right) &= F_{605}\! \left(x \right)\\
F_{609}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{610}\! \left(x \right) &= F_{611}\! \left(x \right)+F_{697}\! \left(x \right)\\
F_{611}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{612}\! \left(x \right)+F_{696}\! \left(x \right)\\
F_{612}\! \left(x \right) &= F_{4}\! \left(x \right) F_{613}\! \left(x \right)\\
F_{613}\! \left(x \right) &= F_{614}\! \left(x \right)+F_{617}\! \left(x \right)\\
F_{614}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{615}\! \left(x \right)\\
F_{615}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{369}\! \left(x \right)+F_{616}\! \left(x \right)\\
F_{616}\! \left(x \right) &= F_{307}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{617}\! \left(x \right) &= F_{618}\! \left(x \right)+F_{644}\! \left(x \right)\\
F_{618}\! \left(x \right) &= F_{619}\! \left(x \right)\\
F_{619}\! \left(x \right) &= F_{4}\! \left(x \right) F_{620}\! \left(x \right)\\
F_{620}\! \left(x \right) &= F_{621}\! \left(x \right)+F_{623}\! \left(x \right)\\
F_{621}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{622}\! \left(x \right)\\
F_{622}\! \left(x \right) &= F_{385}\! \left(x \right)\\
F_{623}\! \left(x \right) &= F_{618}\! \left(x \right)+F_{624}\! \left(x \right)\\
F_{624}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{412}\! \left(x \right)+F_{625}\! \left(x \right)\\
F_{625}\! \left(x \right) &= F_{4}\! \left(x \right) F_{626}\! \left(x \right)\\
F_{626}\! \left(x \right) &= F_{627}\! \left(x \right)+F_{629}\! \left(x \right)\\
F_{627}\! \left(x \right) &= F_{622}\! \left(x \right)+F_{628}\! \left(x \right)\\
F_{628}\! \left(x \right) &= F_{395}\! \left(x \right)\\
F_{629}\! \left(x \right) &= F_{630}\! \left(x \right)+F_{635}\! \left(x \right)\\
F_{630}\! \left(x \right) &= F_{631}\! \left(x \right)\\
F_{631}\! \left(x \right) &= F_{4}\! \left(x \right) F_{632}\! \left(x \right)\\
F_{632}\! \left(x \right) &= F_{633}\! \left(x \right)+F_{634}\! \left(x \right)\\
F_{633}\! \left(x \right) &= F_{622}\! \left(x \right)\\
F_{634}\! \left(x \right) &= F_{630}\! \left(x \right)\\
F_{635}\! \left(x \right) &= F_{636}\! \left(x \right)\\
F_{636}\! \left(x \right) &= F_{4}\! \left(x \right) F_{637}\! \left(x \right)\\
F_{637}\! \left(x \right) &= F_{638}\! \left(x \right)+F_{639}\! \left(x \right)\\
F_{638}\! \left(x \right) &= F_{628}\! \left(x \right)\\
F_{639}\! \left(x \right) &= F_{640}\! \left(x \right)\\
F_{640}\! \left(x \right) &= F_{4}\! \left(x \right) F_{641}\! \left(x \right)\\
F_{641}\! \left(x \right) &= F_{642}\! \left(x \right)+F_{643}\! \left(x \right)\\
F_{642}\! \left(x \right) &= F_{628}\! \left(x \right)\\
F_{643}\! \left(x \right) &= F_{640}\! \left(x \right)\\
F_{644}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{564}\! \left(x \right)+F_{645}\! \left(x \right)\\
F_{645}\! \left(x \right) &= F_{4}\! \left(x \right) F_{646}\! \left(x \right)\\
F_{646}\! \left(x \right) &= F_{647}\! \left(x \right)+F_{649}\! \left(x \right)\\
F_{647}\! \left(x \right) &= F_{615}\! \left(x \right)+F_{648}\! \left(x \right)\\
F_{648}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{445}\! \left(x \right)+F_{449}\! \left(x \right)\\
F_{649}\! \left(x \right) &= F_{650}\! \left(x \right)+F_{676}\! \left(x \right)\\
F_{650}\! \left(x \right) &= F_{651}\! \left(x \right)\\
F_{651}\! \left(x \right) &= F_{4}\! \left(x \right) F_{652}\! \left(x \right)\\
F_{652}\! \left(x \right) &= F_{653}\! \left(x \right)+F_{655}\! \left(x \right)\\
F_{653}\! \left(x \right) &= F_{615}\! \left(x \right)+F_{654}\! \left(x \right)\\
F_{654}\! \left(x \right) &= F_{457}\! \left(x \right)\\
F_{655}\! \left(x \right) &= F_{650}\! \left(x \right)+F_{656}\! \left(x \right)\\
F_{656}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{484}\! \left(x \right)+F_{657}\! \left(x \right)\\
F_{657}\! \left(x \right) &= F_{4}\! \left(x \right) F_{658}\! \left(x \right)\\
