Av(13425, 13452, 13542, 15342, 31425, 31452, 31542, 34125, 34152)
View Raw Data
Generating Function
\(\displaystyle -\frac{\left(15 \sqrt{5 x^{2}-6 x +1}\, x^{6}-135 x^{7}-97 \sqrt{5 x^{2}-6 x +1}\, x^{5}+802 x^{6}+189 \sqrt{5 x^{2}-6 x +1}\, x^{4}-1910 x^{5}-156 \sqrt{5 x^{2}-6 x +1}\, x^{3}+2331 x^{4}+69 \sqrt{5 x^{2}-6 x +1}\, x^{2}-1611 x^{3}-18 \sqrt{5 x^{2}-6 x +1}\, x +633 x^{2}+2 \sqrt{5 x^{2}-6 x +1}-128 x +10\right) \left(x -1\right)^{3} \left(3 x -1\right)}{2 \left(855 x^{11}-6441 x^{10}+22135 x^{9}-45077 x^{8}+60204 x^{7}-55327 x^{6}+35696 x^{5}-16156 x^{4}+5013 x^{3}-1010 x^{2}+118 x -6\right)}\)
Copy to clipboard: Search on PermPAL
Counting Sequence
1, 1, 2, 6, 24, 111, 546, 2747, 13904, 70362, 355368, 1791152, 9013874, 45316931, 227712737, ...
Search on OEIS Search on PermPAL
Implicit Equation for the Generating Function
\(\displaystyle \left(855 x^{11}-6441 x^{10}+22135 x^{9}-45077 x^{8}+60204 x^{7}-55327 x^{6}+35696 x^{5}-16156 x^{4}+5013 x^{3}-1010 x^{2}+118 x -6\right) F \left(x \right)^{2}-\left(3 x -1\right) \left(5 x -1\right) \left(27 x^{6}-155 x^{5}+351 x^{4}-396 x^{3}+243 x^{2}-78 x +10\right) \left(x -1\right)^{3} F \! \left(x \right)+\left(5 x -1\right) \left(3 x -1\right)^{2} \left(-2+x \right)^{2} \left(x -1\right)^{6} = 0\)
Copy to clipboard: Search on PermPAL
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 546\)
\(\displaystyle a(7) = 2747\)
\(\displaystyle a(8) = 13904\)
\(\displaystyle a(9) = 70362\)
\(\displaystyle a(10) = 355368\)
\(\displaystyle a(11) = 1791152\)
\(\displaystyle a(12) = 9013874\)
\(\displaystyle a(13) = 45316931\)
\(\displaystyle a(14) = 227712737\)
\(\displaystyle a(15) = 1144053831\)
\(\displaystyle a(16) = 5748353170\)
\(\displaystyle a(17) = 28889850941\)
\(\displaystyle a(18) = 145241633208\)
\(\displaystyle a(19) = 730467374568\)
\(\displaystyle a{\left(n + 20 \right)} = - \frac{64125 n a{\left(n \right)}}{4 \left(n + 20\right)} + \frac{\left(113 n + 2152\right) a{\left(n + 19 \right)}}{3 \left(n + 20\right)} + \frac{4275 \left(233 n + 276\right) a{\left(n + 1 \right)}}{4 \left(n + 20\right)} - \frac{\left(3965 n + 71668\right) a{\left(n + 18 \right)}}{6 \left(n + 20\right)} - \frac{285 \left(12293 n + 27877\right) a{\left(n + 2 \right)}}{2 \left(n + 20\right)} - \frac{4 \left(41083 n + 661286\right) a{\left(n + 16 \right)}}{3 \left(n + 20\right)} + \frac{\left(43199 n + 738370\right) a{\left(n + 17 \right)}}{6 \left(n + 20\right)} + \frac{\left(3720445 n + 56140364\right) a{\left(n + 15 \right)}}{12 \left(n + 20\right)} - \frac{\left(16279423 n + 229157782\right) a{\left(n + 14 \right)}}{12 \left(n + 20\right)} + \frac{\left(28215782 n + 368562489\right) a{\left(n + 13 \right)}}{6 \left(n + 20\right)} + \frac{\left(29987197 n + 98688052\right) a{\left(n + 3 \right)}}{4 \left(n + 20\right)} - \frac{5 \left(52817833 n + 226038064\right) a{\left(n + 4 \right)}}{12 \left(n + 20\right)} - \frac{\left(78684917 n + 948353184\right) a{\left(n + 12 \right)}}{6 \left(n + 20\right)} - \frac{2 \left(82148273 n + 826668471\right) a{\left(n + 10 \right)}}{3 \left(n + 20\right)} + \frac{\left(89056732 n + 984246993\right) a{\left(n + 11 \right)}}{3 \left(n + 20\right)} + \frac{\left(283620644 n + 1488550661\right) a{\left(n + 5 \right)}}{6 \left(n + 20\right)} + \frac{\left(592797695 n + 4246011563\right) a{\left(n + 7 \right)}}{6 \left(n + 20\right)} - \frac{\left(602946476 n + 4896524009\right) a{\left(n + 8 \right)}}{6 \left(n + 20\right)} - \frac{\left(927593719 n + 5757618994\right) a{\left(n + 6 \right)}}{12 \left(n + 20\right)} + \frac{\left(988037671 n + 8977996682\right) a{\left(n + 9 \right)}}{12 \left(n + 20\right)}, \quad n \geq 20\)
Copy to clipboard:

This specification was found using the strategy pack "Point Placements Req Corrob" and has 590 rules.

