Av(13452, 13542, 31452, 31542, 35142)
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Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3505, 20908, 128618, 809350, 5182356, 33644000, 220881267, 1463706874, ...
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Implicit Equation for the Generating Function
\(\displaystyle x^{3} \left(x -1\right) F \left(x \right)^{6}-x \left(x^{3}+4 x^{2}-6 x +2\right) F \left(x \right)^{5}+x \left(5 x^{2}-8 x +4\right) F \left(x \right)^{4}+\left(-x^{3}+x^{2}-3 x +1\right) F \left(x \right)^{3}+\left(x +3\right) \left(x -1\right) F \left(x \right)^{2}+\left(-x +3\right) F \! \left(x \right)-1 = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 115\)
\(\displaystyle a(6) = 614\)
\(\displaystyle a(7) = 3505\)
\(\displaystyle a(8) = 20908\)
\(\displaystyle a(9) = 128618\)
\(\displaystyle a(10) = 809350\)
\(\displaystyle a(11) = 5182356\)
\(\displaystyle a(12) = 33644000\)
\(\displaystyle a(13) = 220881267\)
\(\displaystyle a(14) = 1463706874\)
\(\displaystyle a(15) = 9776068922\)
\(\displaystyle a(16) = 65735383404\)
\(\displaystyle a(17) = 444599857141\)
\(\displaystyle a(18) = 3022452573452\)
\(\displaystyle a(19) = 20640065878034\)
\(\displaystyle a(20) = 141517132511472\)
\(\displaystyle a(21) = 973806087982356\)
\(\displaystyle a(22) = 6722764379842778\)
\(\displaystyle a(23) = 46548278926824271\)
\(\displaystyle a(24) = 323166267019154276\)
\(\displaystyle a(25) = 2249138366572828402\)
\(\displaystyle a(26) = 15688719004709776726\)
\(\displaystyle a(27) = 109663895830829468040\)
\(\displaystyle a(28) = 768028208309188897280\)
\(\displaystyle a(29) = 5388499610944539135015\)
\(\displaystyle a(30) = 37868836213894328856934\)
\(\displaystyle a(31) = 266545406427271185330745\)
\(\displaystyle a(32) = 1878849824759329730296060\)
\(\displaystyle a(33) = 13261882775939604907187618\)
\(\displaystyle a(34) = 93729178127513300464500450\)
\(\displaystyle a(35) = 663236458518588051737346400\)
\(\displaystyle a(36) = 4698467242507133119683161016\)
\(\displaystyle a(37) = 33320461970652600560210342629\)
\(\displaystyle a(38) = 236541756928568840037909728388\)
\(\displaystyle a(39) = 1680829247439680294170531763074\)
\(\displaystyle a(40) = 11954656680101484482292031449048\)
\(\displaystyle a(41) = 85099833852712495700674427333044\)
\(\displaystyle a(42) = 606289723070108584657046201467376\)
\(\displaystyle a(43) = 4322895056793825231279983199259276\)
\(\displaystyle a(44) = 30845829213871942369070051910408576\)
\(\displaystyle a(45) = 220257562444010751427475256038946100\)
\(\displaystyle a(46) = 1573852960974784786787175501248099470\)
\(\displaystyle a(47) = 11253397136086399744911985897006323376\)
\(\displaystyle a{\left(n + 48 \right)} = - \frac{1372261 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(2 n + 1\right) a{\left(n \right)}}{22020096 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{121 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(117174349 n^{2} + 723457916 n + 820141140\right) a{\left(n + 1 \right)}}{220200960 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{11 \left(n + 2\right) \left(n + 3\right) \left(95272389953 n^{3} + 1073383234590 n^{2} + 3866660692927 n + 4429071314280\right) a{\left(n + 2 \right)}}{220200960 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(n + 3\right) \left(12747651815227 n^{4} + 222920449363144 n^{3} + 1447432003274493 n^{2} + 4135640790891036 n + 4387253013631360\right) a{\left(n + 3 \right)}}{73400320 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(87900 n^{5} + 20601492 n^{4} + 1930989277 n^{3} + 90478001655 n^{2} + 2119281455051 n + 19852139470905\right) a{\left(n + 47 \right)}}{224 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(60223364 n^{5} + 13849056328 n^{4} + 1273682089661 n^{3} + 58559628905069 n^{2} + 1345961736203612 n + 12372427908085536\right) a{\left(n + 46 \right)}}{3584 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(16870368866 n^{5} + 3813513829711 n^{4} + 344770452842068 n^{3} + 15582934662511175 n^{2} + 352114135736478180 n + 3182168319381553248\right) a{\left(n + 45 \right)}}{43008 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(1915536456164 n^{5} + 429798971477305 