Av(13452, 13542, 14352, 14532, 15342, 15432, 31452, 31542, 34152, 41352, 41532, 43152)
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Counting Sequence
1, 1, 2, 6, 24, 108, 512, 2489, 12318, 61876, 314876, 1620571, 8422914, 44153300, 233183079, ...
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Implicit Equation for the Generating Function
\(\displaystyle x^{2} \left(3 x^{3}+2 x^{2}+2 x -3\right) F \left(x \right)^{3}-x \left(2 x^{4}-x^{3}+4 x^{2}-4\right) F \left(x \right)^{2}+\left(2 x^{3}+x^{2}-3 x -1\right) F \! \left(x \right)-\left(x -1\right) \left(x +1\right) = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 108\)
\(\displaystyle a(6) = 512\)
\(\displaystyle a(7) = 2489\)
\(\displaystyle a(8) = 12318\)
\(\displaystyle a(9) = 61876\)
\(\displaystyle a(10) = 314876\)
\(\displaystyle a(11) = 1620571\)
\(\displaystyle a(12) = 8422914\)
\(\displaystyle a(13) = 44153300\)
\(\displaystyle a(14) = 233183079\)
\(\displaystyle a(15) = 1239559566\)
\(\displaystyle a(16) = 6627389610\)
\(\displaystyle a(17) = 35615876803\)
\(\displaystyle a(18) = 192280476242\)
\(\displaystyle a(19) = 1042357008512\)
\(\displaystyle a(20) = 5671728408629\)
\(\displaystyle a(21) = 30965873606107\)
\(\displaystyle a(22) = 169586390487218\)
\(\displaystyle a(23) = 931376770930649\)
\(\displaystyle a(24) = 5128462536139832\)
\(\displaystyle a(25) = 28306653558461117\)
\(\displaystyle a(26) = 156585462707542410\)
\(\displaystyle a(27) = 867973277577261780\)
\(\displaystyle a(28) = 4820487600180304895\)
\(\displaystyle a(29) = 26819413112313827034\)
\(\displaystyle a(30) = 149461972870776511293\)
\(\displaystyle a{\left(n + 31 \right)} = \frac{144 n \left(2 n + 3\right) a{\left(n \right)}}{7 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(685 n + 20642\right) a{\left(n + 30 \right)}}{42 \left(n + 32\right)} - \frac{8 \left(2 n + 5\right) \left(25 n + 32\right) a{\left(n + 1 \right)}}{7 \left(n + 31\right) \left(n + 32\right)} + \frac{3 \left(289 n^{2} + 4460 n + 11488\right) a{\left(n + 3 \right)}}{7 \left(n + 31\right) \left(n + 32\right)} - \frac{8 \left(430 n^{2} + 2691 n + 3584\right) a{\left(n + 2 \right)}}{21 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(8419 n^{2} + 497913 n + 7360358\right) a{\left(n + 29 \right)}}{84 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(9998 n^{2} + 517693 n + 6668656\right) a{\left(n + 27 \right)}}{28 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(11585 n^{2} + 496377 n + 2404816\right) a{\left(n + 5 \right)}}{42 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(15551 n^{2} + 102789 n - 8260196\right) a{\left(n + 26 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(27149 n^{2} + 5449233 n + 39190096\right) a{\left(n + 7 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(46499 n^{2} + 398565 n + 789160\right) a{\left(n + 4 \right)}}{42 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(47983 n^{2} + 2721435 n + 38574464\right) a{\left(n + 28 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(138223 n^{2} + 7621875 n + 104347964\right) a{\left(n + 25 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(162159 n^{2} + 7417430 n + 84298942\right) a{\left(n + 24 \right)}}{28 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(189307 n^{2} + 7827903 n + 82472198\right) a{\left(n + 22 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(330243 n^{2} + 11161597 n + 75475870\right) a{\left(n + 9 \right)}}{56 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(410105 n^{2} + 17866056 n + 193376102\right) a{\left(n + 23 \right)}}{28 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(532499 n^{2} + 6241365 n + 15818992\right) a{\left(n + 6 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(843271 n^{2} + 14373540 n + 57469259\right) a{\left(n + 8 \right)}}{84 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(1822811 n^{2} + 41527467 n + 231481350\right) a{\left(n + 10 \right)}}{56 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(2226734 n^{2} + 94245867 n + 968999206\right) a{\left(n + 17 \right)}}{84 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(2499671 n^{2} + 160240197 n + 1893681640\right) a{\left(n + 15 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(2831663 n^{2} + 113291231 n + 1126036482\right) a{\left(n + 21 \right)}}{56 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(3077051 n^{2} + 115510319 n + 1075145716\right) a{\left(n + 20 \right)}}{56 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(3507365 n^{2} + 123241671 n + 949414552\right) a{\left(n + 11 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(4217281 n^{2} + 193842087 n + 1852881770\right) a{\left(n + 13 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(4844105 n^{2} + 179326515 n + 1653210937\right) a{\left(n + 19 \right)}}{84 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(5139645 n^{2} + 141382539 n + 969365566\right) a{\left(n + 14 \right)}}{56 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(10154516 n^{2} + 300193365 n + 2185788550\right) a{\left(n + 16 \right)}}{84 \left(n + 31\right) \left(n + 32\right)} + \frac{\left(10572365 n^{2} + 275181033 n + 1784166082\right) a{\left(n + 12 \right)}}{168 \left(n + 31\right) \left(n + 32\right)} - \frac{\left(19479725 n^{2} + 647446035 n + 5306254414\right) a{\left(n + 18 \right)}}{168 \left(n + 31\right) \left(n + 32\right)}, \quad n \geq 31\)
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 307 rules.

