Av(12453, 12543, 14253, 14523, 14532, 15243, 15423, 15432, 51243, 51423, 51432)
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Generating Function
\(\displaystyle \frac{\left(-10 x^{4}+38 x^{3}-48 x^{2}+19 x -2\right) \sqrt{5 x^{2}-6 x +1}+8 x^{6}-70 x^{5}+248 x^{4}-404 x^{3}+303 x^{2}-97 x +10}{16 x^{6}-112 x^{5}+304 x^{4}-402 x^{3}+266 x^{2}-80 x +8}\)
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Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2565, 12796, 64493, 327498, 1672550, 8579582, 44162889, 227951798, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(4 x^{2}-6 x +1\right) \left(x -1\right)^{2} \left(-2+x \right)^{2} \left(2 x -1\right)^{2} F \left(x \right)^{2}-\left(x -1\right) \left(2 x -1\right) \left(8 x^{6}-70 x^{5}+248 x^{4}-404 x^{3}+303 x^{2}-97 x +10\right) F \! \left(x \right)+4 x^{8}-48 x^{7}+218 x^{6}-580 x^{5}+875 x^{4}-733 x^{3}+330 x^{2}-73 x +6 = 0\)
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Recurrence
\(\displaystyle a{\left(0 \right)} = 1\)
\(\displaystyle a{\left(1 \right)} = 1\)
\(\displaystyle a{\left(2 \right)} = 2\)
\(\displaystyle a{\left(3 \right)} = 6\)
\(\displaystyle a{\left(4 \right)} = 24\)
\(\displaystyle a{\left(5 \right)} = 109\)
\(\displaystyle a{\left(6 \right)} = 522\)
\(\displaystyle a{\left(7 \right)} = 2565\)
\(\displaystyle a{\left(8 \right)} = 12796\)
\(\displaystyle a{\left(9 \right)} = 64493\)
\(\displaystyle a{\left(10 \right)} = 327498\)
\(\displaystyle a{\left(11 \right)} = 1672550\)
\(\displaystyle a{\left(n + 10 \right)} = - \frac{100 \left(n + 1\right) a{\left(n \right)}}{n + 10} + \frac{20 \left(45 n + 77\right) a{\left(n + 1 \right)}}{n + 10} + \frac{\left(48 n + 427\right) a{\left(n + 9 \right)}}{2 \left(n + 10\right)} - \frac{48 \left(72 n + 179\right) a{\left(n + 2 \right)}}{n + 10} - \frac{3 \left(317 n + 2485\right) a{\left(n + 8 \right)}}{4 \left(n + 10\right)} + \frac{5 \left(507 n + 3464\right) a{\left(n + 7 \right)}}{2 \left(n + 10\right)} + \frac{3 \left(5203 n + 25911\right) a{\left(n + 5 \right)}}{2 \left(n + 10\right)} + \frac{\left(14757 n + 48605\right) a{\left(n + 3 \right)}}{2 \left(n + 10\right)} - \frac{\left(16001 n + 94079\right) a{\left(n + 6 \right)}}{4 \left(n + 10\right)} - \frac{\left(19159 n + 78991\right) a{\left(n + 4 \right)}}{2 \left(n + 10\right)} + \frac{3}{2 \left(n + 10\right)}, \quad n \geq 12\)
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 720 rules.

Finding the specification took 66346 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_{34}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{34}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{719}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{372}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{34}\! \left(x \right) F_{717}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{551}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= -F_{715}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= -F_{551}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= \frac{F_{28}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{34}\! \left(x \right) &= x\\ F_{35}\! \left(x \right) &= -F_{714}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{37}\! \left(x \right) &= -F_{708}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{34}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{706}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{34}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{34}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= \frac{F_{54}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{54}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{20}\! \left(x \right) F_{34}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{34}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= x^{2} F_{63} \left(x \right)^{2}-2 x F_{63} \left(x \right)^{2}+F_{63}\! \left(x \right) x +2 F_{63}\! \left(x \right)-1\\ F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{194}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{34}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{34}\! \left(x \right) F_{75}\! \left(x \right) F_{82}\! \left(x \right)}\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= -F_{193}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{63}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{34}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{34}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{34}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{34}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{75}\! \left(x \right) F_{82}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{34}\! \left(x \right) F_{62}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{98}\! \left(x \right) &= 0\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{106}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{34}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{112}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{112}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{123}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{132}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{130}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{127}\! \left(x \right)\\ F_{132}\! \left(x \right) &= 2 F_{98}\! \left(x \right)+F_{133}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{132}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{140}\! \left(x \right)+F_{154}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{143}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{144}\! \left(x \right) &= 2 F_{98}\! \left(x \right)+F_{145}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{149}\! \left(x \right) &= 3 F_{98}\! \left(x \right)+F_{150}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{127}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right) F_{158}\! \left(x \right) F_{34}\! \left(x \right) F_{63}\! \left(x \right) F_{75}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{168}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right) F_{162}\! \left(x \right)\\ F_{161}\! \left(x \right) &= x^{2} F_{161} \left(x \right)^{2}+2 x^{2} F_{161}\! \left(x \right)-2 x F_{161} \left(x \right)^{2}+x^{2}-3 x F_{161}\! \left(x \right)-x +2 F_{161}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{166}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{34}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right) F_{186}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= \frac{F_{173}\! \left(x \right)}{F_{175}\! \left(x \right) F_{34}\! \left(x \right)}\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= \frac{F_{176}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{176}\! \left(x \right) &= -F_{179}\! \left(x \right)+F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= \frac{F_{178}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{178}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{179}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= \frac{F_{181}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{175}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{186}\! \left(x \right) &= \frac{F_{187}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{190}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{161}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right) F_{34}\! \left(x \right) F_{75}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{175}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{157}\! \left(x \right) F_{158}\! \left(x \right) F_{34}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{199}\! \left(x \right) &= \frac{F_{200}\! \left(x \right)}{F_{2}\! \left(x \right)}\\ F_{200}\! \left(x \right) &= -F_{237}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{203}\! \left(x \right) &= \frac{F_{204}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\ F_{205}\! \left(x \right) &= -F_{235}\! \left(x \right)+F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= \frac{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_{234}\! \left(x \right)+F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{233}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)+F_{229}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{220}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{175}\! \left(x \right) F_{217}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{114}\! \left(x \right) F_{20}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{228}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{175}\! \left(x \right) F_{225}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{225}\! \left(x \right) &= \frac{F_{226}\! \left(x \right)}{F_{34}\! \left(x \right) F_{63}\! \left(x \right)}\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= -F_{8}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{214}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{2}\! \left(x \right) F_{230}\! \left(x \right)\\ F_{230}\! \left(x \right) &= \frac{F_{231}\! \left(x \right)}{F_{20}\! \left(x \right) F_{34}\! \left(x \right)}\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= -F_{213}\! \left(x \right)+F_{177}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{175}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{2}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{236}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{237}\! \left(x \right) &= -F_{240}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{238}\! \left(x \right) &= \frac{F_{239}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{239}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{217}\! \left(x \right) F_{230}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{225}\! \left(x \right) F_{230}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{161}\! \left(x \right) F_{248}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)+F_{257}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{114}\! \left(x \right) F_{250}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{254}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{252}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{172}\! \left(x \right) F_{20}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{248}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{114}\! \left(x \right) F_{259}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{259}\! \left(x \right) &= \frac{F_{260}\! \left(x \right)}{F_{34}\! \left(x \right) F_{63}\! \left(x \right)}\\ F_{260}\! \left(x \right) &= F_{261}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{45}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{263}\! \left(x \right) &= -F_{671}\! \left(x \right)+F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= -F_{650}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= -F_{346}\! \left(x \right)+F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= \frac{F_{267}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\ F_{268}\! \left(x \right) &= -F_{338}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)+F_{336}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{274}\! \left(x \right) &= \frac{F_{275}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{277}\! \left(x \right) &= -F_{278}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{282}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{280}\! \left(x \right)+F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{20}\! \left(x \right) F_{286}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{286}\! \left(x \right) &= \frac{F_{287}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\ F_{288}\! \left(x \right) &= -F_{299}\! \left(x \right)+F_{289}\! \left(x \right)\\ F_{289}\! \left(x \right) &= -F_{292}\! \left(x \right)+F_{290}\! \left(x \right)\\ F_{290}\! \left(x \right) &= \frac{F_{291}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{291}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{296}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{294}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{114}\! \left(x \right) F_{194}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{112}\! \left(x \right) F_{158}\! \left(x \right) F_{298}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{299}\! \left(x \right) &= -F_{335}\! \left(x \right)+F_{300}\! \left(x \right)\\ F_{300}\! \left(x \right) &= -F_{331}\! \left(x \right)+F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= \frac{F_{302}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)\\ F_{303}\! \left(x \right) &= -F_{161}\! \left(x \right)+F_{304}\! \left(x \right)\\ F_{304}\! \left(x \right) &= -F_{307}\! \left(x \right)+F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= \frac{F_{306}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{306}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{308}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{310}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{311}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{319}\! \left(x \right)\\ F_{312}\! \left(x \right) &= F_{313}\! \left(x \right)\\ F_{313}\! \left(x \right) &= F_{314}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{314}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{316}\! \left(x \right) &= F_{317}\! \left(x \right)+F_{318}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{317}\! \left(x \right) &= F_{34}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{318}\! \left(x \right) &= F_{315}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{319}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{324}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{320}\! \left(x \right) &= F_{321}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{321}\! \left(x \right) &= F_{322}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{328}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{324}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{324}\! \left(x \right) &= F_{325}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{325}\! \left(x \right) &= F_{326}\! \left(x \right)+F_{327}\! \left(x \right)\\ F_{326}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{327}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{328}\! \left(x \right)\\ F_{328}\! \left(x \right) &= 2 F_{98}\! \left(x \right)+F_{329}\! \left(x \right)+F_{330}\! \left(x \right)\\ F_{329}\! \left(x \right) &= F_{34}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{330}\! \left(x \right) &= F_{322}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{331}\! \left(x \right) &= -F_{334}\! \left(x \right)+F_{332}\! \left(x \right)\\ F_{332}\! \left(x \right) &= \frac{F_{333}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{333}\! \left(x \right) &= F_{304}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{289}\! \left(x \right)+F_{305}\! \left(x \right)\\ F_{335}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{308}\! \left(x \right)\\ F_{336}\! \left(x \right) &= F_{337}\! \left(x \right)\\ F_{337}\! \left(x \right) &= F_{284}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)\\ F_{339}\! \left(x \right) &= F_{34}\! \left(x \right) F_{340}\! \left(x \right)\\ F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)+F_{345}\! \left(x \right)\\ F_{341}\! \left(x \right) &= F_{342}\! \left(x \right)+F_{343}\! \left(x \right)\\ F_{342}\! \left(x \right) &= F_{161}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{343}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{344}\! \left(x \right)\\ F_{344}\! \left(x \right) &= F_{2}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{345}\! \left(x \right) &= F_{161}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{347}\! \left(x \right)+F_{351}\! \left(x \right)\\ F_{347}\! \left(x \right) &= F_{348}\! \left(x \right)\\ F_{348}\! \left(x \right) &= F_{161}\! \left(x \right) F_{349}\! \left(x \right)\\ F_{349}\! \left(x \right) &= F_{350}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{14}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{351}\! \left(x \right) &= -F_{536}\! \left(x \right)+F_{352}\! \left(x \right)\\ F_{352}\! \left(x \right) &= F_{353}\! \left(x \right)\\ F_{353}\! \left(x \right) &= F_{34}\! \left(x \right) F_{354}\! \left(x \right)\\ F_{354}\! \left(x \right) &= F_{355}\! \left(x \right)+F_{368}\! \left(x \right)\\ F_{355}\! \left(x \right) &= F_{356}\! \left(x \right) F_{360}\! \left(x \right)\\ F_{356}\! \left(x \right) &= \frac{F_{357}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{357}\! \left(x \right) &= F_{358}\! \left(x \right)\\ F_{358}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{10}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{360}\! \left(x \right) &= \frac{F_{361}\! \left(x \right)}{F_{307}\! \left(x \right)}\\ F_{361}\! \left(x \right) &= -F_{364}\! \left(x \right)+F_{362}\! \left(x \right)\\ F_{362}\! \left(x \right) &= \frac{F_{363}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{363}\! \left(x \right) &= F_{304}\! \left(x \right)\\ F_{364}\! \left(x \right) &= -F_{367}\! \left(x \right)+F_{365}\! \left(x \right)\\ F_{365}\! \left(x \right) &= \frac{F_{366}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{366}\! \left(x \right) &= F_{303}\! \left(x \right)\\ F_{367}\! \left(x \right) &= F_{308}\! \left(x \right) F_{360}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{369}\! \left(x \right) F_{532}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{370}\! \left(x \right)+F_{372}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{371}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{372}\! \left(x \right) &= F_{373}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{34}\! \left(x \right) F_{374}\! \left(x \right)\\ F_{374}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{375}\! \left(x \right) &= F_{376}\! \left(x \right)\\ F_{376}\! \left(x \right) &= F_{34}\! \left(x \right) F_{377}\! \left(x \right)\\ F_{377}\! \left(x \right) &= \frac{F_{378}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{378}\! \left(x \right) &= F_{379}\! \left(x \right)\\ F_{379}\! \left(x \right) &= -F_{525}\! \left(x \right)+F_{380}\! \left(x \right)\\ F_{380}\! \left(x \right) &= \frac{F_{381}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{381}\! \left(x \right) &= F_{382}\! \left(x \right)\\ F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)\\ F_{383}\! \left(x \right) &= F_{34}\! \left(x \right) F_{384}\! \left(x \right)\\ F_{384}\! \left(x \right) &= \frac{F_{385}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{385}\! \left(x \right) &= F_{386}\! \left(x \right)\\ F_{386}\! \left(x \right) &= \frac{F_{387}\! \left(x \right)}{F_{75}\! \left(x \right)}\\ F_{387}\! \left(x \right) &= -F_{524}\! \left(x \right)+F_{388}\! \left(x \right)\\ F_{388}\! \left(x \right) &= -F_{499}\! \left(x \right)+F_{389}\! \left(x \right)\\ F_{389}\! \left(x \right) &= \frac{F_{390}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{390}\! \left(x \right) &= F_{391}\! \left(x \right)\\ F_{391}\! \left(x \right) &= -F_{498}\! \left(x \right)+F_{392}\! \left(x \right)\\ F_{392}\! \left(x \right) &= -F_{310}\! \left(x \right)+F_{393}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{394}\! \left(x \right)+F_{395}\! \left(x \right)\\ F_{394}\! \left(x \right) &= F_{0}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{395}\! \left(x \right) &= F_{396}\! \left(x \right)+F_{489}\! \left(x \right)\\ F_{396}\! \left(x \right) &= F_{397}\! \left(x \right)\\ F_{397}\! \left(x \right) &= F_{34}\! \left(x \right) F_{398}\! \left(x \right)\\ F_{398}\! \left(x \right) &= F_{399}\! \left(x \right)+F_{405}\! \left(x \right)\\ F_{399}\! \left(x \right) &= F_{400}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{400}\! \left(x \right) &= F_{396}\! \left(x \right)+F_{401}\! \left(x \right)\\ F_{401}\! \left(x \right) &= F_{402}\! \left(x \right)\\ F_{402}\! \left(x \right) &= F_{20}\! \left(x \right) F_{34}\! \left(x \right) F_{403}\! \left(x \right)\\ F_{403}\! \left(x \right) &= F_{404}\! \left(x \right)\\ F_{404}\! \left(x \right) &= F_{286}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{405}\! \left(x \right) &= F_{406}\! \left(x \right)\\ F_{406}\! \left(x \right) &= F_{34}\! \left(x \right) F_{407}\! \left(x \right)\\ F_{407}\! \left(x \right) &= \frac{F_{408}\! \left(x \right)}{F_{34}\! \left(x \right) F_{75}\! \left(x \right)}\\ F_{408}\! \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_{163}\! \left(x \right) F_{217}\! \left(x \right)\\ F_{411}\! \left(x \right) &= F_{412}\! \left(x \right)\\ F_{412}\! \left(x \right) &= F_{172}\! \left(x \right) F_{34}\! \left(x \right) F_{413}\! \left(x \right)\\ F_{413}\! \left(x \right) &= F_{414}\! \left(x \right)\\ F_{414}\! \left(x \right) &= F_{34}\! \left(x \right) F_{415}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{485}\! \left(x \right)\\ F_{416}\! \left(x \right) &= F_{417}\! \left(x \right)+F_{483}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{418}\! \left(x \right)+F_{470}\! \left(x \right)\\ F_{418}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{419}\! \left(x \right)\\ F_{419}\! \left(x \right) &= F_{420}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{420}\! \left(x \right) &= F_{421}\! \left(x \right)\\ F_{421}\! \left(x \right) &= F_{34}\! \left(x \right) F_{422}\! \left(x \right)\\ F_{422}\! \left(x \right) &= F_{423}\! \left(x \right)+F_{424}\! \left(x \right)\\ F_{423}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{420}\! \left(x \right)\\ F_{424}\! \left(x \right) &= F_{425}\! \left(x \right)\\ F_{425}\! \left(x \right) &= F_{34}\! \left(x \right) F_{426}\! \left(x \right)\\ F_{426}\! \left(x \right) &= F_{427}\! \left(x \right)+F_{432}\! \left(x \right)\\ F_{427}\! \left(x \right) &= F_{428}\! \left(x \right)+F_{429}\! \left(x \right)\\ F_{428}\! \left(x \right) &= F_{4}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{429}\! \left(x \right) &= F_{430}\! \left(x \right)\\ F_{430}\! \left(x \right) &= F_{34}\! \left(x \right) F_{415}\! \left(x \right) F_{431}\! \left(x \right)\\ F_{431}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{432}\! \left(x \right) &= -F_{467}\! \left(x \right)+F_{433}\! \left(x \right)\\ F_{433}\! \left(x \right) &= \frac{F_{434}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{434}\! \left(x \right) &= F_{435}\! \left(x \right)\\ F_{435}\! \left(x \right) &= -F_{465}\! \left(x \right)+F_{436}\! \left(x \right)\\ F_{436}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{437}\! \left(x \right)\\ F_{437}\! \left(x \right) &= F_{438}\! \left(x \right)\\ F_{438}\! \left(x \right) &= F_{34}\! \left(x \right) F_{439}\! \left(x \right)\\ F_{439}\! \left(x \right) &= -F_{463}\! \left(x \right)+F_{440}\! \left(x \right)\\ F_{440}\! \left(x \right) &= \frac{F_{441}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{441}\! \left(x \right) &= F_{442}\! \left(x \right)\\ F_{442}\! \left(x \right) &= -F_{460}\! \left(x \right)+F_{443}\! \left(x \right)\\ F_{443}\! \left(x \right) &= -F_{446}\! \left(x \right)+F_{444}\! \left(x \right)\\ F_{444}\! \left(x \right) &= \frac{F_{445}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{445}\! \left(x \right) &= F_{395}\! \left(x \right)\\ F_{446}\! \left(x \right) &= F_{447}\! \left(x \right)+F_{448}\! \left(x \right)\\ F_{447}\! \left(x \right) &= F_{399}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{448}\! \left(x \right) &= F_{217}\! \left(x \right) F_{449}\! \left(x \right)\\ F_{449}\! \left(x \right) &= F_{450}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{450}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{451}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{451}\! \left(x \right) &= F_{34}\! \left(x \right) F_{452}\! \left(x \right)\\ F_{452}\! \left(x \right) &= F_{453}\! \left(x \right)+F_{454}\! \left(x \right)\\ F_{453}\! \left(x \right) &= F_{450}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{454}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{455}\! \left(x \right)\\ F_{455}\! \left(x \right) &= F_{456}\! \left(x \right)+F_{457}\! \left(x \right)+F_{459}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{456}\! \left(x \right) &= F_{34}\! \left(x \right) F_{450}\! \left(x \right)\\ F_{457}\! \left(x \right) &= F_{34}\! \left(x \right) F_{458}\! \left(x \right)\\ F_{458}\! \left(x \right) &= F_{454}\! \left(x \right)\\ F_{459}\! \left(x \right) &= 0\\ F_{460}\! \left(x \right) &= F_{461}\! \left(x \right)\\ F_{461}\! \left(x \right) &= F_{34}\! \left(x \right) F_{440}\! \left(x \right) F_{462}\! \left(x \right)\\ F_{462}\! \left(x \right) &= F_{449}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{463}\! \left(x \right) &= \frac{F_{464}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{464}\! \left(x \right) &= F_{419}\! \left(x \right)\\ F_{465}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{466}\! \left(x \right)\\ F_{466}\! \left(x \right) &= F_{112}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{467}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{468}\! \left(x \right)\\ F_{468}\! \left(x \right) &= F_{420}\! \left(x \right)+F_{469}\! \left(x \right)\\ F_{469}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{435}\! \left(x \right)\\ F_{470}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{471}\! \left(x \right)\\ F_{471}\! \left(x \right) &= -F_{396}\! \left(x \right)+F_{472}\! \left(x \right)\\ F_{472}\! \left(x \right) &= F_{473}\! \left(x \right)\\ F_{473}\! \left(x \right) &= F_{34}\! \left(x \right) F_{474}\! \left(x \right)\\ F_{474}\! \left(x \right) &= F_{427}\! \left(x \right)+F_{475}\! \left(x \right)\\ F_{475}\! \left(x \right) &= -F_{481}\! \left(x \right)+F_{476}\! \left(x \right)\\ F_{476}\! \left(x \right) &= \frac{F_{477}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{477}\! \left(x \right) &= F_{478}\! \left(x \right)\\ F_{478}\! \left(x \right) &= F_{396}\! \left(x \right)+F_{479}\! \left(x \right)\\ F_{479}\! \left(x \right) &= F_{480}\! \left(x \right)\\ F_{480}\! \left(x \right) &= F_{255}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{481}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{482}\! \left(x \right)\\ F_{482}\! \left(x \right) &= F_{418}\! \left(x \right)+F_{424}\! \left(x \right)\\ F_{483}\! \left(x \right) &= F_{484}\! \left(x \right)\\ F_{484}\! \left(x \right) &= F_{34}\! \left(x \right) F_{415}\! \left(x \right)\\ F_{485}\! \left(x \right) &= F_{486}\! \left(x \right)\\ F_{486}\! \left(x \right) &= F_{34}\! \left(x \right) F_{487}\! \left(x \right)\\ F_{487}\! \left(x \right) &= \frac{F_{488}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{488}\! \left(x \right) &= F_{432}\! \left(x \right)\\ F_{489}\! \left(x \right) &= F_{490}\! \left(x \right)\\ F_{490}\! \left(x \right) &= F_{34}\! \left(x \right) F_{491}\! \left(x \right)\\ F_{491}\! \left(x \right) &= F_{492}\! \left(x \right)+F_{493}\! \left(x \right)\\ F_{492}\! \left(x \right) &= F_{398}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{493}\! \left(x \right) &= F_{449}\! \left(x \right) F_{494}\! \left(x \right)\\ F_{494}\! \left(x \right) &= F_{418}\! \left(x \right)+F_{495}\! \left(x \right)\\ F_{495}\! \left(x \right) &= F_{496}\! \left(x \right)\\ F_{496}\! \left(x \right) &= F_{34}\! \left(x \right) F_{497}\! \left(x \right)\\ F_{497}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{494}\! \left(x \right)\\ F_{498}\! \left(x \right) &= F_{2}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{499}\! \left(x \right) &= F_{500}\! \left(x \right)+F_{503}\! \left(x \right)\\ F_{500}\! \left(x \right) &= F_{501}\! \left(x \right)+F_{502}\! \left(x \right)\\ F_{501}\! \left(x \right) &= F_{423}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{502}\! \left(x \right) &= F_{2}\! \left(x \right) F_{449}\! \left(x \right)\\ F_{503}\! \left(x \right) &= F_{504}\! \left(x \right)\\ F_{504}\! \left(x \right) &= F_{34}\! \left(x \right) F_{505}\! \left(x \right)\\ F_{505}\! \left(x \right) &= F_{506}\! \left(x \right)+F_{514}\! \left(x \right)\\ F_{506}\! \left(x \right) &= F_{507}\! \left(x \right)\\ F_{507}\! \left(x \right) &= F_{2}\! \left(x \right) F_{508}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{508}\! \left(x \right) &= \frac{F_{509}\! \left(x \right)}{F_{217}\! \left(x \right) F_{34}\! \left(x \right) F_{82}\! \left(x \right)}\\ F_{509}\! \left(x \right) &= F_{510}\! \left(x \right)\\ F_{510}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{511}\! \left(x \right)\\ F_{511}\! \left(x \right) &= F_{512}\! \left(x \right)\\ F_{512}\! \left(x \right) &= F_{34}\! \left(x \right) F_{508}\! \left(x \right) F_{513}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{513}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{514}\! \left(x \right) &= F_{515}\! \left(x \right)\\ F_{515}\! \left(x \right) &= F_{34}\! \left(x \right) F_{516}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{516}\! \left(x \right) &= \frac{F_{517}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{517}\! \left(x \right) &= F_{518}\! \left(x \right)\\ F_{518}\! \left(x \right) &= -F_{521}\! \left(x \right)+F_{519}\! \left(x \right)\\ F_{519}\! \left(x \right) &= \frac{F_{520}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{520}\! \left(x \right) &= F_{391}\! \left(x \right)\\ F_{521}\! \left(x \right) &= F_{395}\! \left(x \right)+F_{522}\! \left(x \right)\\ F_{522}\! \left(x \right) &= F_{523}\! \left(x \right)\\ F_{523}\! \left(x \right) &= F_{471}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{524}\! \left(x \right) &= F_{449}\! \left(x \right) F_{495}\! \left(x \right)\\ F_{525}\! \left(x \right) &= F_{526}\! \left(x \right)+F_{528}\! \left(x \right)\\ F_{526}\! \left(x \right) &= \frac{F_{527}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{527}\! \left(x \right) &= F_{10}\! \left(x \right)\\ F_{528}\! \left(x \right) &= F_{529}\! \left(x \right)\\ F_{529}\! \left(x \right) &= F_{34}\! \left(x \right) F_{530}\! \left(x \right)\\ F_{530}\! \left(x \right) &= \frac{F_{531}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{531}\! \left(x \right) &= F_{277}\! \left(x \right)\\ F_{532}\! \left(x \right) &= F_{533}\! \left(x \right)\\ F_{533}\! \left(x \right) &= F_{34}\! \left(x \right) F_{534}\! \left(x \right)\\ F_{534}\! \left(x \right) &= \frac{F_{535}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{535}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{536}\! \left(x \right) &= F_{537}\! \left(x \right)\\ F_{537}\! \left(x \right) &= F_{161}\! \left(x \right) F_{538}\! \left(x \right)\\ F_{538}\! \left(x \right) &= -F_{556}\! \left(x \right)+F_{539}\! \left(x \right)\\ F_{539}\! \left(x \right) &= F_{540}\! \left(x \right)+F_{553}\! \left(x \right)\\ F_{540}\! \left(x \right) &= F_{541}\! \left(x \right)+F_{542}\! \left(x \right)\\ F_{541}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{542}\! \left(x \right) &= F_{543}\! \left(x \right)\\ F_{543}\! \left(x \right) &= F_{34}\! \left(x \right) F_{544}\! \left(x \right)\\ F_{544}\! \left(x \right) &= F_{545}\! \left(x \right)+F_{551}\! \left(x \right)\\ F_{545}\! \left(x \right) &= F_{546}\! \left(x \right)+F_{550}\! \left(x \right)\\ F_{546}\! \left(x \right) &= F_{25}\! \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_{549}\! \left(x \right) &= F_{34}\! \left(x \right) F_{544}\! \left(x \right)\\ F_{550}\! \left(x \right) &= F_{371}\! \left(x \right)\\ F_{551}\! \left(x \right) &= F_{552}\! \left(x \right)\\ F_{552}\! \left(x \right) &= F_{34}\! \left(x \right) F_{377}\! \left(x \right)\\ F_{553}\! \left(x \right) &= F_{554}\! \left(x \right)\\ F_{554}\! \left(x \right) &= F_{34}\! \left(x \right) F_{555}\! \left(x \right)\\ F_{555}\! \left(x \right) &= F_{369}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{556}\! \left(x \right) &= -F_{608}\! \left(x \right)+F_{557}\! \left(x \right)\\ F_{557}\! \left(x \right) &= -F_{563}\! \left(x \right)+F_{558}\! \left(x \right)\\ F_{558}\! \left(x \right) &= -F_{561}\! \left(x \right)+F_{559}\! \left(x \right)\\ F_{559}\! \left(x \right) &= \frac{F_{560}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{560}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{561}\! \left(x \right) &= F_{34}\! \left(x \right) F_{562}\! \left(x \right)\\ F_{562}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{540}\! \left(x \right)\\ F_{563}\! \left(x \right) &= F_{564}\! \left(x \right)+F_{573}\! \left(x \right)\\ F_{564}\! \left(x \right) &= -F_{569}\! \left(x \right)+F_{565}\! \left(x \right)\\ F_{565}\! \left(x \right) &= \frac{F_{566}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{566}\! \left(x \right) &= F_{567}\! \left(x \right)\\ F_{567}\! \left(x \right) &= F_{338}\! \left(x \right)+F_{568}\! \left(x \right)\\ F_{568}\! \left(x \right) &= F_{2}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{569}\! \left(x \right) &= F_{570}\! \left(x \right)\\ F_{570}\! \left(x \right) &= F_{34}\! \left(x \right) F_{571}\! \left(x \right)\\ F_{571}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{572}\! \left(x \right)\\ F_{572}\! \left(x \right) &= F_{2}\! \left(x \right) F_{431}\! \left(x \right)\\ F_{573}\! \left(x \right) &= F_{349}\! \left(x \right)+F_{574}\! \left(x \right)\\ F_{574}\! \left(x \right) &= -F_{350}\! \left(x \right)+F_{575}\! \left(x \right)\\ F_{575}\! \left(x \right) &= -F_{581}\! \left(x \right)+F_{576}\! \left(x \right)\\ F_{576}\! \left(x \right) &= \frac{F_{577}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{577}\! \left(x \right) &= F_{578}\! \left(x \right)\\ F_{578}\! \left(x \right) &= -F_{579}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{579}\! \left(x \right) &= F_{580}\! \left(x \right)\\ F_{580}\! \left(x \right) &= F_{34}\! \left(x \right) F_{341}\! \left(x \right)\\ F_{581}\! \left(x \right) &= F_{582}\! \left(x \right)+F_{605}\! \left(x \right)\\ F_{582}\! \left(x \right) &= F_{583}\! \left(x \right)\\ F_{583}\! \left(x \right) &= -F_{584}\! \left(x \right)+F_{274}\! \left(x \right)\\ F_{584}\! \left(x \right) &= -F_{587}\! \left(x \right)+F_{585}\! \left(x \right)\\ F_{585}\! \left(x \right) &= \frac{F_{586}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{586}\! \left(x \right) &= F_{276}\! \left(x \right)\\ F_{587}\! \left(x \right) &= F_{588}\! \left(x \right)\\ F_{588}\! \left(x \right) &= -F_{604}\! \left(x \right)+F_{589}\! \left(x \right)\\ F_{589}\! \left(x \right) &= \frac{F_{590}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{590}\! \left(x \right) &= F_{591}\! \left(x \right)\\ F_{591}\! \left(x \right) &= -F_{603}\! \left(x \right)+F_{592}\! \left(x \right)\\ F_{592}\! \left(x \right) &= -F_{597}\! \left(x \right)+F_{593}\! \left(x \right)\\ F_{593}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{594}\! \left(x \right)\\ F_{594}\! \left(x \right) &= F_{595}\! \left(x \right)\\ F_{595}\! \left(x \right) &= F_{34}\! \left(x \right) F_{596}\! \left(x \right)\\ F_{596}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{379}\! \left(x \right)\\ F_{597}\! \left(x \right) &= F_{598}\! \left(x \right)+F_{599}\! \left(x \right)\\ F_{598}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{396}\! \left(x \right)\\ F_{599}\! \left(x \right) &= F_{600}\! \left(x \right)+F_{602}\! \left(x \right)\\ F_{600}\! \left(x \right) &= F_{601}\! \left(x \right)\\ F_{601}\! \left(x \right) &= F_{280}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{602}\! \left(x \right) &= -F_{396}\! \left(x \right)+F_{382}\! \left(x \right)\\ F_{603}\! \left(x \right) &= F_{479}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{604}\! \left(x \right) &= F_{585}\! \left(x \right)\\ F_{605}\! \left(x \right) &= F_{606}\! \left(x \right)\\ F_{606}\! \left(x \right) &= -F_{607}\! \left(x \right)+F_{551}\! \left(x \right)\\ F_{607}\! \left(x \right) &= F_{251}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{608}\! \left(x \right) &= F_{609}\! \left(x \right)\\ F_{609}\! \left(x \right) &= -F_{613}\! \left(x \right)+F_{610}\! \left(x \right)\\ F_{610}\! \left(x \right) &= F_{611}\! \left(x \right)+F_{612}\! \left(x \right)\\ F_{611}\! \left(x \right) &= F_{583}\! \left(x \right)\\ F_{612}\! \left(x \right) &= F_{605}\! \left(x \right)\\ F_{613}\! \left(x \right) &= -F_{617}\! \left(x \right)+F_{614}\! \left(x \right)\\ F_{614}\! \left(x \right) &= F_{615}\! \left(x \right)\\ F_{615}\! \left(x \right) &= F_{34}\! \left(x \right) F_{616}\! \left(x \right)\\ F_{616}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{525}\! \left(x \right)\\ F_{617}\! \left(x \right) &= -F_{633}\! \left(x \right)+F_{618}\! \left(x \right)\\ F_{618}\! \left(x \right) &= -F_{623}\! \left(x \right)+F_{619}\! \left(x \right)\\ F_{619}\! \left(x \right) &= \frac{F_{620}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{620}\! \left(x \right) &= F_{621}\! \left(x \right)\\ F_{621}\! \left(x \right) &= F_{34}\! \left(x \right) F_{622}\! \left(x \right)\\ F_{622}\! \left(x \right) &= F_{396}\! \left(x \right)+F_{599}\! \left(x \right)\\ F_{623}\! \left(x \right) &= F_{624}\! \left(x \right)\\ F_{624}\! \left(x \right) &= F_{34}\! \left(x \right) F_{625}\! \left(x \right)\\ F_{625}\! \left(x \right) &= -F_{628}\! \left(x \right)+F_{626}\! \left(x \right)\\ F_{626}\! \left(x \right) &= \frac{F_{627}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{627}\! \left(x \right) &= F_{599}\! \left(x \right)\\ F_{628}\! \left(x \right) &= -F_{631}\! \left(x \right)+F_{629}\! \left(x \right)\\ F_{629}\! \left(x \right) &= \frac{F_{630}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{630}\! \left(x \right) &= F_{602}\! \left(x \right)\\ F_{631}\! \left(x \right) &= F_{632}\! \left(x \right)\\ F_{632}\! \left(x \right) &= F_{34}\! \left(x \right) F_{374}\! \left(x \right)\\ F_{633}\! \left(x \right) &= -F_{646}\! \left(x \right)+F_{634}\! \left(x \right)\\ F_{634}\! \left(x \right) &= F_{635}\! \left(x \right)\\ F_{635}\! \left(x \right) &= -F_{645}\! \left(x \right)+F_{636}\! \left(x \right)\\ F_{636}\! \left(x \right) &= \frac{F_{637}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{637}\! \left(x \right) &= F_{638}\! \left(x \right)\\ F_{638}\! \left(x \right) &= -F_{644}\! \left(x \right)+F_{639}\! \left(x \right)\\ F_{639}\! \left(x \right) &= -F_{641}\! \left(x \right)+F_{640}\! \left(x \right)\\ F_{640}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{478}\! \left(x \right)\\ F_{641}\! \left(x \right) &= F_{642}\! \left(x \right)+F_{643}\! \left(x \right)\\ F_{642}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{312}\! \left(x \right)\\ F_{643}\! \left(x \right) &= F_{2}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{644}\! \left(x \right) &= -F_{642}\! \left(x \right)+F_{598}\! \left(x \right)\\ F_{645}\! \left(x \right) &= F_{30}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{646}\! \left(x \right) &= F_{479}\! \left(x \right)+F_{647}\! \left(x \right)\\ F_{647}\! \left(x \right) &= F_{648}\! \left(x \right)\\ F_{648}\! \left(x \right) &= F_{34}\! \left(x \right) F_{649}\! \left(x \right)\\ F_{649}\! \left(x \right) &= F_{587}\! \left(x \right)\\ F_{650}\! \left(x \right) &= F_{651}\! \left(x \right)\\ F_{651}\! \left(x \right) &= -F_{668}\! \left(x \right)+F_{652}\! \left(x \right)\\ F_{652}\! \left(x \right) &= F_{653}\! \left(x \right)\\ F_{653}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{654}\! \left(x \right)\\ F_{654}\! \left(x \right) &= \frac{F_{655}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{655}\! \left(x \right) &= F_{656}\! \left(x \right)\\ F_{656}\! \left(x \right) &= -F_{664}\! \left(x \right)+F_{657}\! \left(x \right)\\ F_{657}\! \left(x \right) &= F_{658}\! \left(x \right)+F_{660}\! \left(x \right)\\ F_{658}\! \left(x \right) &= \frac{F_{659}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{659}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{660}\! \left(x \right) &= F_{661}\! \left(x \right)\\ F_{661}\! \left(x \right) &= F_{20}\! \left(x \right) F_{34}\! \left(x \right) F_{662}\! \left(x \right)\\ F_{662}\! \left(x \right) &= \frac{F_{663}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{663}\! \left(x \right) &= F_{288}\! \left(x \right)\\ F_{664}\! \left(x \right) &= F_{665}\! \left(x \right)+F_{667}\! \left(x \right)\\ F_{665}\! \left(x \right) &= F_{305}\! \left(x \right)+F_{666}\! \left(x \right)\\ F_{666}\! \left(x \right) &= F_{2}\! \left(x \right) F_{360}\! \left(x \right)\\ F_{667}\! \left(x \right) &= F_{10}\! \left(x \right) F_{360}\! \left(x \right)\\ F_{668}\! \left(x \right) &= F_{34}\! \left(x \right) F_{669}\! \left(x \right)\\ F_{669}\! \left(x \right) &= -F_{342}\! \left(x \right)+F_{670}\! \left(x \right)\\ F_{670}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{548}\! \left(x \right)\\ F_{671}\! \left(x \right) &= F_{672}\! \left(x \right)\\ F_{672}\! \left(x \right) &= F_{34}\! \left(x \right) F_{673}\! \left(x \right) F_{704}\! \left(x \right)\\ F_{673}\! \left(x \right) &= \frac{F_{674}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{674}\! \left(x \right) &= -F_{677}\! \left(x \right)+F_{675}\! \left(x \right)\\ F_{675}\! \left(x \right) &= \frac{F_{676}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{676}\! \left(x \right) &= F_{606}\! \left(x \right)\\ F_{677}\! \left(x \right) &= F_{678}\! \left(x \right)\\ F_{678}\! \left(x \right) &= \frac{F_{679}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{679}\! \left(x \right) &= F_{680}\! \left(x \right)\\ F_{680}\! \left(x \right) &= F_{34}\! \left(x \right) F_{681}\! \left(x \right)\\ F_{681}\! \left(x \right) &= -F_{684}\! \left(x \right)+F_{682}\! \left(x \right)\\ F_{682}\! \left(x \right) &= \frac{F_{683}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{683}\! \left(x \right) &= F_{528}\! \left(x \right)\\ F_{684}\! \left(x \right) &= -F_{685}\! \left(x \right)+F_{530}\! \left(x \right)\\ F_{685}\! \left(x \right) &= -F_{686}\! \left(x \right)+F_{377}\! \left(x \right)\\ F_{686}\! \left(x \right) &= \frac{F_{687}\! \left(x \right)}{F_{175}\! \left(x \right) F_{34}\! \left(x \right)}\\ F_{687}\! \left(x \right) &= F_{688}\! \left(x \right)\\ F_{688}\! \left(x \right) &= -F_{703}\! \left(x \right)+F_{689}\! \left(x \right)\\ F_{689}\! \left(x \right) &= \frac{F_{690}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{690}\! \left(x \right) &= F_{691}\! \left(x \right)\\ F_{691}\! \left(x \right) &= F_{692}\! \left(x \right)+F_{699}\! \left(x \right)\\ F_{692}\! \left(x \right) &= F_{693}\! \left(x \right)\\ F_{693}\! \left(x \right) &= F_{34}\! \left(x \right) F_{694}\! \left(x \right)\\ F_{694}\! \left(x \right) &= F_{695}\! \left(x \right)+F_{698}\! \left(x \right)\\ F_{695}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{696}\! \left(x \right)\\ F_{696}\! \left(x \right) &= F_{697}\! \left(x \right)\\ F_{697}\! \left(x \right) &= F_{175}\! \left(x \right) F_{20}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{698}\! \left(x \right) &= F_{216}\! \left(x \right)\\ F_{699}\! \left(x \right) &= F_{700}\! \left(x \right)\\ F_{700}\! \left(x \right) &= F_{34}\! \left(x \right) F_{701}\! \left(x \right)\\ F_{701}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{702}\! \left(x \right)\\ F_{702}\! \left(x \right) &= F_{175}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{703}\! \left(x \right) &= F_{526}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{704}\! \left(x \right) &= F_{705}\! \left(x \right)\\ F_{705}\! \left(x \right) &= F_{34}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{706}\! \left(x \right) &= F_{707}\! \left(x \right)\\ F_{707}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{562}\! \left(x \right)\\ F_{708}\! \left(x \right) &= F_{709}\! \left(x \right)\\ F_{709}\! \left(x \right) &= F_{34}\! \left(x \right) F_{710}\! \left(x \right)\\ F_{710}\! \left(x \right) &= F_{400}\! \left(x \right)+F_{711}\! \left(x \right)\\ F_{711}\! \left(x \right) &= -F_{432}\! \left(x \right)+F_{712}\! \left(x \right)\\ F_{712}\! \left(x \right) &= \frac{F_{713}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{713}\! \left(x \right) &= F_{602}\! \left(x \right)\\ F_{714}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{600}\! \left(x \right)\\ F_{715}\! \left(x \right) &= F_{711}\! \left(x \right)+F_{716}\! \left(x \right)\\ F_{716}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{399}\! \left(x \right)\\ F_{717}\! \left(x \right) &= \frac{F_{718}\! \left(x \right)}{F_{34}\! \left(x \right)}\\ F_{718}\! \left(x \right) &= F_{288}\! \left(x \right)\\ F_{719}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{255}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 175 rules.