n^{4} + 38564555506683895 n^{3} + 1729694939596068380 n^{2} + 38780119469366045316 n + 347694183245253836880\right) a{\left(n + 44 \right)}}{430080 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(17601641463284 n^{5} + 3358182591896875 n^{4} + 251467786185026005 n^{3} + 9178925521650862955 n^{2} + 161609842351445886411 n + 1077471130017908290950\right) a{\left(n + 43 \right)}}{860160 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(593420218371539 n^{5} + 14765871309868785 n^{4} + 146250488230265755 n^{3} + 720615287065534335 n^{2} + 1766091473726185146 n + 1722150171424313880\right) a{\left(n + 4 \right)}}{146800640 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(2129874242931927 n^{5} + 437669568485816935 n^{4} + 35934968297003162625 n^{3} + 1473509370600526043285 n^{2} + 30173594990458891900668 n + 246831635027417164212240\right) a{\left(n + 42 \right)}}{1146880 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(11898164831140487 n^{5} + 350076582196969432 n^{4} + 4110717639657793969 n^{3} + 24075481609032539984 n^{2} + 70318154421265348848 n + 81927287665148698776\right) a{\left(n + 5 \right)}}{176160768 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(253949122183741763 n^{5} + 8647974566468180955 n^{4} + 117653008387831083195 n^{3} + 799225265200347767075 n^{2} + 2710597596214775904392 n + 3671455946792453864460\right) a{\left(n + 6 \right)}}{293601280 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(276907819115298817 n^{5} + 56073187794044661860 n^{4} + 4539037886298648105380 n^{3} + 183596342847082789120480 n^{2} + 3710637341017822963836663 n + 29977769631186589551737760\right) a{\left(n + 41 \right)}}{6881280 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(2581854725012700094 n^{5} + 99931675788859447725 n^{4} + 1545747741966135636075 n^{3} + 11943156371600126934000 n^{2} + 46091169131040967016906 n + 71072191785046469428560\right) a{\left(n + 7 \right)}}{293601280 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(7731847818067523539 n^{5} + 1534343548471988231030 n^{4} + 121735965980170012722305 n^{3} + 4827021707162289034415350 n^{2} + 95653420111431336101163456 n + 757825630135709448347056440\right) a{\left(n + 40 \right)}}{13762560 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(63453843517874653127 n^{5} + 2747563612692829133605 n^{4} + 47544426601125252572410 n^{3} + 410970663699338063260325 n^{2} + 1774470907627435134938853 n + 3061622629898942268537180\right) a{\left(n + 8 \right)}}{880803840 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(80288145525671635813 n^{5} + 15584158414511776468295 n^{4} + 1209511645096495280251025 n^{3} + 46918094756082980439564355 n^{2} + 909647276302140464336013942 n + 7051745537616294267891863490\right) a{\left(n + 39 \right)}}{13762560 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(838410858087292253413 n^{5} + 40042579806271339264190 n^{4} + 764100673973273647376315 n^{3} + 7281887162520316044027970 n^{2} + 34657133791755013447594092 n + 65898634451773374116555400\right) a{\left(n + 9 \right)}}{1761607680 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(1470103420920584710653 n^{5} + 76401529286438698108120 n^{4} + 1585481449116752269439410 n^{3} + 16421292553893880761821020 n^{2} + 84880682447741533783115427 n + 175153980672266340774562530\right) a{\left(n + 10 \right)}}{587202560 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(1747701998381196551227 n^{5} + 331450358914546110949680 n^{4} + 25135716362639892184494965 n^{3} + 952786520965295024400640400 n^{2} + 18052250014046669292013349008 n + 136769178715006480787288090400\right) a{\left(n + 38 \right)}}{36700160 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(7104343218127887964963 n^{5} + 395094640665699680695316 n^{4} + 8757954457952149092844520 n^{3} + 96692778952339980151945711 n^{2} + 531499089588341632209369366 n + 1163081865309080517025533720\right) a{\left(n + 11 \right)}}{704643072 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(23093778118551864219263 n^{5} + 4275710003684384095013945 n^{4} + 316566562096008140918702915 n^{3} + 11715909466559172156537242715 n^{2} + 216741324080898846014463114522 n + 1603440025405050133256980530000\right) a{\left(n + 37 \right)}}{73400320 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(30113418233043575092784 n^{5} + 100200818398816745117865 n^{4} - 51250317492868497444822220 n^{3} - 1443921689363059700234489035 n^{2} - 14979514747978119511398691314 n - 54988824000660576977286435840\right) a{\left(n + 13 \right)}}{2348810240 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(191371609211320039849357 n^{5} + 10939628525443005752001140 n^{4} + 246824464105638358899344585 n^{3} + 2737977507197157167122962760 n^{2} + 14855670775548911195283760158 n + 31287205771381907712278768160\right) a{\left(n + 12 \right)}}{7046430720 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(377254049686667082544123 n^{5} + 68138800772151427598270405 n^{4} + 4921727694452263742398278125 n^{3} + 177711008092338314375989941355 n^{2} + 3207641527711304381898993510732 n + 23153845636778929650736073903700\right) a{\left(n + 36 \right)}}{220200960 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(2573310228210610676660134 n^{5} + 213427612852978057707668555 n^{4} + 6990513229541192099201200400 n^{3} + 113294969702731500101213778805 n^{2} + 910161553021049860841805232326 n + 2903369524703046679374906893460\right) a{\left(n + 14 \right)}}{7046430720 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(2742707896262077586244797 n^{5} + 482929316235704990174236135 n^{4} + 34006884451900187533377862957 n^{3} + 1197128725367562245710681094201 n^{2} + 21067209765539087568461984308542 n + 148271180449951821976759796155848\right) a{\left(n + 35 \right)}}{352321536 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(14182966601087239933534472 n^{5} + 2368168171783645576009543065 n^{4} + 158148056734806890239744413010 n^{3} + 5279985408878372026543712963720 n^{2} + 88129388801991589034745523816183 n + 588328040592414614946487979091210\right) a{\left(n + 33 \right)}}{146800640 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(18650804307112593115511849 n^{5} + 1550903418590239965620237260 n^{4} + 51428316166092750139773583525 n^{3} + 850311069505992461752841810750 n^{2} + 7011528967300102698685001411136 n + 23071984531195809543915190503600\right) a{\left(n + 15 \right)}}{7046430720 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(28485076469064352392447834 n^{5} + 2469076050166376074639316475 n^{4} + 85495247073774204655367534555 n^{3} + 1478355540741597045371444901325 n^{2} + 12766494405941851538785417927071 n + 44048829956289382495084698156060\right) a{\left(n + 16 \right)}}{2348810240 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(52469088412039523749413461 n^{5} + 8999975518453504948757589955 n^{4} + 617408971106125520845944707995 n^{3} + 21174345199846745062214852076965 n^{2} + 363039677828185651296875134081944 n + 2489412192599806066982013170363280\right) a{\left(n + 34 \right)}}{1761607680 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(156839581440052343137394027 n^{5} + 25471713934466519162196119315 n^{4} + 1654534222105173015850323992640 n^{3} + 53730393413981041113713861795795 n^{2} + 872353471319456600867870442315873 n + 5664800770272925350522645010233510\right) a{\left(n + 32 \right)}}{587202560 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(304336605893047449726144686 n^{5} + 27684374396556482356064867395 n^{4} + 1006617127418433728866405185025 n^{3} + 18287842700572719404082517386620 n^{2} + 166011459980241493643332947498804 n + 602406107837729873785866696071040\right) a{\left(n + 17 \right)}}{7046430720 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(1195681269914584127639295851 n^{5} + 114259035997890654429121260105 n^{4} + 4365464483556978407752401188735 n^{3} + 83358226531192692453763327037535 n^{2} + 795513771095007815094601551318014 n + 3035436007604196508462597823945280\right) a{\left(n + 18 \right)}}{9395240960 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(3735376452578875089860231503 n^{5} + 411251329940588974513022043317 n^{4} + 18107413701571570374070420803941 n^{3} + 398557523230519323605444790519265 n^{2} + 4385411070095274651233908451875854 n + 19297607450098268541678859945629792\right) a{\left(n + 21 \right)}}{2818572288 