Av(12354, 12453, 12543, 13254, 13452, 13542, 14253, 14352, 21354, 21453, 21543)
Counting Sequence
1, 1, 2, 6, 24, 109, 527, 2645, 13613, 71395, 380094, 2048688, 11157789, 61311984, 339513674, ...
Implicit Equation for the Generating Function
\(\displaystyle x^{3} \left(3 x^{7}-3 x^{6}+6 x^{5}+29 x^{4}-17 x^{3}-16 x^{2}+16 x -4\right) F \left(x
\right)^{4}+x^{2} \left(x^{9}-2 x^{8}+2 x^{7}+6 x^{6}-73 x^{5}-46 x^{4}+113 x^{3}-x^{2}-48 x +16\right) F \left(x
\right)^{3}+x \left(4 x^{9}-4 x^{8}-22 x^{7}+104 x^{6}+98 x^{5}-170 x^{4}-32 x^{3}+81 x^{2}-7 x -8\right) F \left(x
\right)^{2}+\left(6 x^{9}+3 x^{8}-72 x^{7}-55 x^{6}+100 x^{5}+33 x^{4}-48 x^{3}-9 x^{2}+9 x +1\right) F \! \left(x \right)+4 x^{8}+18 x^{7}+12 x^{6}-21 x^{5}-11 x^{4}+10 x^{3}+5 x^{2}-2 x -1 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 109\)
\(\displaystyle a(6) = 527\)
\(\displaystyle a(7) = 2645\)
\(\displaystyle a(8) = 13613\)
\(\displaystyle a(9) = 71395\)
\(\displaystyle a(10) = 380094\)
\(\displaystyle a(11) = 2048688\)
\(\displaystyle a(12) = 11157789\)
\(\displaystyle a(13) = 61311984\)
\(\displaystyle a(14) = 339513674\)
\(\displaystyle a(15) = 1892739265\)
\(\displaystyle a(16) = 10614437709\)
\(\displaystyle a(17) = 59839071100\)
\(\displaystyle a(18) = 338929444360\)
\(\displaystyle a(19) = 1927801353627\)
\(\displaystyle a(20) = 11006917644885\)
\(\displaystyle a(21) = 63061765711589\)
\(\displaystyle a(22) = 362435177624980\)
\(\displaystyle a(23) = 2089017682564901\)
\(\displaystyle a(24) = 12072560326983946\)
\(\displaystyle a(25) = 69937816981982519\)
\(\displaystyle a(26) = 406069428055799163\)
\(\displaystyle a(27) = 2362614568240198586\)
\(\displaystyle a(28) = 13772923925824565610\)
\(\displaystyle a(29) = 80434601561109906502\)
\(\displaystyle a(30) = 470534657972075514137\)
\(\displaystyle a(31) = 2756929227330404669066\)
\(\displaystyle a(32) = 16177171486817707031040\)
\(\displaystyle a(33) = 95056978597699910246121\)
\(\displaystyle a(34) = 559286967150081333271139\)
\(\displaystyle a(35) = 3294750098297827071932464\)
\(\displaystyle a(36) = 19432013809369619057770403\)
\(\displaystyle a(37) = 114734367063547050218002881\)
\(\displaystyle a(38) = 678148141768962504599746626\)
\(\displaystyle a(39) = 4012248548529381369041643346\)
\(\displaystyle a(40) = 23760844004259810445425423139\)
\(\displaystyle a(41) = 140840258447877684104208584791\)
\(\displaystyle a(42) = 835534177942533858148407100655\)
\(\displaystyle a(43) = 4960859174804905072463129567492\)
\(\displaystyle a(44) = 29477376560033380250373025747616\)
\(\displaystyle a(45) = 175285119620878925529190524845762\)
\(\displaystyle a(46) = 1043065460378039695660922927721240\)
\(\displaystyle a(47) = 6211196477277786226885758328315541\)
\(\displaystyle a(48) = 37010407172259953486302521055205171\)
\(\displaystyle a(49) = 220671274871484688516465187110543602\)
\(\displaystyle a(50) = 1316528396082622208798021105214516734\)
\(\displaystyle a(51) = 7858993291380979247182422272194557096\)
\(\displaystyle a(52) = 46940339506963292223470366004870227880\)
\(\displaystyle a(53) = 280516917854106700606597315477771637625\)
\(\displaystyle a(54) = 1677246209374045224609910897644063185341\)
\(\displaystyle a(55) = 10033475131564753607919901255427688954704\)
\(\displaystyle a(56) = 60050280522744636403821977009680855674470\)
\(\displaystyle a(57) = 359567566484712193868006489326242400521840\)
\(\displaystyle a(58) = 2153976052026900640832658008909542982298783\)
\(\displaystyle a(59) = 12908909325124406237858012374601355938327619\)
\(\displaystyle a(60) = 77396319258135006256185449880459989727058672\)
\(\displaystyle a(61) = 464223588705037656693573953955312202635026405\)
\(\displaystyle a(62) = 2785509154619417158047546164984382552978875307\)
\(\displaystyle a(63) = 16720416060365780859526266677892948323491057066\)
\(\displaystyle a(64) = 100403659245741279750133574135087763725016724193\)
\(\displaystyle a(65) = 603124646674632155336517285943841442876449015122\)
\(\displaystyle a(66) = 3624223812899052215266803141002860541624767762533\)
\(\displaystyle a(67) = 21785567295975991348854445874078331472962656289209\)
\(\displaystyle a(68) = 130997918955751213871311976513302212819727812703744\)
\(\displaystyle a(69) = 787947881162913751725329216543996827025579910983972\)
\(\displaystyle a(70) = 4740937693453312990098961807066038404331525635452787\)