Finding the specification took 32530 seconds.

This tree is too big to show here. Click to view tree on new page.

Copy 590 equations to clipboard:
\(\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_{12}\! \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_{7}\! \left(x \right)\\ F_{6}\! \left(x \right) &= x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{12}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{586}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{12}\! \left(x \right) &= x\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{509}\! \left(x \right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{12}\! \left(x \right) F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= -F_{132}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{508}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{12}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{507}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{505}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{12}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{496}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38} \left(x \right)^{2} F_{12}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{12}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{12}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{12}\! \left(x \right) F_{38}\! \left(x \right) F_{41}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{48}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{503}\! \left(x \right)\\ F_{50}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= -F_{279}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{12}\! \left(x \right) F_{42} \left(x \right)^{2}}\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{42}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{12}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{57}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{42}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{12}\! \left(x \right) F_{71}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{72}\! \left(x \right) &= x^{2} F_{72} \left(x \right)^{2}-2 x F_{72} \left(x \right)^{2}+F_{72}\! \left(x \right) x +2 F_{72}\! \left(x \right)-1\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{12}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{12}\! \left(x \right) F_{79}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{12}\! \left(x \right) F_{42}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{51}\! \left(x \right) F_{79}\! \left(x \right)}\\ F_{84}\! \left(x \right) &= -F_{97}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= -F_{95}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= -F_{91}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{90}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{39}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{12}\! \left(x \right) F_{71}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{95}\! \left(x \right) &= -F_{96}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{38}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{97}\! \left(x \right) &= -F_{502}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{498}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= -F_{497}\! \left(x \right)+F_{100}\! \left(x \right)\\ F_{100}\! \left(x \right) &= \frac{F_{101}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= -F_{280}\! \left(x \right)+F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= -F_{92}\! \left(x \right)+F_{104}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{452}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{112}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{114}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{115}\! \left(x \right) &= -F_{118}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{117}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{111}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{119}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= -F_{123}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{123}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{12}\! \left(x \right) F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{12}\! \left(x \right) F_{130}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{130}\! \left(x \right) &= \frac{F_{131}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= -F_{450}\! \left(x \right)+F_{133}\! \left(x \right)\\ F_{133}\! \left(x \right) &= \frac{F_{134}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{12}\! \left(x \right) F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{12}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{12}\! \left(x \right) F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{258}\! \left(x \right)\\ F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{248}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{246}\! \left(x \right)\\ F_{148}\! \left(x \right) &= \frac{F_{149}\! \left(x \right)}{F_{12}\! \left(x \right) F_{72}\! \left(x \right)}\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{153}\! \left(x \right)\\ F_{152}\! \left(x \right) &= 4 x F_{152} \left(x \right)^{2}+x^{2}-F_{152} \left(x \right)^{2}+F_{152}\! \left(x \right)\\ F_{153}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= -F_{237}\! \left(x \right)+F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= -F_{157}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{12}\! \left(x \right) F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{171}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{12}\! \left(x \right) F_{163}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{163}\! \left(x \right) &= \frac{F_{164}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= -F_{170}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= -F_{169}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= \frac{F_{168}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{168}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{2}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{77}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{12}\! \left(x \right) F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{175}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= \frac{F_{177}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= -F_{181}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= \frac{F_{180}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{180}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{12}\! \left(x \right) F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= \frac{F_{184}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{184}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right) F_{208}\! \left(x \right) F_{212}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{12}\! \left(x \right) F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{12}\! \left(x \right) F_{193}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{197}\! \left(x \right)+F_{198}\! \left(x \right)\\ F_{196}\! \left(x \right) &= 0\\ F_{197}\! \left(x \right) &= F_{12}\! \left(x \right) F_{194}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{12}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{12}\! \left(x \right) F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{203}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{193}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{193}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{12}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{12}\! \left(x \right) F_{189}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{208}\! \left(x \right) &= \frac{F_{209}\! \left(x \right)}{F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{72}\! \left(x \right)}\\ F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{212}\! \left(x \right) &= \frac{F_{213}\! \left(x \right)}{F_{235}\! \left(x \right)}\\ F_{213}\! \left(x \right) &= -F_{221}\! \left(x \right)+F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= \frac{F_{215}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{12}\! \left(x \right) F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{12}\! \left(x \right) F_{208}\! \left(x \right) F_{71}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{72}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{223}\! \left(x \right) &= \frac{F_{224}\! \left(x \right)}{F_{42}\! \left(x \right)}\\ F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\ F_{225}\! \left(x \right) &= -F_{233}\! \left(x \right)+F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{230}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x \right) F_{72}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{228}\! \left(x \right) &= \frac{F_{229}\! \left(x \right)}{F_{12}\! \left(x \right) F_{42}\! \left(x \right) F_{72}\! \left(x \right)}\\ F_{229}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\ F_{231}\! \left(x \right) &= -F_{232}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{147}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{12}\! \left(x \right) F_{175}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{235}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{194}\! \left(x \right) F_{208}\! \left(x \right) F_{212}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{238}\! \left(x \right) &= 4 F_{238} \left(x \right)^{2} x +x^{2}-8 F_{238}\! \left(x \right) x -F_{238} \left(x \right)^{2}+4 x +3 F_{238}\! \left(x \right)-1\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{12}\! \left(x \right) F_{241}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{243}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{111}\! \left(x \right) F_{154}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{111}\! \left(x \right) F_{12}\! \left(x \right) F_{151}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{12}\! \left(x \right) F_{148}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{248}\! \left(x \right) &= -F_{257}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{251}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{254}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{253}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{253}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{254}\! \left(x \right) &= -F_{255}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{255}\! \left(x \right) &= -F_{256}\! \left(x \right)+F_{216}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{38}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{6}\! \left(x \right) F_{79}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{208}\! \left(x \right) F_{260}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{260}\! \left(x \right) &= \frac{F_{261}\! \left(x \right)}{F_{341}\! \left(x \right) F_{38} \left(x \right)^{3}}\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= -F_{448}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{263}\! \left(x \right) &= \frac{F_{264}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{446}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{267}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{293}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{238}\! \left(x \right) F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= \frac{F_{270}\! \left(x \right)}{F_{72}\! \left(x \right)}\\ F_{270}\! \left(x \right) &= -F_{271}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{271}\! \left(x \right) &= -F_{292}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{272}\! \left(x \right) &= \frac{F_{273}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{12}\! \left(x \right) F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{277}\! \left(x \right) &= -F_{284}\! \left(x \right)+F_{278}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{12}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{12}\! \left(x \right) F_{286}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{288}\! \left(x \right)\\ F_{287}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{288}\! \left(x \right) &= F_{289}\! \left(x \right)\\ F_{289}\! \left(x \right) &= F_{12}\! \left(x \right) F_{290}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{290}\! \left(x \right) &= \frac{F_{291}\! \left(x \right)}{F_{12}\! \left(x \right) F_{38}\! \left(x \right) F_{51}\! \left(x \right)}\\ F_{291}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{269}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{293}\! \left(x \right) &= -F_{444}\! \left(x \right)+F_{294}\! \left(x \right)\\ F_{294}\! \left(x \right) &= \frac{F_{295}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)\\ F_{296}\! \left(x \right) &= -F_{443}\! \left(x \right)+F_{297}\! \left(x \right)\\ F_{297}\! \left(x \right) &= -F_{410}\! \left(x \right)+F_{298}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)+F_{301}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{238}\! \left(x \right) F_{300}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{274}\! \left(x \right)\\ F_{301}\! \left(x \right) &= -F_{307}\! \left(x \right)+F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= -F_{305}\! \left(x \right)+F_{303}\! \left(x \right)\\ F_{303}\! \left(x \right) &= \frac{F_{304}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{304}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{152}\! \left(x \right) F_{306}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{300}\! \left(x \right)\\ F_{307}\! \left(x \right) &= -F_{409}\! \left(x \right)+F_{308}\! \left(x \right)\\ F_{308}\! \left(x \right) &= -F_{319}\! \left(x \right)+F_{309}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)+F_{315}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{306}\! \left(x \right)+F_{311}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{312}\! \left(x \right) &= F_{313}\! \left(x \right)\\ F_{313}\! \left(x \right) &= F_{12}\! \left(x \right) F_{314}\! \left(x \right)\\ F_{314}\! \left(x \right) &= F_{145}\! \left(x \right)\\ F_{315}\! \left(x \right) &= -F_{318}\! \left(x \right)+F_{316}\! \left(x \right)\\ F_{316}\! \left(x \right) &= \frac{F_{317}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{317}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{318}\! \left(x \right) &= F_{300}\! \left(x \right)+F_{312}\! \left(x \right)\\ F_{319}\! \left(x \right) &= F_{311}\! \left(x \right)+F_{320}\! \left(x \right)\\ F_{320}\! \left(x \right) &= F_{321}\! \left(x \right)\\ F_{321}\! \left(x \right) &= F_{12}\! \left(x \right) F_{322}\! \left(x \right)\\ F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{402}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)+F_{371}\! \left(x \right)\\ F_{324}\! \left(x \right) &= F_{325}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{325}\! \left(x \right) &= \frac{F_{326}\! \left(x \right)}{F_{2}\! \left(x \right)}\\ F_{326}\! \left(x \right) &= -F_{329}\! \left(x \right)+F_{327}\! \left(x \right)\\ F_{327}\! \left(x \right) &= \frac{F_{328}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{328}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{367}\! \left(x \right)\\ F_{330}\! \left(x \right) &= -F_{331}\! \left(x \right)+F_{327}\! \left(x \right)\\ F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)\\ F_{332}\! \left(x \right) &= F_{12}\! \left(x \right) F_{333}\! \left(x \right)\\ F_{333}\! \left(x \right) &= F_{334}\! \left(x \right)+F_{338}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{335}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{335}\! \left(x \right) &= -F_{331}\! \left(x \right)+F_{336}\! \left(x \right)\\ F_{336}\! \left(x \right) &= \frac{F_{337}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{337}\! \left(x \right) &= F_{300}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)\\ F_{339}\! \left(x \right) &= F_{12}\! \left(x \right) F_{340}\! \left(x \right) F_{365}\! \left(x \right)\\ F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)+F_{347}\! \left(x \right)\\ F_{341}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{342}\! \left(x \right)\\ F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)\\ F_{343}\! \left(x \right) &= F_{12}\! \left(x \right) F_{344}\! \left(x \right)\\ F_{344}\! \left(x \right) &= F_{345}\! \left(x \right)+F_{346}\! \left(x \right)\\ F_{345}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{347}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{348}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{349}\! \left(x \right)+F_{351}\! \left(x \right)\\ F_{349}\! \left(x \right) &= F_{12}\! \left(x \right) F_{350}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{342}\! \left(x \right)+F_{348}\! \left(x \right)\\ F_{351}\! \left(x \right) &= F_{12}\! \left(x \right) F_{352}\! \left(x \right)\\ F_{352}\! \left(x \right) &= F_{346}\! \left(x \right)+F_{353}\! \left(x \right)\\ F_{353}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{354}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{355}\! \left(x \right)+F_{357}\! \left(x \right)\\ F_{355}\! \left(x \right) &= F_{12}\! \left(x \right) F_{356}\! \left(x \right)\\ F_{356}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{357}\! \left(x \right) &= F_{12}\! \left(x \right) F_{358}\! \left(x \right)\\ F_{358}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{360}\! \left(x \right)+F_{362}\! \left(x \right)+F_{364}\! \left(x \right)\\ F_{360}\! \left(x \right) &= F_{12}\! \left(x \right) F_{361}\! \left(x \right)\\ F_{361}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{362}\! \left(x \right) &= F_{12}\! \left(x \right) F_{363}\! \left(x \right)\\ F_{363}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{364}\! \left(x \right) &= F_{12}\! \left(x \right) F_{354}\! \left(x \right)\\ F_{365}\! \left(x \right) &= \frac{F_{366}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{366}\! \left(x \right) &= F_{281}\! \left(x \right)\\ F_{367}\! \left(x \right) &= F_{368}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{12}\! \left(x \right) F_{369}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{338}\! \left(x \right)+F_{370}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{330}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{372}\! \left(x \right)\\ F_{372}\! \left(x \right) &= F_{373}\! \left(x \right) F_{374}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{342}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{374}\! \left(x \right) &= -F_{19}\! \left(x \right)+F_{375}\! \left(x \right)\\ F_{375}\! \left(x \right) &= F_{376}\! \left(x \right)\\ F_{376}\! \left(x \right) &= F_{12}\! \left(x \right) F_{377}\! \left(x \right)\\ F_{377}\! \left(x \right) &= -F_{383}\! \left(x \right)+F_{378}\! \left(x \right)\\ F_{378}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{379}\! \left(x \right)\\ F_{379}\! \left(x \right) &= -F_{382}\! \left(x \right)+F_{380}\! \left(x \right)\\ F_{380}\! \left(x \right) &= \frac{F_{381}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{381}\! \left(x \right) &= F_{251}\! \left(x \right)\\ F_{382}\! \left(x \right) &= F_{249}\! \left(x \right)\\ F_{383}\! \left(x \right) &= -F_{401}\! \left(x \right)+F_{384}\! \left(x \right)\\ F_{384}\! \left(x \right) &= F_{385}\! \left(x \right)\\ F_{385}\! \left(x \right) &= F_{12}\! \left(x \right) F_{386}\! \left(x \right)\\ F_{386}\! \left(x \right) &= \frac{F_{387}\! \left(x \right)}{F_{12}\! \left(x \right) F_{42}\! \left(x \right)}\\ F_{387}\! \left(x \right) &= F_{388}\! \left(x \right)\\ F_{388}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{389}\! \left(x \right)\\ F_{389}\! \left(x \right) &= -F_{392}\! \left(x \right)+F_{390}\! \left(x \right)\\ F_{390}\! \left(x \right) &= \frac{F_{391}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{391}\! \left(x \right) &= F_{254}\! \left(x \right)\\ F_{392}\! \left(x \right) &= F_{393}\! \left(x \right)+F_{400}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{394}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{394}\! \left(x \right) &= -F_{397}\! \left(x \right)+F_{395}\! \left(x \right)\\ F_{395}\! \left(x \right) &= \frac{F_{396}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{396}\! \left(x \right) &= F_{255}\! \left(x \right)\\ F_{397}\! \left(x \right) &= F_{398}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{398}\! \left(x \right) &= \frac{F_{399}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{399}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{400}\! \left(x \right) &= F_{253}\! \left(x \right) F_{398}\! \left(x \right)\\ F_{401}\! \left(x \right) &= F_{248}\! \left(x \right)\\ F_{402}\! \left(x \right) &= F_{341}\! \left(x \right) F_{403}\! \left(x \right)\\ F_{403}\! \left(x \right) &= -F_{406}\! \left(x \right)+F_{404}\! \left(x \right)\\ F_{404}\! \left(x \right) &= \frac{F_{405}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{405}\! \left(x \right) &= F_{315}\! \left(x \right)\\ F_{406}\! \left(x \right) &= \frac{F_{407}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\ F_{408}\! \left(x \right) &= -F_{25}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{409}\! \left(x \right) &= F_{0}\! \left(x \right) F_{238}\! \left(x \right)\\ F_{410}\! \left(x \right) &= F_{411}\! \left(x \right)+F_{412}\! \left(x \right)\\ F_{411}\! \left(x \right) &= F_{238}\! \left(x \right) F_{274}\! \left(x \right)\\ F_{412}\! \left(x \right) &= F_{413}\! \left(x \right)\\ F_{413}\! \left(x \right) &= F_{12}\! \left(x \right) F_{414}\! \left(x \right)\\ F_{414}\! \left(x \right) &= F_{415}\! \left(x \right)+F_{431}\! \left(x \right)\\ F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{420}\! \left(x \right)\\ F_{416}\! \left(x \right) &= F_{417}\! \left(x \right) F_{419}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{418}\! \left(x \right)\\ F_{418}\! \left(x \right) &= F_{342}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{419}\! \left(x \right) &= -F_{41}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{420}\! \left(x \right) &= -F_{430}\! \left(x \right)+F_{421}\! \left(x \right)\\ F_{421}\! \left(x \right) &= -F_{424}\! \left(x \right)+F_{422}\! \left(x \right)\\ F_{422}\! \left(x \right) &= \frac{F_{423}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{423}\! \left(x \right) &= F_{301}\! \left(x \right)\\ F_{424}\! \left(x \right) &= F_{341}\! \left(x \right) F_{425}\! \left(x \right)\\ F_{425}\! \left(x \right) &= -F_{428}\! \left(x \right)+F_{426}\! \left(x \right)\\ F_{426}\! \left(x \right) &= \frac{F_{427}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{427}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{428}\! \left(x \right) &= F_{429}\! \left(x \right)\\ F_{429}\! \left(x \right) &= F_{12}\! \left(x \right) F_{148}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{430}\! \left(x \right) &= F_{417}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{431}\! \left(x \right) &= F_{341}\! \left(x \right) F_{432}\! \left(x \right)\\ F_{432}\! \left(x \right) &= -F_{439}\! \left(x \right)+F_{433}\! \left(x \right)\\ F_{433}\! \left(x \right) &= \frac{F_{434}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{434}\! \left(x \right) &= F_{435}\! \left(x \right)\\ F_{435}\! \left(x \right) &= -F_{436}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{436}\! \left(x \right) &= -F_{152}\! \left(x \right)+F_{437}\! \left(x \right)\\ F_{437}\! \left(x \right) &= F_{438}\! \left(x \right)\\ F_{438}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{439}\! \left(x \right) &= F_{440}\! \left(x \right)+F_{441}\! \left(x \right)\\ F_{440}\! \left(x \right) &= F_{153}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{441}\! \left(x \right) &= -F_{442}\! \left(x \right)+F_{428}\! \left(x \right)\\ F_{442}\! \left(x \right) &= F_{151}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{443}\! \left(x \right) &= F_{152}\! \left(x \right) F_{238}\! \left(x \right)\\ F_{444}\! \left(x \right) &= F_{445}\! \left(x \right)\\ F_{445}\! \left(x \right) &= F_{38} \left(x \right)^{3} F_{12}\! \left(x \right) F_{341}\! \left(x \right)\\ F_{446}\! \left(x \right) &= F_{447}\! \left(x \right)\\ F_{447}\! \left(x \right) &= F_{38} \left(x \right)^{3} F_{187}\! \left(x \right) F_{341}\! \left(x \right)\\ F_{448}\! \left(x \right) &= F_{449}\! \left(x \right) F_{51}\! \left(x \right)\\ F_{449}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{444}\! \left(x \right)\\ F_{450}\! \left(x \right) &= F_{451}\! \left(x \right)\\ F_{451}\! \left(x \right) &= F_{12}\! \left(x \right) F_{148}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{452}\! \left(x \right) &= F_{453}\! \left(x \right)\\ F_{453}\! \left(x \right) &= F_{12}\! \left(x \right) F_{454}\! \left(x \right)\\ F_{454}\! \left(x \right) &= F_{455}\! \left(x \right)+F_{468}\! \left(x \right)\\ F_{455}\! \left(x \right) &= F_{456}\! \left(x \right)+F_{467}\! \left(x \right)\\ F_{456}\! \left(x \right) &= -F_{459}\! \left(x \right)+F_{457}\! \left(x \right)\\ F_{457}\! \left(x \right) &= \frac{F_{458}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{458}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{459}\! \left(x \right) &= -F_{462}\! \left(x \right)+F_{460}\! \left(x \right)\\ F_{460}\! \left(x \right) &= \frac{F_{461}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{461}\! \left(x \right) &= F_{48}\! \left(x \right)\\ F_{462}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{463}\! \left(x \right)\\ F_{463}\! \left(x \right) &= -F_{466}\! \left(x \right)+F_{464}\! \left(x \right)\\ F_{464}\! \left(x \right) &= F_{465}\! \left(x \right)\\ F_{465}\! \left(x \right) &= F_{12}\! \left(x \right) F_{290}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{466}\! \left(x \right) &= F_{235}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{467}\! \left(x \right) &= F_{290}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{468}\! \left(x \right) &= F_{469}\! \left(x \right)+F_{471}\! \left(x \right)\\ F_{469}\! \left(x \right) &= -F_{456}\! \left(x \right)+F_{470}\! \left(x \right)\\ F_{470}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{471}\! \left(x \right) &= F_{472}\! \left(x \right)\\ F_{472}\! \left(x \right) &= -F_{490}\! \left(x \right)+F_{473}\! \left(x \right)\\ F_{473}\! \left(x \right) &= F_{474}\! \left(x \right)+F_{475}\! \left(x \right)\\ F_{474}\! \left(x \right) &= F_{2}\! \left(x \right) F_{6}\! \left(x \right) F_{79}\! \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_{12}\! \left(x \right)}\\ F_{477}\! \left(x \right) &= F_{478}\! \left(x \right)\\ F_{478}\! \left(x \right) &= F_{12}\! \left(x \right) F_{479}\! \left(x \right)\\ F_{479}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{480}\! \left(x \right)\\ F_{480}\! \left(x \right) &= F_{246}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{481}\! \left(x \right) &= F_{0}\! \left(x \right) F_{482}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{482}\! \left(x \right) &= \frac{F_{483}\! \left(x \right)}{F_{0}\! \left(x \right) F_{72}\! \left(x \right)}\\ F_{483}\! \left(x \right) &= -F_{486}\! \left(x \right)+F_{484}\! \left(x \right)\\ F_{484}\! \left(x \right) &= \frac{F_{485}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{485}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{486}\! \left(x \right) &= -F_{487}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{487}\! \left(x \right) &= F_{235}\! \left(x \right) F_{488}\! \left(x \right)\\ F_{488}\! \left(x \right) &= -F_{489}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{489}\! \left(x \right) &= F_{0}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{490}\! \left(x \right) &= F_{491}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{491}\! \left(x \right) &= \frac{F_{492}\! \left(x \right)}{F_{38}\! \left(x \right) F_{51}\! \left(x \right)}\\ F_{492}\! \left(x \right) &= F_{493}\! \left(x \right)\\ F_{493}\! \left(x \right) &= -F_{494}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{494}\! \left(x \right) &= \frac{F_{495}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{495}\! \left(x \right) &= F_{496}\! \left(x \right)\\ F_{496}\! \left(x \right) &= -F_{95}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{497}\! \left(x \right) &= F_{2}\! \left(x \right) F_{51}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{498}\! \left(x \right) &= \frac{F_{499}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{499}\! \left(x \right) &= F_{500}\! \left(x \right)\\ F_{500}\! \left(x \right) &= -F_{16}\! \left(x \right)+F_{501}\! \left(x \right)\\ F_{501}\! \left(x \right) &= -F_{103}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{502}\! \left(x \right) &= F_{51}\! \left(x \right) F_{77}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{503}\! \left(x \right) &= -F_{504}\! \left(x \right)+F_{284}\! \left(x \right)\\ F_{504}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{505}\! \left(x \right) &= F_{506}\! \left(x \right)\\ F_{506}\! \left(x \right) &= F_{12}\! \left(x \right) F_{228}\! \left(x \right) F_{42}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{507}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{508}\! \left(x \right) &= F_{312}\! \left(x \right)\\ F_{509}\! \left(x \right) &= F_{510}\! \left(x \right)\\ F_{510}\! \left(x \right) &= F_{511}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{511}\! \left(x \right) &= F_{512}\! \left(x \right)\\ F_{512}\! \left(x \right) &= F_{12}\! \left(x \right) F_{513}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{513}\! \left(x \right) &= \frac{F_{514}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{514}\! \left(x \right) &= F_{515}\! \left(x \right)\\ F_{515}\! \left(x \right) &= \frac{F_{516}\! \left(x \right)}{F_{42}\! \left(x \right) F_{565}\! \left(x \right)}\\ F_{516}\! \left(x \right) &= F_{517}\! \left(x \right)\\ F_{517}\! \left(x \right) &= -F_{585}\! \left(x \right)+F_{518}\! \left(x \right)\\ F_{518}\! \left(x \right) &= \frac{F_{519}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{519}\! \left(x \right) &= F_{520}\! \left(x \right)\\ F_{520}\! \left(x \right) &= F_{521}\! \left(x \right)\\ F_{521}\! \left(x \right) &= F_{12}\! \left(x \right) F_{522}\! \left(x \right)\\ F_{522}\! \left(x \right) &= F_{523}\! \left(x \right)+F_{583}\! \left(x \right)\\ F_{523}\! \left(x \right) &= F_{524}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{524}\! \left(x \right) &= F_{520}\! \left(x \right)+F_{525}\! \left(x \right)\\ F_{525}\! \left(x \right) &= \frac{F_{526}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{526}\! \left(x \right) &= F_{527}\! \left(x \right)\\ F_{527}\! \left(x \right) &= F_{528}\! \left(x \right)\\ F_{528}\! \left(x \right) &= F_{12}\! \left(x \right) F_{529}\! \left(x \right)\\ F_{529}\! \left(x \right) &= -F_{558}\! \left(x \right)+F_{530}\! \left(x \right)\\ F_{530}\! \left(x \right) &= -F_{538}\! \left(x \right)+F_{531}\! \left(x \right)\\ F_{531}\! \left(x \right) &= F_{532}\! \left(x \right)+F_{534}\! \left(x \right)\\ F_{532}\! \left(x \right) &= \frac{F_{533}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{533}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{534}\! \left(x \right) &= F_{535}\! \left(x \right)\\ F_{535}\! \left(x \right) &= F_{12}\! \left(x \right) F_{536}\! \left(x \right)\\ F_{536}\! \left(x \right) &= \frac{F_{537}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{537}\! \left(x \right) &= F_{486}\! \left(x \right)\\ F_{538}\! \left(x \right) &= -F_{542}\! \left(x \right)+F_{539}\! \left(x \right)\\ F_{539}\! \left(x \right) &= \frac{F_{540}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{540}\! \left(x \right) &= F_{541}\! \left(x \right)\\ F_{541}\! \left(x \right) &= -F_{279}\! \left(x \right)+F_{331}\! \left(x \right)\\ F_{542}\! \left(x \right) &= F_{543}\! \left(x \right)\\ F_{543}\! \left(x \right) &= F_{2}\! \left(x \right) F_{544}\! \left(x \right)\\ F_{544}\! \left(x \right) &= -F_{558}\! \left(x \right)+F_{545}\! \left(x \right)\\ F_{545}\! \left(x \right) &= \frac{F_{546}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{546}\! \left(x \right) &= F_{547}\! \left(x \right)\\ F_{547}\! \left(x \right) &= -F_{527}\! \left(x \right)+F_{548}\! \left(x \right)\\ F_{548}\! \left(x \right) &= -F_{555}\! \left(x \right)+F_{549}\! \left(x \right)\\ F_{549}\! \left(x \right) &= \frac{F_{550}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{550}\! \left(x \right) &= F_{551}\! \left(x \right)\\ F_{551}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{552}\! \left(x \right)\\ F_{552}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{553}\! \left(x \right)\\ F_{553}\! \left(x \right) &= \frac{F_{554}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{554}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{555}\! \left(x \right) &= -F_{335}\! \left(x \right)+F_{556}\! \left(x \right)\\ F_{556}\! \left(x \right) &= \frac{F_{557}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{557}\! \left(x \right) &= F_{552}\! \left(x \right)\\ F_{558}\! \left(x \right) &= F_{559}\! \left(x \right)\\ F_{559}\! \left(x \right) &= F_{12}\! \left(x \right) F_{560}\! \left(x \right)\\ F_{560}\! \left(x \right) &= F_{561}\! \left(x \right)+F_{569}\! \left(x \right)\\ F_{561}\! \left(x \right) &= F_{530}\! \left(x \right) F_{562}\! \left(x \right)\\ F_{562}\! \left(x \right) &= \frac{F_{563}\! \left(x \right)}{F_{12}\! \left(x \right) F_{55}\! \left(x \right)}\\ F_{563}\! \left(x \right) &= F_{564}\! \left(x \right)\\ F_{564}\! \left(x \right) &= -F_{565}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{565}\! \left(x \right) &= F_{566}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{566}\! \left(x \right) &= F_{567}\! \left(x \right)\\ F_{567}\! \left(x \right) &= F_{12}\! \left(x \right) F_{568}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{568}\! \left(x \right) &= F_{358}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{569}\! \left(x \right) &= F_{570}\! \left(x \right)\\ F_{570}\! \left(x \right) &= F_{571}\! \left(x \right) F_{72}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{571}\! \left(x \right) &= F_{572}\! \left(x \right)\\ F_{572}\! \left(x \right) &= \frac{F_{573}\! \left(x \right)}{F_{51}\! \left(x \right)}\\ F_{573}\! \left(x \right) &= -F_{576}\! \left(x \right)+F_{574}\! \left(x \right)\\ F_{574}\! \left(x \right) &= \frac{F_{575}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{575}\! \left(x \right) &= F_{547}\! \left(x \right)\\ F_{576}\! \left(x \right) &= F_{577}\! \left(x \right)\\ F_{577}\! \left(x \right) &= F_{12}\! \left(x \right) F_{578}\! \left(x \right)\\ F_{578}\! \left(x \right) &= F_{579}\! \left(x \right)+F_{581}\! \left(x \right)\\ F_{579}\! \left(x \right) &= F_{562}\! \left(x \right) F_{580}\! \left(x \right)\\ F_{580}\! \left(x \right) &= F_{530}\! \left(x \right)+F_{544}\! \left(x \right)\\ F_{581}\! \left(x \right) &= F_{582}\! \left(x \right)\\ F_{582}\! \left(x \right) &= F_{51}\! \left(x \right) F_{571}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{583}\! \left(x \right) &= F_{584}\! \left(x \right)\\ F_{584}\! \left(x \right) &= F_{193}\! \left(x \right) F_{565}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{585}\! \left(x \right) &= F_{208}\! \left(x \right) F_{525}\! \left(x \right)\\ F_{586}\! \left(x \right) &= F_{587}\! \left(x \right)\\ F_{587}\! \left(x \right) &= F_{12}\! \left(x \right) F_{588}\! \left(x \right)\\ F_{588}\! \left(x \right) &= \frac{F_{589}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{589}\! \left(x \right) &= F_{103}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Row And Col Placements Req Corrob" and has 287 rules.