Finding the specification took 6580 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_{2}\! \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_{13}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{10}\! \left(x \right) &= \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{11}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{12}\! \left(x \right) &= x\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{297}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{0}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{182}\! \left(x \right)\\ F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{25}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{12}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{2}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{12}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= -F_{230}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{228}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= -F_{214}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= -F_{48}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= -F_{53}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{52}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= -F_{210}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{2}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{12}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{12}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{68}\! \left(x \right) &= 0\\ F_{69}\! \left(x \right) &= F_{12}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{12}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{73}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{12}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{12}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{12}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{12}\! \left(x \right) F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{12}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{12}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{12}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{2}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{10}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{0}\! \left(x \right) F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\ F_{105}\! \left(x \right) &= -F_{110}\! \left(x \right)+F_{106}\! \left(x \right)\\ F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{110}\! \left(x \right) &= -F_{178}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{0}\! \left(x \right) F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{172}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{12}\! \left(x \right) F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{125}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{137}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{12}\! \left(x \right) F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{130}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{126}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{12}\! \left(x \right) F_{133}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{12}\! \left(x \right) F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{12}\! \left(x \right) F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{143}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{86}\! \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_{12}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{140}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{155}\! \left(x \right)+F_{159}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{12}\! \left(x \right) F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{144}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{12}\! \left(x \right) F_{151}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{12}\! \left(x \right) F_{154}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{12}\! \left(x \right) F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{158}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{152}\! \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_{90}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{12}\! \left(x \right) F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{170}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{12}\! \left(x \right) F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{165}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{12}\! \left(x \right) F_{86}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{162}\! \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_{175}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{176}\! \left(x \right) &= -F_{177}\! \left(x \right)+F_{106}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{113}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{12}\! \left(x \right) F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= -F_{207}\! \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_{185}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{12}\! \left(x \right) F_{188}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{199}\! \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_{193}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right)\\ F_{193}\! \left(x \right) &= \frac{F_{194}\! \left(x \right)}{F_{114}\! \left(x \right)}\\ F_{194}\! \left(x \right) &= -F_{198}\! \left(x \right)+F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= \frac{F_{196}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= -F_{105}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{103}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{200}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= -F_{204}\! \left(x \right)+F_{202}\! \left(x \right)\\ F_{202}\! \left(x \right) &= \frac{F_{203}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{203}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\ F_{205}\! \left(x \right) &= \frac{F_{206}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{206}\! \left(x \right) &= F_{26}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{208}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{12}\! \left(x \right) F_{191}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{111}\! \left(x \right) F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{0}\! \left(x \right) F_{216}\! \left(x \right) F_{217}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{217}\! \left(x \right) &= \frac{F_{218}\! \left(x \right)}{F_{12}\! \left(x \right) F_{223}\! \left(x \right)}\\ F_{218}\! \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_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{224}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{0}\! \left(x \right) F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{219}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= \frac{F_{227}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}\\ F_{227}\! \left(x \right) &= F_{219}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{0}\! \left(x \right) F_{109}\! \left(x \right) F_{217}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{0}\! \left(x \right) F_{217}\! \left(x \right) F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{0}\! \left(x \right) F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= -F_{293}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{236}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{237}\! \left(x \right)\\ F_{237}\! \left(x \right) &= \frac{F_{238}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{238}\! \left(x \right) &= F_{185}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{291}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{0}\! \left(x \right) F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{12}\! \left(x \right) F_{246}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{248}\! \left(x \right)\\ F_{248}\! \left(x \right) &= -F_{251}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= \frac{F_{250}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{250}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{12}\! \left(x \right) F_{253}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)+F_{261}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{256}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{243}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{12}\! \left(x \right) F_{258}\! \left(x \right) F_{65}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{12}\! \left(x \right) F_{253}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{12}\! \left(x \right) F_{247}\! \left(x \right) F_{65}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{12}\! \left(x \right) F_{247}\! \left(x \right) F_{60}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{12}\! \left(x \right) F_{267}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{271}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{269}\! \left(x \right) &= \frac{F_{270}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{270}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)+F_{274}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{12}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{0}\! \left(x \right) F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= -F_{285}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{12}\! \left(x \right) F_{279}\! \left(x \right)\\ F_{279}\! \left(x \right) &= -F_{280}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{280}\! \left(x \right) &= -F_{284}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{281}\! \left(x \right) &= \frac{F_{282}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= -F_{189}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{217}\! \left(x \right) F_{259}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{286}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{12}\! \left(x \right) F_{287}\! \left(x \right)\\ F_{287}\! \left(x \right) &= -F_{290}\! \left(x \right)+F_{288}\! \left(x \right)\\ F_{288}\! \left(x \right) &= \frac{F_{289}\! \left(x \right)}{F_{12}\! \left(x \right)}\\ F_{289}\! \left(x \right) &= F_{189}\! \left(x \right)\\ F_{290}\! \left(x \right) &= F_{216}\! \left(x \right) F_{217}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{12}\! \left(x \right) F_{269}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{12}\! \left(x \right) F_{295}\! \left(x \right)\\ F_{295}\! \left(x \right) &= -F_{296}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{217}\! \left(x \right) F_{232}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{191}\! \left(x \right) F_{299}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{300}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{12}\! \left(x \right) F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{12}\! \left(x \right) F_{304}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{305}\! \left(x \right)+F_{306}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{114}\! \left(x \right) F_{243}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{12}\! \left(x \right) F_{301}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Req Corrob" and has 311 rules.

Finding the specification took 3325 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_{17}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{17}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{17}\! \left(x \right) &= x\\ F_{18}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{17}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{26}\! \left(x \right) &= 0\\ F_{27}\! \left(x \right) &= F_{17}\! \left(x \right) F_{20}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{17}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{31}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{17}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{17}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{17}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{17}\! \left(x \right) F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{17}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{17}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{17}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{61}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{17}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{13}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{17}\! \left(x \right) F_{23}\! \left(x \right) F_{46}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{17}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{17}\! \left(x \right) F_{23}\! \left(x \right) F_{46}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{17}\! \left(x \right) F_{18}\! \left(x \right) F_{46}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{76}\! \left(x \right) &= \frac{F_{77}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{77}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right) F_{91}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{17}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{17}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{13}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{17}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{17}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{209}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= -F_{197}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{100}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{14}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{80}\! \left(x \right)}\\ F_{106}\! \left(x \right) &= -F_{136}\! \left(x \right)+F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= \frac{F_{108}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= -F_{135}\! \left(x \right)+F_{110}\! \left(x \right)\\ F_{110}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{113}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= -F_{14}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{0}\! \left(x \right) F_{117}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{117}\! \left(x \right) &= \frac{F_{118}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= -F_{122}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{121}\! \left(x \right) &= F_{113}\! \left(x \right)\\ F_{122}\! \left(x \right) &= -F_{126}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{127}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)\\ F_{128}\! \left(x \right) &= \frac{F_{129}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{129}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{126}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{190}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{143}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{155}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{148}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{161}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{173}\! \left(x \right)+F_{177}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{170}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{17}\! \left(x \right) F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{170}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{17}\! \left(x \right) F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{170}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{17}\! \left(x \right) F_{178}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{189}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{17}\! \left(x \right) F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{188}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{17}\! \left(x \right) F_{185}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{17}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{17}\! \left(x \right) F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{114}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{123}\! \left(x \right) F_{17}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{198}\! \left(x \right) &= \frac{F_{199}\! \left(x \right)}{F_{17}\! \left(x \right) F_{204}\! \left(x \right)}\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{17}\! \left(x \right) F_{202}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{0}\! \left(x \right) F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{200}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{17}\! \left(x \right) F_{207}\! \left(x \right)\\ F_{207}\! \left(x \right) &= \frac{F_{208}\! \left(x \right)}{F_{0}\! \left(x \right) F_{17}\! \left(x \right)}\\ F_{208}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{125}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{304}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{17}\! \left(x \right) F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{215}\! \left(x \right) &= -F_{99}\! \left(x \right)+F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= -F_{219}\! \left(x \right)+F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= \frac{F_{218}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{218}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= \frac{F_{221}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{17}\! \left(x \right) F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{17}\! \left(x \right) F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= \frac{F_{227}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= -F_{231}\! \left(x \right)+F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= \frac{F_{230}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{230}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{233}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{2}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{17}\! \left(x \right) F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{259}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{17}\! \left(x \right) F_{239}\! \left(x \right)\\ F_{239}\! \left(x \right) &= -F_{257}\! \left(x \right)+F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= \frac{F_{241}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)\\ F_{242}\! \left(x \right) &= -F_{246}\! \left(x \right)+F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= \frac{F_{244}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= -F_{232}\! \left(x \right)+F_{229}\! \left(x \right)\\ F_{246}\! \left(x \right) &= \frac{F_{247}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)\\ F_{248}\! \left(x \right) &= -F_{251}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= \frac{F_{250}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{250}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{253}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{17}\! \left(x \right) F_{255}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{256}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{5}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{0}\! \left(x \right) F_{198}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{0}\! \left(x \right) F_{261}\! \left(x \right)\\ F_{261}\! \left(x \right) &= -F_{270}\! \left(x \right)+F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{17}\! \left(x \right) F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= -F_{265}\! \left(x \right)+F_{226}\! \left(x \right)\\ F_{265}\! \left(x \right) &= -F_{269}\! \left(x \right)+F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= \frac{F_{267}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\ F_{268}\! \left(x \right) &= -F_{97}\! \left(x \right)+F_{228}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{198}\! \left(x \right) F_{70}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{17}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{17}\! \left(x \right) F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= -F_{279}\! \left(x \right)+F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{0}\! \left(x \right) F_{125}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{0}\! \left(x \right) F_{114}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{0}\! \left(x \right) F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= -F_{300}\! \left(x \right)+F_{284}\! \left(x \right)\\ F_{284}\! \left(x \right) &= -F_{292}\! \left(x \right)+F_{285}\! \left(x \right)\\ F_{285}\! \left(x \right) &= \frac{F_{286}\! \left(x \right)}{F_{17}\! \left(x \right)}\\ F_{286}\! \left(x \right) &= F_{287}\! \left(x \right)\\ F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{289}\! \left(x \right)\\ F_{288}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{289}\! \left(x \right) &= F_{290}\! \left(x \right)\\ F_{290}\! \left(x \right) &= F_{17}\! \left(x \right) F_{291}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{293}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{262}\! \left(x \right)+F_{294}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{296}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{0}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{17}\! \left(x \right) F_{298}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{272}\! \left(x \right)+F_{299}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= F_{17}\! \left(x \right) F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= -F_{303}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{114}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{17}\! \left(x \right) F_{306}\! \left(x \right)\\ F_{306}\! \left(x \right) &= F_{307}\! \left(x \right)+F_{310}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{308}\! \left(x \right)+F_{309}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{4}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{0}\! \left(x \right) F_{228}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{212}\! \left(x \right) F_{4}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 115 rules.

Finding the specification took 1622 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_{18}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{18}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{12}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{12}\! \left(x \right) &= 0\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{14}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{16}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{17}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{18}\! \left(x \right) &= x\\ F_{19}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x , 1\right)\\ F_{22}\! \left(x , y\right) &= F_{11}\! \left(x \right)+F_{23}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= y F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{26}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{12}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{18}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{18}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right)\\ F_{32}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= -F_{102}\! \left(x \right)-F_{2}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{2}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{18}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{2}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{42}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{43}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{18}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{18}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{0}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{50}\! \left(x , 1\right)\\ F_{50}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{52}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= y F_{25}\! \left(x \right)\\ F_{53}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)\\ F_{54}\! \left(x \right) &= F_{10}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{56}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{0}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{18}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{18}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{18} \left(x \right)^{2} F_{0}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{62}\! \left(x \right)\\ F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{94}\! \left(x \right)}\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= \frac{F_{68}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{2}\! \left(x \right)-F_{74}\! \left(x \right)-F_{86}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{18}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{73}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x , 1\right)\\ F_{79}\! \left(x , y\right) &= F_{20}\! \left(x \right)+F_{80}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{81}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{84}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{85}\! \left(x , y\right) &= y x\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x , 1\right)\\ F_{88}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{50}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\ F_{89}\! \left(x \right) &= F_{2}\! \left(x \right) F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{91}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{92}\! \left(x \right)-F_{93}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{18}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{18}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{18}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{19}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{0}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{0}\! \left(x \right) F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{18}\! \left(x \right)}\\ F_{112}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{30}\! \left(x \right) F_{55}\! \left(x \right)\\ \end{align*}\)