\(\displaystyle a(71) = 28533885611184097903661797583693343688441466812527990\)
\(\displaystyle a(72) = 171784471857830234407175106237476107073382733530421981\)
\(\displaystyle a(73) = 1034498265302331398467749945652713957061215814812850640\)
\(\displaystyle a(74) = 6231537282973319294939833045898702379262538098445690758\)
\(\displaystyle a(75) = 37547153853384425605741689035840492778797538867076455405\)
\(\displaystyle a(76) = 226293557714758051047356358145836394968539531547784939424\)
\(\displaystyle a(77) = 1364199136833748932188681356579619452497833839731087505900\)
\(\displaystyle a(78) = 8226042389157823116432418637108521016737894611608488789887\)
\(\displaystyle a(79) = 49614543036088206552921168124915022557824379244703395223941\)
\(\displaystyle a(80) = 299315575502482638053085326359755668039054589058588563751601\)
\(\displaystyle a(81) = 1806131600964495142653978152917267481048474122905463777316557\)
\(\displaystyle a(82) = 10901011448171857616422104842551099459837057901460876778529075\)
\(\displaystyle a(83) = 65808076023777338175352833882793313232085609965884492951163784\)
\(\displaystyle a(84) = 397360169868338257559762836758444028434215487216618767907320279\)
\(\displaystyle a(85) = 2399827568963475894829827798175536905220619140488265916874247195\)
\(\displaystyle a(86) = 14496535121414971275087182872790257019780019287441442995535293642\)
\(\displaystyle a(87) = 87586027284911361668935314318888173971760078746095722433586152456\)
\(\displaystyle a(88) = 529285417621959783403259313334083720515728423630459316966112143482\)
\(\displaystyle a(89) = 3199098577067537879648693849282899700764811913645257518567753583140\)
\(\displaystyle a(90) = 19339537353738622693422565716990863482540042097945834062367558187005\)
\(\displaystyle a(91) = 116934734462577193287394245887420548518603594918119924124197223281345\)
\(\displaystyle a(92) = 707160950758090675742331029231554995089398380830106405745215940629387\)
\(\displaystyle a(93) = 4277289405151115220817215903722885523276676481761596024461394205722506\)
\(\displaystyle a(94) = 25875754676654321006825030460811129384009080963590889782260584720143363\)
\(\displaystyle a(95) = 156563270530676598410493494737380787134052521652874173375653431330734287\)
\(\displaystyle a{\left(n + 96 \right)} = - \frac{5 \left(n - 1\right) \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{24272 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(n + 2\right) \left(1931 n^{2} + 7019 n - 30\right) a{\left(n + 1 \right)}}{145632 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(236746 n + 22276539\right) a{\left(n + 95 \right)}}{4551 \left(n + 97\right)} - \frac{\left(17453886 n^{2} + 3266701107 n + 152847256276\right) a{\left(n + 94 \right)}}{13653 \left(n + 96\right) \left(n + 97\right)} - \frac{\left(91468 n^{3} + 842853 n^{2} + 2193686 n + 1432065\right) a{\left(n + 2 \right)}}{291264 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(1053416 n^{3} + 13846577 n^{2} + 54086644 n + 60898669\right) a{\left(n + 3 \right)}}{291264 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(10011419 n^{3} + 193037064 n^{2} + 1072041655 n + 1737800874\right) a{\left(n + 4 \right)}}{582528 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(81689498 n^{3} + 638867479 n^{2} - 171460139 n - 5398499596\right) a{\left(n + 5 \right)}}{1165056 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(5417127130 n^{3} + 99324198985 n^{2} + 597152797493 n + 1187780648738\right) a{\left(n + 6 \right)}}{3495168 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(9806420255 n^{3} + 2737611223104 n^{2} + 254740130364073 n + 7901095242961728\right) a{\left(n + 93 \right)}}{491508 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(11291843166 n^{3} + 254579830757 n^{2} + 1900078485509 n + 4694420441732\right) a{\left(n + 7 \right)}}{1165056 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(110018908019 n^{3} + 30374489802429 n^{2} + 2795199837401344 n + 85739101139026344\right) a{\left(n + 92 \right)}}{491508 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(166738322367 n^{3} + 4265009473098 n^{2} + 36895100146543 n + 107147557555108\right) a{\left(n + 8 \right)}}{6990336 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(473913395065 n^{3} + 129340965278652 n^{2} + 11766059859787727 n + 356766247908220656\right) a{\left(n + 91 \right)}}{245754 