Finding the specification took 5017 seconds.

This tree is too big to show here. Click to view tree on new page.

Copy 287 equations to clipboard:
\(\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_{26}\! \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_{26}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{11}\! \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) &= x^{2} F_{10} \left(x \right)^{2}-2 x F_{10} \left(x \right)^{2}+x F_{10}\! \left(x \right)+2 F_{10}\! \left(x \right)-1\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{16}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= \frac{F_{22}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{22}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{25}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{26}\! \left(x \right) &= x\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{26}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{26}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{34}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{0}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{26}\! \left(x \right) F_{42}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{26}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{62}\! \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_{48}\! \left(x \right) &= F_{26}\! \left(x \right) F_{46}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{26}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{53}\! \left(x \right)+F_{54}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{26}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{26}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{51}\! \left(x \right)+F_{57}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{26}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{26}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{26}\! \left(x \right) F_{52}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{26}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{26}\! \left(x \right) F_{46}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{26}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= -F_{21}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{26}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{10}\! \left(x \right) F_{26}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{71}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{110}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{26}\! \left(x \right) F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{77}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{26}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{26}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{85}\! \left(x \right) &= -F_{15}\! \left(x \right)-F_{86}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{86}\! \left(x \right) &= 0\\ F_{87}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{26}\! \left(x \right) F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{26}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{94}\! \left(x \right)+F_{95}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{26}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{26}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{26}\! \left(x \right) F_{87}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{71}\! \left(x \right)+F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{26}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{26}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{103}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{101}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{106}\! \left(x \right)+F_{108}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{107}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{105}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{26}\! \left(x \right) F_{32}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{26}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{26}\! \left(x \right) F_{33}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{119}\! \left(x \right)+F_{120}\! \left(x \right)+F_{35}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{116}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{26}\! \left(x \right) F_{46}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{122}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{124}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{130}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{132}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{130}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{26}\! \left(x \right) F_{36}\! \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_{26}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{237}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{140}\! \left(x \right) &= -F_{229}\! \left(x \right)+F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{142}\! \left(x \right)+F_{202}\! \left(x \right)+F_{226}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{170}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{157}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{156}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{26}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{161}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{158}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{167}\! \left(x \right)+F_{169}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{26}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{177}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{174}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right) F_{26}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{42} \left(x \right)^{2}\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{179}\! \left(x \right) F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{179}\! \left(x \right) F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{174}\! \left(x \right) F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{194}\! \left(x \right)+F_{195}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{192}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{191}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{200}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{191}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{192}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{172}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{221}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{208}\! \left(x \right)+F_{219}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{210}\! \left(x \right) F_{26}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{212}\! \left(x \right)+F_{214}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{87} \left(x \right)^{2}\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{210}\! \left(x \right) F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{179}\! \left(x \right) F_{216}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{26}\! \left(x \right) F_{49}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{207}\! \left(x \right) F_{216}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{205}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{191}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{233}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{46}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{207}\! \left(x \right) F_{216}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{210}\! \left(x \right) F_{26}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{237}\! \left(x \right) &= \frac{F_{238}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{255}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= -F_{246}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{244}\! \left(x \right) &= \frac{F_{245}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{245}\! \left(x \right) &= -F_{252}\! \left(x \right)-F_{86}\! \left(x \right)+F_{246}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)+F_{251}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{249}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{179}\! \left(x \right) F_{26}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{246}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{253}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{253}\! \left(x \right) &= -F_{254}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{10}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{257}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)+F_{272}\! \left(x \right)+F_{278}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{26}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{261}\! \left(x \right)+F_{262}\! \left(x \right)+F_{269}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{26}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{26}\! \left(x \right) F_{263}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{129}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{265}\! \left(x \right) &= \frac{F_{266}\! \left(x \right)}{F_{26}\! \left(x \right)}\\ F_{266}\! \left(x \right) &= -F_{267}\! \left(x \right)-F_{268}\! \left(x \right)-F_{86}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{249}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{26}\! \left(x \right) F_{36}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{216}\! \left(x \right) F_{26}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{26}\! \left(x \right) F_{260}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{26}\! \left(x \right) F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= -F_{274}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{275}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{10}\! \left(x \right) F_{26}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)\\ F_{279}\! \left(x \right) &= -F_{281}\! \left(x \right)-F_{86}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{239}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{26}\! \left(x \right) F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)+F_{285}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{14}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{270}\! \left(x \right)+F_{286}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{26}\! \left(x \right) F_{285}\! \left(x \right)\\ \end{align*}\)