###### Av(1432, 3214)
Generating Function
$$\displaystyle \frac{48 \left(x -\frac{1}{2}\right) \left(x -1\right)^{7} \left(-\frac{\left(x -\frac{1}{2}\right) \left(x -1\right)^{7} \left(x^{4}-9 x^{3}+12 x^{2}-6 x +1\right) \sqrt{1-4 x}}{12}-\frac{1}{24}+\frac{19 x}{24}-\frac{161 x^{2}}{24}+\frac{2131 x^{5}}{8}-\frac{2711 x^{4}}{24}+\frac{135 x^{3}}{4}+x^{13}-\frac{49 x^{12}}{4}+\frac{477 x^{11}}{8}-\frac{2147 x^{10}}{12}+367 x^{9}-\frac{2151 x^{8}}{4}+\frac{4611 x^{7}}{8}-\frac{3651 x^{6}}{8}\right) \left(x^{4}-9 x^{3}+12 x^{2}-6 x +1\right)}{288 x^{25}-7048 x^{24}+77296 x^{23}-519862 x^{22}+2463500 x^{21}-8840770 x^{20}+25067610 x^{19}-57688062 x^{18}+109678760 x^{17}-174358686 x^{16}+233666598 x^{15}-265413334 x^{14}+256339858 x^{13}-210793266 x^{12}+147522800 x^{11}-87671664 x^{10}+44059778 x^{9}-18603834 x^{8}+6538916 x^{7}-1888430 x^{6}+440014 x^{5}-80586 x^{4}+11156 x^{3}-1096 x^{2}+68 x -2}$$
Counting Sequence
1, 1, 2, 6, 22, 87, 348, 1374, 5335, 20462, 77988, 296787, 1130969, 4321239, 16559467, ...
Implicit Equation for the Generating Function
$$\displaystyle \left(144 x^{25}-3524 x^{24}+38648 x^{23}-259931 x^{22}+1231750 x^{21}-4420385 x^{20}+12533805 x^{19}-28844031 x^{18}+54839380 x^{17}-87179343 x^{16}+116833299 x^{15}-132706667 x^{14}+128169929 x^{13}-105396633 x^{12}+73761400 x^{11}-43835832 x^{10}+22029889 x^{9}-9301917 x^{8}+3269458 x^{7}-944215 x^{6}+220007 x^{5}-40293 x^{4}+5578 x^{3}-548 x^{2}+34 x -1\right) F \left(x \right)^{2}-\left(2 x -1\right) \left(x^{4}-9 x^{3}+12 x^{2}-6 x +1\right) \left(24 x^{13}-294 x^{12}+1431 x^{11}-4294 x^{10}+8808 x^{9}-12906 x^{8}+13833 x^{7}-10953 x^{6}+6393 x^{5}-2711 x^{4}+810 x^{3}-161 x^{2}+19 x -1\right) \left(x -1\right)^{7} F \! \left(x \right)+x \left(x^{4}-9 x^{3}+12 x^{2}-6 x +1\right)^{2} \left(2 x -1\right)^{2} \left(x -1\right)^{14} = 0$$
Recurrence
$$\displaystyle a \! \left(0\right) = 1$$
$$\displaystyle a \! \left(1\right) = 1$$
$$\displaystyle a \! \left(2\right) = 2$$
$$\displaystyle a \! \left(3\right) = 6$$
$$\displaystyle a \! \left(4\right) = 22$$
$$\displaystyle a \! \left(5\right) = 87$$
$$\displaystyle a \! \left(6\right) = 348$$
$$\displaystyle a \! \left(7\right) = 1374$$
$$\displaystyle a \! \left(8\right) = 5335$$
$$\displaystyle a \! \left(9\right) = 20462$$
$$\displaystyle a \! \left(10\right) = 77988$$
$$\displaystyle a \! \left(11\right) = 296787$$
$$\displaystyle a \! \left(12\right) = 1130969$$
$$\displaystyle a \! \left(13\right) = 4321239$$
$$\displaystyle a \! \left(14\right) = 16559467$$
$$\displaystyle a \! \left(15\right) = 63633036$$
$$\displaystyle a \! \left(16\right) = 245113705$$
$$\displaystyle a \! \left(17\right) = 946140207$$
$$\displaystyle a \! \left(18\right) = 3658715938$$
$$\displaystyle a \! \left(19\right) = 14170931497$$
$$\displaystyle a \! \left(20\right) = 54966429252$$
$$\displaystyle a \! \left(21\right) = 213487762758$$
$$\displaystyle a \! \left(22\right) = 830195102515$$
$$\displaystyle a \! \left(23\right) = 3232062132146$$
$$\displaystyle a \! \left(24\right) = 12596093756080$$
$$\displaystyle a \! \left(25\right) = 49137833964185$$