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(4453059313807702139202452507 n^{5} + 702807282965147272437310839505 n^{4} + 44364462158507948136081365555215 n^{3} + 1400124877235099735349970529108615 n^{2} + 22091857167543973067959369795885278 n + 139419279680624834486652932627761200\right) a{\left(n + 31 \right)}}{7046430720 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(4502194825426387366502260453 n^{5} + 451649537247705941958966500870 n^{4} + 18117717646017028460984441424635 n^{3} + 363279551121010601509444332495130 n^{2} + 3640950497603237971616056834917612 n + 14592027877836148958302961814941280\right) a{\left(n + 19 \right)}}{14092861440 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(4523863281037894222106651099 n^{5} + 693175643692426273112977886440 n^{4} + 42481628025196693231113954094825 n^{3} + 1301649814005246946025261078733680 n^{2} + 19939917669888387461097564306950976 n + 122174259863027891315307901308574020\right) a{\left(n + 30 \right)}}{3523215360 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(5216409798861513352680111376 n^{5} + 726402227213486900788387381715 n^{4} + 40457422872228038623950725507950 n^{3} + 1126535814586850645045650187875105 n^{2} + 15682583500914541724999562272742364 n + 87318451544337941491739835469114410\right) a{\left(n + 27 \right)}}{1174405120 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(5277263562044206768991988401 n^{5} + 784215098426536563670647886585 n^{4} + 46610669253955069325381280885395 n^{3} + 1385064522026160844792166862050695 n^{2} + 20577372564482441919810180605272224 n + 122274452922794508016218296666446620\right) a{\left(n + 29 \right)}}{2348810240 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(6530390400356011267464375287 n^{5} + 686846458422385597814285028395 n^{4} + 28889360452563204517153064992315 n^{3} + 607412546241057967621403962186325 n^{2} + 6384059006217101419778887458348638 n + 26832861090726132628585618593078240\right) a{\left(n + 20 \right)}}{9395240960 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(7973876947351988075257112079 n^{5} + 1147818515759492489611599226035 n^{4} + 66084193307264754114301263015685 n^{3} + 1902186546635747691152143852591085 n^{2} + 27374119523497789896971761849980816 n + 157561122556483173536151493504933380\right) a{\left(n + 28 \right)}}{2348810240 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(9485477836111064932937179653 n^{5} + 1275918343582773551253455967033 n^{4} + 68642955003234303432322285458265 n^{3} + 1846240787159825254027056326609287 n^{2} + 24825600841171684911534536592366322 n + 133511891446098882157170704575246224\right) a{\left(n + 26 \right)}}{1879048192 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(12560707639531989023657759005 n^{5} + 1444976196374158618243726892843 n^{4} + 66480395087073961391473122765173 n^{3} + 1529050868406270854068785912245317 n^{2} + 17581048491290608638372634421866374 n + 80844611999722977668829418365687576\right) a{\left(n + 22 \right)}}{5637144576 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(23496860034591082886067432367 n^{5} + 3048004741164763128997244551460 n^{4} + 158133779223548514975003222858685 n^{3} + 4101535234096398801986048974640220 n^{2} + 53183942547760782062954926935027308 n + 275814006494461262988055156466712360\right) a{\left(n + 25 \right)}}{4697620480 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} - \frac{\left(46650464079766361698388361383 n^{5} + 5596794619267737868615167427270 n^{4} + 268543877280336885814600933781605 n^{3} + 6441585722098562021494689862192010 n^{2} + 77245122668253282337045277016218172 n + 370458101777353329835109817887580000\right) a{\left(n + 23 \right)}}{14092861440 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)} + \frac{\left(61153134784819744274791605749 n^{5} + 7636278758349941179243752126790 n^{4} + 381366409382040427465410682318315 n^{3} + 9521602699671222794063510604668750 n^{2} + 118845813757928628749119942786643856 n + 593270996419961331005944831200417180\right) a{\left(n + 24 \right)}}{14092861440 \left(n + 46\right) \left(n + 48\right) \left(n + 50\right) \left(2 n + 93\right) \left(2 n + 97\right)}, \quad n \geq 48\)
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 288 rules.