Finding the specification took 3472 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_{1}\! \left(x \right)+F_{110}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{10}\! \left(x \right) &= 0\\ F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{12}\! \left(x , y\right) &= -\frac{y \left(F_{9}\! \left(x , 1\right)-F_{9}\! \left(x , y\right)\right)}{-1+y}\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= y x\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x \right)+F_{29}\! \left(x , y\right)\\ F_{18}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)\\ F_{31}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x , y\right)\\ F_{33}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= F_{19}\! \left(x \right)+F_{33}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{39}\! \left(x , y\right)\\ F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{41}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{19}\! \left(x \right)+F_{39}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{23}\! \left(x \right)+F_{43}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{48}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{26}\! \left(x \right)+F_{46}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{51}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{51}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\ F_{53}\! \left(x , y\right) &= y F_{54}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\ F_{58}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\ F_{59}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{166}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{4}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{5}\! \left(x \right)-F_{95}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{70}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{71}\! \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_{18}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{75}\! \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_{25}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{80}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{23}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{4}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{83}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{4}\! \left(x \right) F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{19}\! \left(x \right) F_{4}\! \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_{91}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= 2 F_{10}\! \left(x \right)+F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{26}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{4}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{4}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{99}\! \left(x \right) &= -F_{10}\! \left(x \right)-F_{6}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{100}\! \left(x \right) &= -F_{105}\! \left(x \right)-F_{62}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{104}\! \left(x \right) &= x^{2} F_{104} \left(x \right)^{2}-2 x F_{104} \left(x \right)^{2}+F_{104}\! \left(x \right) x +2 F_{104}\! \left(x \right)-1\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= \frac{F_{109}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{109}\! \left(x \right) &= -F_{10}\! \left(x \right)-F_{110}\! \left(x \right)+F_{103}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= -F_{21}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x , 1\right)\\ F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right)+F_{148}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{61}\! \left(x \right)\\ F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)\\ F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{124}\! \left(x , y\right) &= -\frac{-F_{120}\! \left(x , y\right) y +F_{120}\! \left(x , 1\right)}{-1+y}\\ F_{125}\! \left(x , y\right) &= F_{126}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{126}\! \left(x , y\right)+F_{147}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= F_{127}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)\\ F_{130}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{144}\! \left(x , y\right)\\ F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{141}\! \left(x , y\right)\\ F_{131}\! \left(x , y\right) &= -\frac{-F_{132}\! \left(x , y\right) y +F_{132}\! \left(x , 1\right)}{-1+y}\\ F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{18}\! \left(x \right)+F_{38}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\ F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{137}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)\\ F_{139}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{62}\! \left(x \right)\\ F_{140}\! \left(x , y\right) &= -\frac{-F_{139}\! \left(x , y\right) y +F_{139}\! \left(x , 1\right)}{-1+y}\\ F_{140}\! \left(x , y\right) &= F_{111}\! \left(x \right)+F_{56}\! \left(x , y\right)\\ F_{141}\! \left(x , y\right) &= y F_{142}\! \left(x , y\right)\\ F_{142}\! \left(x , y\right) &= -\frac{-y F_{143}\! \left(x , y\right)+F_{143}\! \left(x , 1\right)}{-1+y}\\ F_{143}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\ F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)+F_{61}\! \left(x \right)\\ F_{145}\! \left(x , y\right) &= y F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{147}\! \left(x , y\right) &= y F_{148}\! \left(x , y\right)\\ F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\ F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right) F_{159}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\ F_{151}\! \left(x , y\right) &= F_{152}\! \left(x \right)+F_{155}\! \left(x , y\right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{155}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{156}\! \left(x , y\right)+F_{158}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{157}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{157}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{151}\! \left(x , y\right)\\ F_{159}\! \left(x \right) &= \frac{F_{160}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{160}\! \left(x \right) &= F_{100}\! \left(x \right)\\ F_{161}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)\\ F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)+F_{165}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= -\frac{-F_{60}\! \left(x , y\right) y +F_{60}\! \left(x , 1\right)}{-1+y}\\ F_{165}\! \left(x , y\right) &= -\frac{-y F_{148}\! \left(x , y\right)+F_{148}\! \left(x , 1\right)}{-1+y}\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{168}\! \left(x \right)+F_{61}\! \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_{60}\! \left(x , 1\right)\\ F_{172}\! \left(x \right) &= F_{147}\! \left(x , 1\right)\\ F_{173}\! \left(x , y\right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= -F_{167}\! \left(x \right)+F_{159}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Req Corrob" and has 265 rules.