F_{658}\! \left(x \right) &= F_{659}\! \left(x \right)+F_{661}\! \left(x \right)\\
F_{659}\! \left(x \right) &= F_{654}\! \left(x \right)+F_{660}\! \left(x \right)\\
F_{660}\! \left(x \right) &= F_{467}\! \left(x \right)\\
F_{661}\! \left(x \right) &= F_{662}\! \left(x \right)+F_{667}\! \left(x \right)\\
F_{662}\! \left(x \right) &= F_{663}\! \left(x \right)\\
F_{663}\! \left(x \right) &= F_{4}\! \left(x \right) F_{664}\! \left(x \right)\\
F_{664}\! \left(x \right) &= F_{665}\! \left(x \right)+F_{666}\! \left(x \right)\\
F_{665}\! \left(x \right) &= F_{654}\! \left(x \right)\\
F_{666}\! \left(x \right) &= F_{662}\! \left(x \right)\\
F_{667}\! \left(x \right) &= F_{668}\! \left(x \right)\\
F_{668}\! \left(x \right) &= F_{4}\! \left(x \right) F_{669}\! \left(x \right)\\
F_{669}\! \left(x \right) &= F_{670}\! \left(x \right)+F_{671}\! \left(x \right)\\
F_{670}\! \left(x \right) &= F_{660}\! \left(x \right)\\
F_{671}\! \left(x \right) &= F_{672}\! \left(x \right)\\
F_{672}\! \left(x \right) &= F_{4}\! \left(x \right) F_{673}\! \left(x \right)\\
F_{673}\! \left(x \right) &= F_{674}\! \left(x \right)+F_{675}\! \left(x \right)\\
F_{674}\! \left(x \right) &= F_{660}\! \left(x \right)\\
F_{675}\! \left(x \right) &= F_{672}\! \left(x \right)\\
F_{676}\! \left(x \right) &= 3 F_{22}\! \left(x \right)+F_{560}\! \left(x \right)+F_{677}\! \left(x \right)\\
F_{677}\! \left(x \right) &= F_{4}\! \left(x \right) F_{678}\! \left(x \right)\\
F_{678}\! \left(x \right) &= F_{679}\! \left(x \right)+F_{681}\! \left(x \right)\\
F_{679}\! \left(x \right) &= F_{648}\! \left(x \right)+F_{680}\! \left(x \right)\\
F_{680}\! \left(x \right) &= F_{543}\! \left(x \right)\\
F_{681}\! \left(x \right) &= F_{682}\! \left(x \right)+F_{687}\! \left(x \right)\\
F_{682}\! \left(x \right) &= F_{683}\! \left(x \right)\\
F_{683}\! \left(x \right) &= F_{4}\! \left(x \right) F_{684}\! \left(x \right)\\
F_{684}\! \left(x \right) &= F_{685}\! \left(x \right)+F_{686}\! \left(x \right)\\
F_{685}\! \left(x \right) &= F_{648}\! \left(x \right)\\
F_{686}\! \left(x \right) &= F_{682}\! \left(x \right)\\
F_{687}\! \left(x \right) &= F_{688}\! \left(x \right)\\
F_{688}\! \left(x \right) &= F_{4}\! \left(x \right) F_{689}\! \left(x \right)\\
F_{689}\! \left(x \right) &= F_{690}\! \left(x \right)+F_{691}\! \left(x \right)\\
F_{690}\! \left(x \right) &= F_{680}\! \left(x \right)\\
F_{691}\! \left(x \right) &= F_{692}\! \left(x \right)\\
F_{692}\! \left(x \right) &= F_{4}\! \left(x \right) F_{693}\! \left(x \right)\\
F_{693}\! \left(x \right) &= F_{694}\! \left(x \right)+F_{695}\! \left(x \right)\\
F_{694}\! \left(x \right) &= F_{680}\! \left(x \right)\\
F_{695}\! \left(x \right) &= F_{692}\! \left(x \right)\\
F_{696}\! \left(x \right) &= F_{363}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{697}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{127}\! \left(x \right)+F_{698}\! \left(x \right)\\
F_{698}\! \left(x \right) &= F_{4}\! \left(x \right) F_{699}\! \left(x \right)\\
F_{699}\! \left(x \right) &= F_{700}\! \left(x \right)+F_{702}\! \left(x \right)\\
F_{700}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{701}\! \left(x \right)\\
F_{701}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{702}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{703}\! \left(x \right)\\
F_{703}\! \left(x \right) &= F_{704}\! \left(x \right)\\
F_{704}\! \left(x \right) &= F_{4}\! \left(x \right) F_{705}\! \left(x \right)\\
F_{705}\! \left(x \right) &= F_{706}\! \left(x \right)+F_{707}\! \left(x \right)\\
F_{706}\! \left(x \right) &= F_{701}\! \left(x \right)\\
F_{707}\! \left(x \right) &= F_{708}\! \left(x \right)\\
F_{708}\! \left(x \right) &= F_{4}\! \left(x \right) F_{709}\! \left(x \right)\\
F_{709}\! \left(x \right) &= F_{710}\! \left(x \right)+F_{711}\! \left(x \right)\\
F_{710}\! \left(x \right) &= F_{701}\! \left(x \right)\\
F_{711}\! \left(x \right) &= F_{708}\! \left(x \right)\\
\end{align*}\)