Av(12453, 13452, 14352, 21453, 23451, 24351, 31452, 32451, 34251, 41352, 42351, 43251)
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Generating Function
\(\displaystyle \frac{\left(-6 x^{8}-46 x^{7}-24 x^{6}-347 x^{5}+341 x^{4}-119 x^{3}+18 x^{2}-x \right) \sqrt{1-4 x}-4 x^{9}-18 x^{8}+70 x^{7}-148 x^{6}+893 x^{5}-503 x^{4}-4 x^{3}+59 x^{2}-14 x +1}{4 x^{8}+48 x^{7}+132 x^{6}+52 x^{5}+154 x^{4}-224 x^{3}+93 x^{2}-16 x +1}\)
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Counting Sequence
1, 1, 2, 6, 24, 108, 512, 2488, 12238, 60560, 300550, 1493450, 7423892, 36901488, 183370896, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(x^{2}+4 x -1\right) \left(4 x^{6}+32 x^{5}+8 x^{4}+52 x^{3}-46 x^{2}+12 x -1\right) F \left(x \right)^{2}+\left(8 x^{9}+36 x^{8}-140 x^{7}+296 x^{6}-1786 x^{5}+1006 x^{4}+8 x^{3}-118 x^{2}+28 x -2\right) F \! \left(x \right)+4 x^{10}+24 x^{9}+64 x^{8}+320 x^{7}+124 x^{6}+1024 x^{5}-877 x^{4}+168 x^{3}+28 x^{2}-12 x +1 = 0\)
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Recurrence
\(\displaystyle a{\left(0 \right)} = 1\)
\(\displaystyle a{\left(1 \right)} = 1\)
\(\displaystyle a{\left(2 \right)} = 2\)
\(\displaystyle a{\left(3 \right)} = 6\)
\(\displaystyle a{\left(4 \right)} = 24\)
\(\displaystyle a{\left(5 \right)} = 108\)
\(\displaystyle a{\left(6 \right)} = 512\)
\(\displaystyle a{\left(7 \right)} = 2488\)
\(\displaystyle a{\left(8 \right)} = 12238\)
\(\displaystyle a{\left(9 \right)} = 60560\)
\(\displaystyle a{\left(10 \right)} = 300550\)
\(\displaystyle a{\left(11 \right)} = 1493450\)
\(\displaystyle a{\left(12 \right)} = 7423892\)
\(\displaystyle a{\left(13 \right)} = 36901488\)
\(\displaystyle a{\left(14 \right)} = 183370896\)
\(\displaystyle a{\left(15 \right)} = 910854048\)
\(\displaystyle a{\left(16 \right)} = 4522583344\)
\(\displaystyle a{\left(17 \right)} = 22446436190\)
\(\displaystyle a{\left(n + 16 \right)} = \frac{48 \left(2 n - 1\right) a{\left(n \right)}}{n + 15} + \frac{2 \left(19 n + 264\right) a{\left(n + 15 \right)}}{n + 15} - \frac{4 \left(159 n + 2035\right) a{\left(n + 14 \right)}}{n + 15} + \frac{8 \left(233 n + 63\right) a{\left(n + 1 \right)}}{n + 15} + \frac{8 \left(1489 n + 1521\right) a{\left(n + 2 \right)}}{n + 15} + \frac{8 \left(4075 n + 9322\right) a{\left(n + 3 \right)}}{n + 15} + \frac{\left(6143 n + 71927\right) a{\left(n + 13 \right)}}{n + 15} + \frac{19 \left(7939 n + 75699\right) a{\left(n + 11 \right)}}{n + 15} + \frac{8 \left(15728 n + 58643\right) a{\left(n + 5 \right)}}{n + 15} - \frac{2 \left(18814 n + 199839\right) a{\left(n + 12 \right)}}{n + 15} + \frac{4 \left(19545 n + 87091\right) a{\left(n + 4 \right)}}{n + 15} - \frac{16 \left(34305 n + 218258\right) a{\left(n + 8 \right)}}{n + 15} - \frac{4 \left(36603 n + 238886\right) a{\left(n + 6 \right)}}{n + 15} + \frac{14 \left(44874 n + 330479\right) a{\left(n + 9 \right)}}{n + 15} + \frac{2 \left(112409 n + 690213\right) a{\left(n + 7 \right)}}{n + 15} - \frac{\left(392307 n + 3313799\right) a{\left(n + 10 \right)}}{n + 15}, \quad n \geq 18\)
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 233 rules.