$$\displaystyle a \! \left(26\right) = 191862494482159$$
$$\displaystyle a \! \left(27\right) = 749774566697732$$
$$\displaystyle a \! \left(28\right) = 2932330178971502$$
$$\displaystyle a \! \left(29\right) = 11476615621742724$$
$$\displaystyle a \! \left(30\right) = 44948262174272349$$
$$\displaystyle a \! \left(31\right) = 176153480322826269$$
$$\displaystyle a \! \left(32\right) = 690767051696163996$$
$$\displaystyle a \! \left(n +32\right) = \frac{\left(47 n +1459\right) a \! \left(n +31\right)}{n +32}-\frac{\left(4116161101+169319588 n \right) a \! \left(n +24\right)}{n +32}+\frac{2 \left(19824599 n +501019369\right) a \! \left(n +25\right)}{n +32}-\frac{\left(202995749+7737472 n \right) a \! \left(n +26\right)}{n +32}+\frac{\left(1234249 n +33569300\right) a \! \left(n +27\right)}{n +32}-\frac{\left(4411102+156641 n \right) a \! \left(n +28\right)}{n +32}+\frac{\left(15199 n +442631\right) a \! \left(n +29\right)}{n +32}-\frac{2 \left(529 n +15914\right) a \! \left(n +30\right)}{n +32}+\frac{3 \left(7736988433 n +150935415510\right) a \! \left(n +19\right)}{n +32}-\frac{7 \left(1650980866 n +33789552251\right) a \! \left(n +20\right)}{n +32}+\frac{6 \left(835571789 n +17902782961\right) a \! \left(n +21\right)}{n +32}-\frac{2 \left(942938050 n +21108955667\right) a \! \left(n +22\right)}{n +32}+\frac{\left(611270878 n +14271861635\right) a \! \left(n +23\right)}{n +32}-\frac{221 \left(383212855 n +6378468032\right) a \! \left(n +16\right)}{n +32}+\frac{3 \left(20905511855 n +367879330324\right) a \! \left(n +17\right)}{n +32}-\frac{3 \left(13585581285 n +252037565164\right) a \! \left(n +18\right)}{n +32}+\frac{7 \left(13601957132 n +187725403603\right) a \! \left(n +13\right)}{n +32}-\frac{\left(1540246114148+104447093749 n \right) a \! \left(n +14\right)}{n +32}+\frac{3 \left(33467048233 n +525247495261\right) a \! \left(n +15\right)}{n +32}-\frac{7 \left(4528892768 n +49712159977\right) a \! \left(n +10\right)}{n +32}+\frac{\left(52675554227 n +627744870643\right) a \! \left(n +11\right)}{n +32}-\frac{3 \left(25292404521 n +325219220552\right) a \! \left(n +12\right)}{n +32}-\frac{17 \left(427841521 n +3888290849\right) a \! \left(n +8\right)}{n +32}+\frac{9 \left(1825924211 n +18322693273\right) a \! \left(n +9\right)}{n +32}+\frac{\left(212300951 n +1308369967\right) a \! \left(n +5\right)}{n +32}-\frac{6 \left(140444394 n +1005557395\right) a \! \left(n +6\right)}{n +32}+\frac{2 \left(1358289449 n +11045694490\right) a \! \left(n +7\right)}{n +32}+\frac{4 \left(1562623 n +6333176\right) a \! \left(n +3\right)}{n +32}-\frac{2 \left(21035909 n +107926267\right) a \! \left(n +4\right)}{n +32}+\frac{16 \left(4427+2536 n \right) a \! \left(n +1\right)}{n +32}-\frac{8 \left(80653 n +235955\right) a \! \left(n +2\right)}{n +32}-\frac{576 \left(1+2 n \right) a \! \left(n \right)}{n +32}, \quad n \geq 33$$
Heatmap

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

### This specification was found using the strategy pack "Insertion Row And Col Placements Tracked Fusion" and has 327 rules.

Found on January 17, 2022.

Finding the specification took 971 seconds.