Finding the specification took 64266 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{12}\! \left(x \right) x +F_{12} \left(x \right)^{2}-2 F_{12}\! \left(x \right)+2\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{19}\! \left(x \right)\\ F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{18}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{19}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{4}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{17}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{0}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{0}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{49}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{46}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{4}\! \left(x \right) F_{56}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{60}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{64}\! \left(x \right) x +F_{64} \left(x \right)^{2}+x\\ F_{65}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{67}\! \left(x \right) &= -F_{70}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{69}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{2}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{71}\! \left(x \right) &= -F_{75}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{2}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{4}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{17}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{245}\! \left(x \right) F_{4}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{228}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{0} \left(x \right)^{2}}\\ F_{90}\! \left(x \right) &= -F_{218}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= -F_{205}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= -F_{171}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{4}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= -F_{170}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{145}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{107}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{2}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{118}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{115}\! \left(x \right) &= -F_{118}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{117}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= -F_{37}\! \left(x \right)+F_{115}\! \left(x \right)\\ F_{123}\! \left(x \right) &= -F_{120}\! \left(x \right)+F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= -F_{37}\! \left(x \right)+F_{127}\! \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_{4}\! \left(x \right)}\\ F_{129}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{136}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{135}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{105}\! \left(x \right) F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{147}\! \left(x \right) &= \frac{F_{148}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{134}\! \left(x \right) F_{151}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{157}\! \left(x \right)\\ F_{152}\! \left(x \right) &= -F_{155}\! \left(x \right)+F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= \frac{F_{154}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{154}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{152}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{160}\! \left(x \right) &= \frac{F_{161}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= -F_{165}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= \frac{F_{164}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{164}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{167}\! \left(x \right) &= \frac{F_{168}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{168}\! \left(x \right) &= F_{127}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{151}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{29}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{134}\! \left(x \right) F_{173}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{173}\! \left(x \right) &= \frac{F_{174}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= -F_{176}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{178}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{178}\! \left(x \right) &= \frac{F_{179}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{4}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{187}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{204}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{203}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{197}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{0}\! \left(x \right) F_{189}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{192}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{202}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{0}\! \left(x \right) F_{198}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{202}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{183}\! \left(x \right) F_{198}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{134}\! \left(x \right) F_{209}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{209}\! \left(x \right) &= \frac{F_{210}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= -F_{214}\! \left(x \right)+F_{212}\! \left(x \right)\\ F_{212}\! \left(x \right) &= \frac{F_{213}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{213}\! \left(x \right) &= F_{176}\! \left(x \right)\\ F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{216}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{46}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{0} \left(x \right)^{3} F_{178}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{0} \left(x \right)^{2} F_{178}\! \left(x \right) F_{220}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{0}\! \left(x \right) F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{224}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{112}\! \left(x \right) F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{134}\! \left(x \right) F_{4}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{228}\! \left(x \right) &= \frac{F_{229}\! \left(x \right)}{F_{4}\! \left(x \right) F_{46}\! \left(x \right)}\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{243}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{234}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{220}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{237}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{237}\! \left(x \right) &= \frac{F_{238}\! \left(x \right)}{F_{0}\! \left(x \right) F_{4}\! \left(x \right)}\\ F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\ F_{239}\! \left(x \right) &= -F_{242}\! \left(x \right)+F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= \frac{F_{241}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{241}\! \left(x \right) &= F_{220}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{0}\! \left(x \right) F_{234}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{228}\! \left(x \right) F_{4}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{233}\! \left(x \right) F_{4}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{286}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{253}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{233}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{245}\! \left(x \right) F_{257}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{257}\! \left(x \right) &= \frac{F_{258}\! \left(x \right)}{F_{4}\! \left(x \right) F_{55}\! \left(x \right)}\\ F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{268}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{261}\! \left(x \right)+F_{266}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\ F_{262}\! \left(x \right) &= F_{263}\! \left(x \right) F_{4}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{263}\! \left(x \right) &= \frac{F_{264}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{263}\! \left(x \right) F_{4}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{268}\! \left(x \right) &= -F_{285}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= -F_{283}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= \frac{F_{271}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\ F_{272}\! \left(x \right) &= -F_{274}\! \left(x \right)+F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= -F_{19}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{2}\! \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_{280}\! \left(x \right) &= F_{263}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{0}\! \left(x \right) F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= -F_{278}\! \left(x \right)+F_{233}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{284}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{278}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{282}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{287}\! \left(x \right)\\ F_{287}\! \left(x \right) &= F_{237}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point And Col Placements Req Corrob" and has 196 rules.