Finding the specification took 62846 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_{19}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{19}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= \frac{F_{8}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{258}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{161}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{249}\! \left(x \right)+F_{250}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{17}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= x\\ F_{20}\! \left(x \right) &= F_{19}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= -F_{244}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{25}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{29}\! \left(x \right) &= 0\\ F_{30}\! \left(x \right) &= F_{19}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= -F_{42}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{19}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{39}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{19}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{19}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{42}\! \left(x \right) &= x^{2} F_{42} \left(x \right)^{2}-2 x F_{42} \left(x \right)^{2}+x F_{42}\! \left(x \right)+2 F_{42}\! \left(x \right)-1\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{19}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{120}\! \left(x \right) F_{19}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{19}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{19}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{19}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{64}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{19}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{19}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{19}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{19}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{19}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{81}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{19}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{19}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{19}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{19}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{19}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{97}\! \left(x \right) &= 2 F_{29}\! \left(x \right)+F_{100}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{19}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{105}\! \left(x \right)+F_{119}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{114}\! \left(x \right)\\ F_{109}\! \left(x \right) &= 2 F_{29}\! \left(x \right)+F_{110}\! \left(x \right)+F_{112}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{114}\! \left(x \right) &= 3 F_{29}\! \left(x \right)+F_{115}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{114}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{19}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{228}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{125}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{127}\! \left(x \right) &= \frac{F_{128}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{226}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{161}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{140}\! \left(x \right)+F_{141}\! \left(x \right)+F_{160}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{139}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{142}\! \left(x \right) &= \frac{F_{143}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{143}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{150}\! \left(x \right)-F_{152}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{145}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{144}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{144}\! \left(x \right) F_{145}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= 2 F_{29}\! \left(x \right)+F_{156}\! \left(x \right)+F_{158}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{155}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{153}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{135}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{151}\! \left(x \right) F_{161}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{139}\! \left(x \right) F_{168}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{189}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{188}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{177}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{144}\! \left(x \right) F_{170}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)+F_{182}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{179}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{178}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{145}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{144}\! \left(x \right) F_{179}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{145}\! \left(x \right) F_{178}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{19}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{19}\! \left(x \right) F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{151}\! \left(x \right) F_{168}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{225}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{19}\! \left(x \right) F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= -F_{224}\! \left(x \right)+F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= \frac{F_{199}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= -F_{217}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{212}\! \left(x \right)\\ F_{202}\! \left(x \right) &= \frac{F_{203}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{203}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{208}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{19}\! \left(x \right) F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{151}\! \left(x \right) F_{19}\! \left(x \right) F_{204}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{216}\! \left(x \right)+F_{218}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{19}\! \left(x \right) F_{213}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{19}\! \left(x \right) F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{213}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{19}\! \left(x \right) F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= 2 F_{29}\! \left(x \right)+F_{221}\! \left(x \right)+F_{222}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{19}\! \left(x \right) F_{220}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{19}\! \left(x \right) F_{209}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{161}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{151}\! \left(x \right) F_{169}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= -F_{125}\! \left(x \right)+F_{230}\! \left(x \right)\\ F_{230}\! \left(x \right) &= \frac{F_{231}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{19}\! \left(x \right) F_{233}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{197}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{151}\! \left(x \right) F_{19}\! \left(x \right) F_{236}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{19}\! \left(x \right) F_{238}\! \left(x \right)\\ F_{238}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{247}\! \left(x \right)\\ F_{240}\! \left(x \right) &= -F_{244}\! \left(x \right)+F_{241}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{120}\! \left(x \right) F_{19}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{161}\! \left(x \right) F_{19}\! \left(x \right) F_{23}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{16}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)\\ F_{251}\! \left(x \right) &= -F_{244}\! \left(x \right)-F_{252}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{19}\! \left(x \right) F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= \frac{F_{254}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)\\ F_{255}\! \left(x \right) &= \frac{F_{256}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{256}\! \left(x \right) &= -F_{257}\! \left(x \right)-F_{29}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{19}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{261}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{19}\! \left(x \right) F_{263}\! \left(x \right)\\ F_{263}\! \left(x \right) &= \frac{F_{264}\! \left(x \right)}{F_{19}\! \left(x \right)}\\ F_{264}\! \left(x \right) &= F_{197}\! \left(x \right)\\ \end{align*}\)