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Copy 327 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_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{11}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\ F_{8}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)\\ F_{10}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\ F_{11}\! \left(x \right) &= x\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= y x\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{11}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{203}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{2}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{11}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{30}\! \left(x \right) &= 0\\ F_{31}\! \left(x \right) &= F_{11}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{11}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{11}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{25} \left(x \right)^{2}\\ F_{41}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{11}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{11}\! \left(x \right) F_{25}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{0}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{11}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{11}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{11}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{25}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{24}\! \left(x \right) F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{2}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{11}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x , 1\right)\\ F_{68}\! \left(x , y\right) &= F_{35}\! \left(x \right) F_{69}\! \left(x , y\right)\\ F_{69}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{70}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{69}\! \left(x , y\right)\\ F_{72}\! \left(x \right) &= F_{34}\! \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) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{11}\! \left(x \right) F_{24}\! \left(x \right) F_{25}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{11}\! \left(x \right) F_{24}\! \left(x \right) F_{29}\! \left(x \right) F_{38}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{2}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{11}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{11}\! \left(x \right) F_{24}\! \left(x \right) F_{25}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{20}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{11}\! \left(x \right) F_{24}\! \left(x \right) F_{51}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{2}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x , 1\right)\\ F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{102}\! \left(x , y\right)\\ F_{101}\! \left(x , y\right) &= F_{25}\! \left(x \right) F_{70}\! \left(x , y\right)\\ F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{189}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{13}\! \left(x , y\right)\\ F_{104}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{105}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{11}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{110}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{25}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{130}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{11}\! \left(x \right) F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{130}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{11}\! \left(x \right) F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{128}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{11}\! \left(x \right) F_{123}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{124}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{11}\! \left(x \right) F_{125}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{126}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{11}\! \left(x \right) F_{125}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{11}\! \left(x \right) F_{129}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{128}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{11}\! \left(x \right) F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{134}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{11}\! \left(x \right) F_{123}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{137}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{11}\! \left(x \right) F_{136}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{142}\! \left(x \right)+F_{185}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{11}\! \left(x \right) F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x , 1\right)\\ F_{143}\! \left(x , y\right) &= -\frac{y \left(F_{144}\! \left(x , 1\right)-F_{144}\! \left(x , y\right)\right)}{-1+y}\\ F_{144}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)\\ F_{145}\! \left(x , y\right) &= F_{146}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\ F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{164}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right)\\ F_{148}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{149}\! \left(x , y\right)\\ F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{160}\! \left(x , y\right)\\ F_{150}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{151}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{151}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{152}\! \left(x , y\right)\\ F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)+F_{158}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{153}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{154}\! \left(x , y\right)\\ F_{154}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)+F_{157}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\ F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{154}\! \left(x , y\right) F_{69}\! \left(x , y\right)\\ F_{157}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{154}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right)\\ F_{159}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{152}\! \left(x , y\right) F_{24}\! \left(x \right)\\ F_{160}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{161}\! \left(x , y\right) F_{69}\! \left(x , y\right)\\ F_{161}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)+F_{162}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)\\ F_{163}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{161}\! \left(x , y\right) F_{69}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{165}\! \left(x , y\right)\\ F_{165}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{166}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{167}\! \left(x , y\right)\\ F_{167}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)+F_{168}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{168}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{167}\! \left(x , y\right)\\ F_{169}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)+F_{170}\! \left(x , y\right)+F_{172}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{170}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{171}\! \left(x , y\right)\\ F_{171}\! \left(x , y\right) &= F_{113}\! \left(x \right)+F_{169}\! \left(x , y\right)\\ F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)\\ F_{173}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{174}\! \left(x , y\right)\\ F_{174}\! \left(x , y\right) &= -\frac{F_{175}\! \left(x , 1\right) y -F_{175}\! \left(x , y\right)}{-1+y}\\ F_{175}\! \left(x , y\right) &= F_{176}\! \left(x , y\right)+F_{180}\! \left(x , y\right)\\ F_{176}\! \left(x , y\right) &= F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{177}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{150}\! \left(x , y\right)\\ F_{178}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)\\ F_{179}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{175}\! \left(x , y\right)\\ F_{180}\! \left(x , y\right) &= F_{181}\! \left(x , y\right) F_{25}\! \left(x \right)\\ F_{181}\! \left(x , y\right) &= F_{182}\! \left(x , y\right)+F_{183}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{182}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{152}\! \left(x , y\right)\\ F_{183}\! \left(x , y\right) &= F_{184}\! \left(x , y\right)\\ F_{184}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{181}\! \left(x , y\right) F_{24}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{11}\! \left(x \right) F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{174}\! \left(x , 1\right)\\ F_{188}\! \left(x \right) &= F_{105}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{189}\! \left(x , y\right) &= F_{190}\! \left(x , y\right)\\ F_{190}\! \left(x , y\right) &= -\frac{y \left(F_{191}\! \left(x , 1\right)-F_{191}\! \left(x , y\right)\right)}{-1+y}\\ F_{191}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{192}\! \left(x , y\right)\\ F_{192}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{193}\! \left(x , y\right)\\ F_{193}\! \left(x , y\right) &= F_{152}\! \left(x , y\right) F_{25}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{2}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{20}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{118}\! \left(x \right) F_{2}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{215}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x , 1\right)\\ F_{208}\! \left(x , y\right) &= F_{209}\! \left(x , y\right)\\ F_{209}\! \left(x , y\right) &= F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{210}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{211}\! \left(x , y\right)\\ F_{211}\! \left(x , y\right) &= F_{209}\! \left(x , y\right)+F_{80}\! \left(x \right)\\ F_{212}\! \left(x , y\right) &= -\frac{y \left(F_{213}\! \left(x , 1\right)-F_{213}\! \left(x , y\right)\right)}{-1+y}\\ F_{213}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{214}\! \left(x , y\right)\\ F_{214}\! \left(x , y\right) &= F_{209}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x , 1\right)\\ F_{217}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{223}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right) F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{11}\! \left(x \right) F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{231}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{198}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{2}\! \left(x \right) F_{215}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{242}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{25} \left(x \right)^{3} F_{2}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{202}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)+F_{273}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{24}\! \left(x \right) F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{249}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{11}\! \left(x \right) F_{120}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{11}\! \left(x \right) F_{251}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{256}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{25}\! \left(x \right) F_{254}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{255}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{271}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{25}\! \left(x \right) F_{258}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{259}\! \left(x \right) &= 2 F_{30}\! \left(x \right)+F_{260}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{11}\! \left(x \right) F_{261}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{259}\! \left(x \right)+F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{11}\! \left(x \right) F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{262}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{11}\! \left(x \right) F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{11}\! \left(x \right) F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{267}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{265}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{247}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{118}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right) F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{137}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{278}\! \left(x , 1\right)\\ F_{278}\! \left(x , y\right) &= F_{279}\! \left(x , y\right)+F_{280}\! \left(x , y\right)\\ F_{279}\! \left(x , y\right) &= F_{209}\! \left(x , y\right) F_{24}\! \left(x \right)\\ F_{280}\! \left(x , y\right) &= F_{169}\! \left(x , y\right)+F_{281}\! \left(x , y\right)\\ F_{281}\! \left(x , y\right) &= F_{282}\! \left(x , y\right)+F_{30}\! \left(x \right)+F_{311}\! \left(x , y\right)+F_{319}\! \left(x , y\right)\\ F_{282}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{283}\! \left(x , y\right)\\ F_{283}\! \left(x , y\right) &= F_{281}\! \left(x , y\right)+F_{284}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{286}\! \left(x , 1\right)\\ F_{286}\! \left(x , y\right) &= F_{287}\! \left(x , y\right)\\ F_{287}\! \left(x , y\right) &= F_{288}\! \left(x , y\right)+F_{295}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{288}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{289}\! \left(x , y\right)\\ F_{289}\! \left(x , y\right) &= F_{290}\! \left(x , y\right)+F_{291}\! \left(x , y\right)\\ F_{290}\! \left(x , y\right) &= F_{287}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\ F_{291}\! \left(x , y\right) &= F_{292}\! \left(x , y\right)+F_{297}\! \left(x , y\right)\\ F_{292}\! \left(x , y\right) &= F_{293}\! \left(x , y\right)+F_{295}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{293}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{294}\! \left(x , y\right)\\ F_{294}\! \left(x , y\right) &= F_{292}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\ F_{295}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{296}\! \left(x , y\right)\\ F_{296}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{292}\! \left(x , y\right)\\ F_{297}\! \left(x , y\right) &= F_{298}\! \left(x , y\right)+F_{30}\! \left(x \right)+F_{307}\! \left(x , y\right)+F_{309}\! \left(x , y\right)\\ F_{298}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{299}\! \left(x , y\right)\\ F_{299}\! \left(x , y\right) &= F_{300}\! \left(x , y\right)+F_{303}\! \left(x , y\right)\\ F_{300}\! \left(x , y\right) &= F_{301}\! \left(x , y\right)\\ F_{301}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{302}\! \left(x , y\right)\\ F_{302}\! \left(x , y\right) &= F_{300}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\ F_{303}\! \left(x , y\right) &= 2 F_{30}\! \left(x \right)+F_{304}\! \left(x , y\right)+F_{305}\! \left(x , y\right)\\ F_{304}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{299}\! \left(x , y\right)\\ F_{305}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{306}\! \left(x , y\right)\\ F_{306}\! \left(x , y\right) &= F_{292}\! \left(x , y\right)+F_{303}\! \left(x , y\right)\\ F_{307}\! \left(x , y\right) &= -\frac{y \left(F_{308}\! \left(x , 1\right)-F_{308}\! \left(x , y\right)\right)}{-1+y}\\ F_{308}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{291}\! \left(x , y\right)\\ F_{309}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{310}\! \left(x , y\right)\\ F_{310}\! \left(x , y\right) &= F_{206}\! \left(x \right)+F_{297}\! \left(x , y\right)\\ F_{311}\! \left(x , y\right) &= -\frac{y \left(F_{312}\! \left(x , 1\right)-F_{312}\! \left(x , y\right)\right)}{-1+y}\\ F_{312}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{313}\! \left(x , y\right)\\ F_{313}\! \left(x , y\right) &= F_{281}\! \left(x , y\right)+F_{314}\! \left(x , y\right)\\ F_{314}\! \left(x , y\right) &= F_{30}\! \left(x \right)+F_{315}\! \left(x , y\right)+F_{317}\! \left(x , y\right)\\ F_{315}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{316}\! \left(x , y\right)\\ F_{316}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{314}\! \left(x , y\right)\\ F_{317}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{318}\! \left(x , y\right)\\ F_{318}\! \left(x , y\right) &= F_{314}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\ F_{319}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{320}\! \left(x , y\right)\\ F_{320}\! \left(x , y\right) &= F_{321}\! \left(x , y\right)+F_{324}\! \left(x , y\right)\\ F_{321}\! \left(x , y\right) &= F_{322}\! \left(x , y\right)\\ F_{322}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{323}\! \left(x , y\right)\\ F_{323}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{321}\! \left(x , y\right)\\ F_{324}\! \left(x , y\right) &= 2 F_{30}\! \left(x \right)+F_{319}\! \left(x , y\right)+F_{325}\! \left(x , y\right)\\ F_{325}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{326}\! \left(x , y\right)\\ F_{326}\! \left(x , y\right) &= F_{29}\! \left(x \right)+F_{324}\! \left(x , y\right)\\ \end{align*}

### This specification was found using the strategy pack "Insertion Row And Col Placements Tracked Fusion Req Corrob" and has 354 rules.

Found on January 17, 2022.

Finding the specification took 706 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_{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_{15}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{12}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\ F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)\\ F_{11}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\ F_{12}\! \left(x \right) &= x\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= y x\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{12}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{12}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{20}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{60}\! \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) &= F_{19}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{35}\! \left(x \right) &= 0\\ F_{36}\! \left(x \right) &= F_{12}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{12}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x , 1\right)\\ F_{54}\! \left(x , y\right) &= F_{24}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right) F_{34}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{61}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{12}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{12}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{71}\! \left(x \right) &= 2 F_{35}\! \left(x \right)+F_{72}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{12}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{12}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{12}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{78}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x , 1\right)\\ F_{79}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{80}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{81}\! \left(x , y\right)+F_{84}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{81}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= -\frac{y \left(F_{85}\! \left(x , 1\right)-F_{85}\! \left(x , y\right)\right)}{-1+y}\\ F_{85}\! \left(x , y\right) &= F_{35}\! \left(x \right)+F_{79}\! \left(x , y\right)+F_{86}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{87}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{6}\! \left(x \right)+F_{85}\! \left(x , y\right)\\ F_{88}\! \left(x \right) &= F_{86}\! \left(x , 1\right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{2}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{12}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{20}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{20} \left(x \right)^{2} F_{2}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x , 1\right)\\ F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)\\ F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)+F_{111}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{110}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)+F_{77}\! \left(x \right)\\ F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)\\ F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right) F_{12}\! \left(x \right)\\ F_{113}\! \left(x , y\right) &= -\frac{y \left(F_{114}\! \left(x , 1\right)-F_{114}\! \left(x , y\right)\right)}{-1+y}\\ F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{117}\! \left(x , y\right)\\ F_{115}\! \left(x , y\right) &= F_{116}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{116}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{117}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)+F_{118}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{20}\! \left(x \right)\\ F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{126}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{121}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{122}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)\\ F_{123}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{124}\! \left(x , y\right) F_{22}\! \left(x \right)\\ F_{124}\! \left(x , y\right) &= F_{122}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{22}\! \left(x \right)\\ F_{125}\! \left(x , y\right) &= F_{124}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{128}\! \left(x , y\right) F_{22}\! \left(x \right)\\ F_{128}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)+F_{126}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{24}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{2}\! \left(x \right) F_{20}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{145}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{12}\! \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_{136}\! \left(x \right)+F_{138}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{12}\! \left(x \right) F_{140}\! \left(x \right) F_{144}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{142}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{12}\! \left(x \right) F_{140}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{12}\! \left(x \right) F_{140}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{12}\! \left(x \right) F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{153}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{149}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{12}\! \left(x \right) F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{151}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{12}\! \left(x \right) F_{150}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{12}\! \left(x \right) F_{154}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{155}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{12}\! \left(x \right) F_{154}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{165}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{20} \left(x \right)^{2}\\ F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{30}\! \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_{20}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{12}\! \left(x \right) F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{172}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{20} \left(x \right)^{3} F_{2}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{184}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{104}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{12}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{198}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{12}\! \left(x \right) F_{191}\! \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_{195}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x , 1\right)\\ F_{194}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{85}\! \left(x , y\right)\\ F_{195}\! \left(x \right) &= F_{0}\! \left(x \right) F_{20}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{0}\! \left(x \right) F_{133}\! \left(x \right) F_{20}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{12}\! \left(x \right) F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{218}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{209}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{203}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= 2 F_{35}\! \left(x \right)+F_{205}\! \left(x \right)+F_{207}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{20} \left(x \right)^{3} F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{20} \left(x \right)^{2} F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{216}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{214}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{12}\! \left(x \right) F_{133}\! \left(x \right) F_{163}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{20}\! \left(x \right) F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{223}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{296}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x , 1\right)\\ F_{228}\! \left(x , y\right) &= -\frac{F_{229}\! \left(x , 1\right) y -F_{229}\! \left(x , y\right)}{-1+y}\\ F_{229}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{230}\! \left(x , y\right)\\ F_{230}\! \left(x , y\right) &= F_{231}\! \left(x , y\right)+F_{295}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{231}\! \left(x , y\right) &= F_{232}\! \left(x , y\right)\\ F_{232}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{233}\! \left(x , y\right)\\ F_{233}\! \left(x , y\right) &= F_{234}\! \left(x , y\right)+F_{244}\! \left(x , y\right)\\ F_{234}\! \left(x , y\right) &= F_{235}\! \left(x , y , 1\right)\\ F_{235}\! \left(x , y , z\right) &= -\frac{z \left(F_{236}\! \left(x , y , 1\right)-F_{236}\! \left(x , y , z\right)\right)}{-1+z}\\ F_{236}\! \left(x , y , z\right) &= F_{237}\! \left(x , z\right) F_{242}\! \left(x , y\right)\\ F_{237}\! \left(x , y\right) &= F_{238}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{238}\! \left(x , y\right) &= F_{239}\! \left(x , y\right)+F_{240}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{239}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{237}\! \left(x , y\right)\\ F_{240}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{241}\! \left(x , y\right)\\ F_{241}\! \left(x , y\right) &= F_{20}\! \left(x \right)+F_{238}\! \left(x , y\right)\\ F_{242}\! \left(x , y\right) &= F_{243}\! \left(x , y\right)\\ F_{243}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{244}\! \left(x , y\right) &= F_{245}\! \left(x , y\right)+F_{249}\! \left(x , y\right)\\ F_{245}\! \left(x , y\right) &= F_{246}\! \left(x , y\right)\\ F_{246}\! \left(x , y\right) &= F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{247}\! \left(x , y\right)\\ F_{247}\! \left(x , y\right) &= F_{242}\! \left(x , y\right)+F_{248}\! \left(x , y\right)\\ F_{248}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)^{2}\\ F_{249}\! \left(x , y\right) &= F_{250}\! \left(x , y , 1\right)\\ F_{250}\! \left(x , y , z\right) &= F_{251}\! \left(x , y , z\right)+F_{270}\! \left(x , y , z\right)\\ F_{251}\! \left(x , y , z\right) &= -\frac{z \left(F_{252}\! \left(x , y , 1\right)-F_{252}\! \left(x , y , z\right)\right)}{-1+z}\\ F_{252}\! \left(x , y , z\right) &= F_{253}\! \left(x , y , z\right)+F_{259}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{253}\! \left(x , y , z\right) &= F_{254}\! \left(x , y , z\right)\\ F_{254}\! \left(x , y , z\right) &= F_{12}\! \left(x \right) F_{255}\! \left(x , y , z\right)\\ F_{255}\! \left(x , y , z\right) &= F_{235}\! \left(x , y , z\right)+F_{256}\! \left(x , y , z\right)\\ F_{256}\! \left(x , y , z\right) &= F_{250}\! \left(x , y , z\right)+F_{257}\! \left(x , y , z\right)\\ F_{257}\! \left(x , y , z\right) &= F_{258}\! \left(x , y , z\right)\\ F_{258}\! \left(x , y , z\right) &= F_{22}\! \left(x \right) F_{247}\! \left(x , y\right) F_{55}\! \left(x , z\right)\\ F_{259}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{260}\! \left(x , y , z\right)\\ F_{260}\! \left(x , y , z\right) &= F_{252}\! \left(x , y , z\right)+F_{261}\! \left(x , y\right)\\ F_{261}\! \left(x , y\right) &= F_{262}\! \left(x , y\right)\\ F_{262}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{263}\! \left(x , y\right)\\ F_{263}\! \left(x , y\right) &= F_{264}\! \left(x , y\right)+F_{265}\! \left(x , y\right)\\ F_{264}\! \left(x , y\right) &= F_{171}\! \left(x \right) F_{242}\! \left(x , y\right)\\ F_{265}\! \left(x , y\right) &= F_{266}\! \left(x , y\right)+F_{267}\! \left(x , y\right)\\ F_{266}\! \left(x , y\right) &= F_{22}\! \left(x \right) F_{247}\! \left(x , y\right)\\ F_{267}\! \left(x , y\right) &= F_{268}\! \left(x , y\right)+F_{269}\! \left(x , y\right)\\ F_{268}\! \left(x , y\right) &= F_{260}\! \left(x , y , 1\right)\\ F_{269}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{270}\! \left(x , y , z\right) &= -\frac{z \left(F_{271}\! \left(x , y , 1\right)-F_{271}\! \left(x , y , z\right)\right)}{-1+z}\\ F_{271}\! \left(x , y , z\right) &= F_{272}\! \left(x , y , z\right) F_{55}\! \left(x , y\right)\\ F_{272}\! \left(x , y , z\right) &= F_{273}\! \left(x , y , z\right)+F_{286}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{273}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{274}\! \left(x , y , z\right)\\ F_{274}\! \left(x , y , z\right) &= F_{275}\! \left(x , y , z\right)+F_{283}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{275}\! \left(x , y , z\right) &= F_{276}\! \left(x , y , z\right)\\ F_{276}\! \left(x , y , z\right) &= F_{12}\! \left(x \right) F_{277}\! \left(x , y , z\right) F_{57}\! \left(x , y\right)\\ F_{277}\! \left(x , y , z\right) &= F_{275}\! \left(x , y , z\right)+F_{278}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{278}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{279}\! \left(x , y , z\right)\\ F_{279}\! \left(x , y , z\right) &= F_{280}\! \left(x , y , z\right)+F_{281}\! \left(x , y , z\right)+F_{57}\! \left(x , z\right)\\ F_{280}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{279}\! \left(x , y , z\right)\\ F_{281}\! \left(x , y , z\right) &= F_{282}\! \left(x , y , z\right)\\ F_{282}\! \left(x , y , z\right) &= F_{12}\! \left(x \right) F_{279}\! \left(x , y , z\right) F_{57}\! \left(x , z\right)\\ F_{283}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{284}\! \left(x , y , z\right)\\ F_{284}\! \left(x , y , z\right) &= F_{281}\! \left(x , y , z\right)+F_{285}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{285}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{284}\! \left(x , y , z\right)\\ F_{286}\! \left(x , y , z\right) &= F_{287}\! \left(x , y , z\right)\\ F_{287}\! \left(x , y , z\right) &= F_{12}\! \left(x \right) F_{288}\! \left(x , y , z\right)\\ F_{288}\! \left(x , y , z\right) &= F_{289}\! \left(x , y , z\right)+F_{291}\! \left(x , y , z\right)\\ F_{289}\! \left(x , y , z\right) &= F_{286}\! \left(x , y , z\right)+F_{290}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{290}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{277}\! \left(x , y , z\right)\\ F_{291}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{292}\! \left(x , y , z\right) F_{57}\! \left(x , z\right)\\ F_{292}\! \left(x , y , z\right) &= F_{280}\! \left(x , y , z\right)+F_{293}\! \left(x , y , z\right)+F_{35}\! \left(x \right)\\ F_{293}\! \left(x , y , z\right) &= F_{294}\! \left(x , y , z\right)\\ F_{294}\! \left(x , y , z\right) &= F_{12}\! \left(x \right) F_{292}\! \left(x , y , z\right) F_{57}\! \left(x , z\right)\\ F_{295}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{268}\! \left(x , y\right)\\ F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{322}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)+F_{309}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{300}\! \left(x \right)\\ F_{300}\! \left(x \right) &= 2 F_{35}\! \left(x \right)+F_{301}\! \left(x \right)+F_{307}\! \left(x \right)\\ F_{301}\! \left(x \right) &= F_{12}\! \left(x \right) F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{306}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{304}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{12}\! \left(x \right) F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{303}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{301}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{12}\! \left(x \right) F_{308}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{300}\! \left(x \right)+F_{303}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{311}\! \left(x , 1\right)\\ F_{311}\! \left(x , y\right) &= -\frac{F_{312}\! \left(x , 1\right) y -F_{312}\! \left(x , y\right)}{-1+y}\\ F_{312}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x \right) F_{313}\! \left(x , y\right)\\ F_{313}\! \left(x , y\right) &= F_{314}\! \left(x , y\right)+F_{320}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{314}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{315}\! \left(x , y\right)\\ F_{315}\! \left(x , y\right) &= F_{316}\! \left(x , y\right)+F_{318}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{316}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{317}\! \left(x , y\right)\\ F_{317}\! \left(x , y\right) &= F_{20}\! \left(x \right)+F_{315}\! \left(x , y\right)\\ F_{318}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{319}\! \left(x , y\right)\\ F_{319}\! \left(x , y\right) &= F_{315}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{320}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{321}\! \left(x , y\right)\\ F_{321}\! \left(x , y\right) &= F_{242}\! \left(x , y\right)+F_{313}\! \left(x , y\right)\\ F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{324}\! \left(x , 1\right)\\ F_{324}\! \left(x , y\right) &= -\frac{F_{325}\! \left(x , 1\right) y -F_{325}\! \left(x , y\right)}{-1+y}\\ F_{325}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{20}\! \left(x \right) F_{326}\! \left(x , y\right)\\ F_{326}\! \left(x , y\right) &= F_{327}\! \left(x , y\right)+F_{344}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{327}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{328}\! \left(x , y\right)\\ F_{328}\! \left(x , y\right) &= F_{329}\! \left(x , y\right)+F_{343}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{329}\! \left(x , y\right) &= F_{330}\! \left(x , y\right)\\ F_{330}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{331}\! \left(x , y\right)\\ F_{331}\! \left(x , y\right) &= F_{332}\! \left(x , y\right)+F_{342}\! \left(x , y\right)\\ F_{332}\! \left(x , y\right) &= F_{333}\! \left(x , y\right)+F_{338}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{333}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{334}\! \left(x , y\right)\\ F_{334}\! \left(x , y\right) &= F_{335}\! \left(x , y\right)+F_{337}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{335}\! \left(x , y\right) &= F_{336}\! \left(x , y\right)\\ F_{336}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{334}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\ F_{337}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{124}\! \left(x , y\right)\\ F_{338}\! \left(x , y\right) &= F_{339}\! \left(x , y\right)\\ F_{339}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{340}\! \left(x , y\right)\\ F_{340}\! \left(x , y\right) &= F_{332}\! \left(x , y\right)+F_{341}\! \left(x , y\right)\\ F_{341}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{128}\! \left(x , y\right) F_{22}\! \left(x \right)\\ F_{342}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{334}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\ F_{343}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{12}\! \left(x \right)\\ F_{344}\! \left(x , y\right) &= F_{345}\! \left(x , y\right)\\ F_{345}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{346}\! \left(x , y\right)\\ F_{346}\! \left(x , y\right) &= F_{347}\! \left(x , y\right)+F_{349}\! \left(x , y\right)\\ F_{347}\! \left(x , y\right) &= F_{344}\! \left(x , y\right)+F_{348}\! \left(x , y\right)+F_{35}\! \left(x \right)\\ F_{348}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{332}\! \left(x , y\right)\\ F_{349}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right) F_{350}\! \left(x , y\right)\\ F_{350}\! \left(x , y\right) &= F_{35}\! \left(x \right)+F_{351}\! \left(x , y\right)+F_{352}\! \left(x , y\right)\\ F_{351}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\ F_{352}\! \left(x , y\right) &= F_{353}\! \left(x , y\right)\\ F_{353}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right) F_{350}\! \left(x , y\right)\\ \end{align*}