Finding the specification took 44741 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{195}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{16}\! \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_{4}\! \left(x \right)\\ F_{11}\! \left(x \right) &= \frac{F_{12}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{27}\! \left(x \right) &= x F_{27}\! \left(x \right)+F_{27} \left(x \right)^{2}-2 F_{27}\! \left(x \right)+2\\ F_{28}\! \left(x \right) &= -F_{42}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{30}\! \left(x \right) &= -F_{37}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{33}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{0}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= -F_{27}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= \frac{F_{41}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{49}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{52}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{51}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{4}\! \left(x \right) F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{4}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{59}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{4}\! \left(x \right) F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{53}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{4}\! \left(x \right) F_{45}\! \left(x \right) F_{5}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{4}\! \left(x \right) F_{45}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{43}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{71}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{4}\! \left(x \right) F_{45}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{193}\! \left(x \right)+F_{194}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{4}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{7}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{4}\! \left(x \right) F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{5}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{4}\! \left(x \right) F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{74}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{88}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{174}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{4}\! \left(x \right) F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{0}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= -F_{166}\! \left(x \right)+F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{100}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{101}\! \left(x \right)-F_{145}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{102}\! \left(x \right) &= \frac{F_{103}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{103}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{104}\! \left(x \right)-F_{144}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{106}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{107}\! \left(x \right)-F_{108}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{53}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{114}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{53}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{109}\! \left(x \right) F_{116}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\ F_{119}\! \left(x \right) &= -F_{99}\! \left(x \right)+F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{121}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{122}\! \left(x \right)-F_{140}\! \left(x \right)-F_{143}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\ F_{125}\! \left(x \right) &= \frac{F_{126}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{126}\! \left(x \right) &= -F_{100}\! \left(x \right)-F_{127}\! \left(x \right)-F_{128}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{127}\! \left(x \right) &= 0\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{137}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{47}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{116}\! \left(x \right) F_{4}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{116}\! \left(x \right) F_{139}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{129}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{142}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{4}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{161}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{159}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{87}\! \left(x \right) F_{99}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right) F_{157}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{154}\! \left(x \right) &= \frac{F_{155}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{156}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{156}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= F_{154}\! \left(x \right) F_{4}\! \left(x \right) F_{97}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)+F_{164}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{116}\! \left(x \right) F_{157}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{154}\! \left(x \right) F_{166}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{169}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{118}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{0}\! \left(x \right) F_{154}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{4}\! \left(x \right) F_{50}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{116}\! \left(x \right) F_{180}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{4}\! \left(x \right) F_{74}\! \left(x \right) F_{87}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{154}\! \left(x \right) F_{4}\! \left(x \right) F_{81}\! \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_{4}\! \left(x \right)\\ F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{188}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{189}\! \left(x \right)-F_{193}\! \left(x \right)-F_{194}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{187}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{4}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{180}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{4}\! \left(x \right) F_{74}\! \left(x \right)\\ \end{align*}\)