Finding the specification took 16805 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_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{11}\! \left(x \right)\\ F_{10}\! \left(x \right) &= x\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{19}\! \left(x \right) &= x^{2} F_{19} \left(x \right)^{2}+4 x^{2} F_{19}\! \left(x \right)+4 x F_{19} \left(x \right)^{2}+4 x^{2}-5 x F_{19}\! \left(x \right)-F_{19} \left(x \right)^{2}-x +2 F_{19}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{19}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{10}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{10}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{10}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{26}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{10}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{10}\! \left(x \right) F_{53}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{53}\! \left(x \right)}\\ F_{62}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{10}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{10}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{81}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{19}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{86}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{53}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{10}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{90}\! \left(x \right) &= -F_{97}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= \frac{F_{92}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{96}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{97}\! \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_{13}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{10}\! \left(x \right) F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{107}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{10}\! \left(x \right) F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{231}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{230}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{10}\! \left(x \right) F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= -F_{228}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= -F_{227}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{10}\! \left(x \right) F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{10}\! \left(x \right) F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{133}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{12}\! \left(x \right) F_{123}\! \left(x \right)\\ F_{133}\! \left(x \right) &= -F_{39}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= -F_{143}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= \frac{F_{136}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{140}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{13}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{10}\! \left(x \right) F_{145}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{145}\! \left(x \right) &= \frac{F_{146}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{146}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{10}\! \left(x \right) F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{170}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{161}\! \left(x \right) &= -F_{162}\! \left(x \right)+F_{125}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{10}\! \left(x \right) F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{10}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{166}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{10}\! \left(x \right) F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{12}\! \left(x \right) F_{159}\! \left(x \right)\\ F_{174}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= -F_{177}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{10}\! \left(x \right) F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{106}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{185}\! \left(x \right) &= -F_{226}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{10}\! \left(x \right) F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{123}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= -F_{199}\! \left(x \right)+F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= \frac{F_{198}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{198}\! \left(x \right) &= F_{190}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{10}\! \left(x \right) F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{203}\! \left(x \right) &= -F_{223}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= \frac{F_{205}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{10}\! \left(x \right) F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{222}\! \left(x \right)\\ F_{208}\! \left(x \right) &= \frac{F_{209}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{212}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{19}\! \left(x \right) F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{217}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{213}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{10}\! \left(x \right) F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)+F_{221}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{15}\! \left(x \right) F_{216}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{29}\! \left(x \right) F_{61}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= \frac{F_{224}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{224}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{8}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{10}\! \left(x \right) F_{117}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{2}\! \left(x \right) F_{213}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{213}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{10}\! \left(x \right) F_{56}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 254 rules.

Finding the specification took 49322 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_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{11}\! \left(x \right)\\ F_{10}\! \left(x \right) &= x\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{19}\! \left(x \right) &= x^{2} F_{19} \left(x \right)^{2}+4 x^{2} F_{19}\! \left(x \right)+4 x F_{19} \left(x \right)^{2}+4 x^{2}-5 x F_{19}\! \left(x \right)-F_{19} \left(x \right)^{2}-x +2 F_{19}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{19}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{10}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{10}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{10}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{10}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{10}\! \left(x \right) F_{49}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{49}\! \left(x \right)}\\ F_{56}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{10}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{10}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{75}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{19}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{80}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{49}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{10}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{84}\! \left(x \right) &= -F_{91}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{90}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{0}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{94}\! \left(x \right) &= 8 x^{5} F_{94} \left(x \right)^{2}-8 \sqrt{1-4 x}\, x^{4} F_{94}\! \left(x \right)+16 x^{5} F_{94}\! \left(x \right)+32 x^{4} F_{94} \left(x \right)^{2}-8 \sqrt{1-4 x}\, x^{4}-32 \sqrt{1-4 x}\, x^{3} F_{94}\! \left(x \right)+8 x^{5}-96 x^{4} F_{94}\! \left(x \right)-8 x^{3} F_{94} \left(x \right)^{2}+48 \sqrt{1-4 x}\, x^{3}+8 \sqrt{1-4 x}\, x^{2} F_{94}\! \left(x \right)+64 x^{4}+56 x^{3} F_{94}\! \left(x \right)-28 \sqrt{1-4 x}\, x^{2}-96 x^{3}-8 x^{2} F_{94}\! \left(x \right)+4 \sqrt{1-4 x}\, x +36 x^{2}-4 x +F_{94}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{10}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{13}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{110}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{10}\! \left(x \right) F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{10}\! \left(x \right) F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{252}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{251}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{10}\! \left(x \right) F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= -F_{249}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= -F_{248}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= \frac{F_{122}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= -F_{193}\! \left(x \right)+F_{125}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{10}\! \left(x \right) F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{76}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{10}\! \left(x \right) F_{133}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{12}\! \left(x \right) F_{125}\! \left(x \right)\\ F_{135}\! \left(x \right) &= -F_{39}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{140}\! \left(x \right) &= -F_{143}\! \left(x \right)+F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= \frac{F_{142}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{142}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{13}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{10}\! \left(x \right) F_{147}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{147}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{10}\! \left(x \right) F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{12}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= \frac{F_{157}\! \left(x \right)}{F_{10}\! \left(x \right) F_{12}\! \left(x \right)}\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= -F_{166}\! \left(x \right)+F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= \frac{F_{160}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)\\ F_{161}\! \left(x \right) &= -F_{164}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= \frac{F_{163}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{163}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{12} \left(x \right)^{2} F_{2}\! \left(x \right)\\ F_{166}\! \left(x \right) &= \frac{F_{167}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= -F_{171}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= \frac{F_{170}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{170}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{10}\! \left(x \right) F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{101}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{12}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{10}\! \left(x \right) F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{184}\! \left(x \right) &= \frac{F_{185}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= -F_{150}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{10}\! \left(x \right) F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{147}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{10}\! \left(x \right) F_{147}\! \left(x \right) F_{156}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{195}\! \left(x \right) &= -F_{196}\! \left(x \right)+F_{127}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{10}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{203}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{10}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{10}\! \left(x \right) F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{208}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{12}\! \left(x \right) F_{193}\! \left(x \right)\\ F_{208}\! \left(x \right) &= -F_{211}\! \left(x \right)+F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= -F_{150}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{10}\! \left(x \right) F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{246}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{222}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{218}\! \left(x \right) &= -F_{221}\! \left(x \right)+F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= \frac{F_{220}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{220}\! \left(x \right) &= F_{210}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= -F_{229}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{225}\! \left(x \right) &= \frac{F_{226}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{10}\! \left(x \right) F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{243}\! \left(x \right)\\ F_{229}\! \left(x \right) &= \frac{F_{230}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{233}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{19}\! \left(x \right) F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{236}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{234}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{10}\! \left(x \right) F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{29}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{15}\! \left(x \right) F_{237}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)\\ F_{244}\! \left(x \right) &= \frac{F_{245}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{245}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{79}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{10}\! \left(x \right) F_{119}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{2}\! \left(x \right) F_{234}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{234}\! \left(x \right) F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{87}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 233 rules.

Finding the specification took 16805 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_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{11}\! \left(x \right)\\ F_{10}\! \left(x \right) &= x\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{19}\! \left(x \right) &= x^{2} F_{19} \left(x \right)^{2}+4 x^{2} F_{19}\! \left(x \right)+4 x F_{19} \left(x \right)^{2}+4 x^{2}-5 x F_{19}\! \left(x \right)-F_{19} \left(x \right)^{2}-x +2 F_{19}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{19}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{10}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{10}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{10}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{26}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{10}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{10}\! \left(x \right) F_{53}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{53}\! \left(x \right)}\\ F_{62}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{10}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{10}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{81}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{10}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{19}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{86}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{53}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{10}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{90}\! \left(x \right) &= -F_{97}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= \frac{F_{92}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{96}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{97}\! \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_{13}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{10}\! \left(x \right) F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{107}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{10}\! \left(x \right) F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{231}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{230}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{10}\! \left(x \right) F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{117}\! \left(x \right) &= -F_{228}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= -F_{227}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{10}\! \left(x \right) F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{10}\! \left(x \right) F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{133}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{12}\! \left(x \right) F_{123}\! \left(x \right)\\ F_{133}\! \left(x \right) &= -F_{39}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{134}\! \left(x \right) &= -F_{143}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= \frac{F_{136}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{140}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{13}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{10}\! \left(x \right) F_{145}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{145}\! \left(x \right) &= \frac{F_{146}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{146}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{10}\! \left(x \right) F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{170}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{161}\! \left(x \right) &= -F_{162}\! \left(x \right)+F_{125}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{10}\! \left(x \right) F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{10}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{166}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{10}\! \left(x \right) F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{12}\! \left(x \right) F_{159}\! \left(x \right)\\ F_{174}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= -F_{177}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{10}\! \left(x \right) F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{106}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{185}\! \left(x \right) &= -F_{226}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{10}\! \left(x \right) F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{123}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= -F_{199}\! \left(x \right)+F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= \frac{F_{198}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{198}\! \left(x \right) &= F_{190}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{10}\! \left(x \right) F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{203}\! \left(x \right) &= -F_{223}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= \frac{F_{205}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{10}\! \left(x \right) F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{222}\! \left(x \right)\\ F_{208}\! \left(x \right) &= \frac{F_{209}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{212}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{19}\! \left(x \right) F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{217}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{213}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{10}\! \left(x \right) F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)+F_{221}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{15}\! \left(x \right) F_{216}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{29}\! \left(x \right) F_{61}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= \frac{F_{224}\! \left(x \right)}{F_{10}\! \left(x \right)}\\ F_{224}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{8}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{10}\! \left(x \right) F_{117}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{2}\! \left(x \right) F_{213}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{213}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{10}\! \left(x \right) F_{56}\! \left(x \right)\\ \end{align*}\)