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(874220742321 n^{3} + 29962767418265 n^{2} + 309715001653608 n + 999657703731892\right) a{\left(n + 9 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(6492672978644 n^{3} + 1751079281284179 n^{2} + 157412416718272771 n + 4716532373209280976\right) a{\left(n + 90 \right)}}{491508 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(25596884273893 n^{3} + 918058933207746 n^{2} + 10502188113611531 n + 38766387879776994\right) a{\left(n + 10 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(29812758660421 n^{3} + 1238224801431879 n^{2} + 16335628016368136 n + 69379688127937320\right) a{\left(n + 11 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(34053996487537 n^{3} + 1462281598172624 n^{2} + 20119804006656373 n + 89643062751763602\right) a{\left(n + 12 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(71615042948765 n^{3} + 19082538355419054 n^{2} + 1694765279016534553 n + 50167678801924021860\right) a{\left(n + 89 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(315721570151257 n^{3} + 83106428234833416 n^{2} + 7291133804609784713 n + 213198794812202949366\right) a{\left(n + 88 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(604490781155707 n^{3} + 30962816168866551 n^{2} + 494098196261413364 n + 2515432269330453276\right) a{\left(n + 13 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(847196034423773 n^{3} + 32953968902269446 n^{2} + 420407732638213537 n + 1751882347287564864\right) a{\left(n + 14 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1078561135625707 n^{3} + 280428848702700717 n^{2} + 24300582223039374674 n + 701819355775971149904\right) a{\left(n + 87 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1112103805360769 n^{3} + 281159241498026893 n^{2} + 23685426182308532320 n + 664852789117485533678\right) a{\left(n + 85 \right)}}{327672 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1275573463419677 n^{3} + 12466104004482698 n^{2} - 584948479507778701 n - 7308963649273391958\right) a{\left(n + 16 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(2441699937680182 n^{3} + 142977972727265256 n^{2} + 2624006530730762327 n + 15414064305524467926\right) a{\left(n + 15 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(2629496670552121 n^{3} + 675038712418882788 n^{2} + 57753644941448887463 n + 1646730152090055735768\right) a{\left(n + 86 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(3016993230978887 n^{3} + 766740494118952799 n^{2} + 64961546484714685074 n + 1834844108694192939772\right) a{\left(n + 84 \right)}}{655344 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(17044630331068036 n^{3} + 16565642331995239284 n^{2} + 692320812708310627967 n + 7381114104892067536257\right) a{\left(n + 22 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(25863716188239338 n^{3} + 5779736637648219 n^{2} - 24941364029626424159 n - 299370372848021967132\right) a{\left(n + 18 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(26741499025689065 n^{3} + 6508258401585778257 n^{2} + 527818920481360459518 n + 14264015168279555623872\right) a{\left(n + 81 \right)}}{655344 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(33745879689267748 n^{3} + 1990475566085270403 n^{2} + 38144123095380135713 n + 238774190112279666456\right) a{\left(n + 17 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(68629193630289001 n^{3} + 17099587877034870945 n^{2} + 1420098188908502792924 n + 39310359042726326212056\right) a{\left(n + 83 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(80764022359999277 n^{3} + 4586138353356016388 n^{2} + 86021738394945830849 n + 532440853983964959266\right) a{\left(n + 19 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(113741247179650309 n^{3} - 1030391536123194039 n^{2} - 175983756260484892564 n - 2192912088847826037150\right) a{\left(n + 20 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(154411263217333418 n^{3} + 37987066638217354869 n^{2} + 3114746807709077102791 n + 85121429442020146083120\right) a{\left(n + 82 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(472304447927134333 n^{3} + 113374202572992357720 n^{2} + 9071409777686877383711 n + 241938079002512710101774\right) a{\left(n + 80 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(517558520064422976 n^{3} + 29968938077491010567 n^{2} + 568769602476852371571 n + 3520017385269536815376\right) a{\left(n + 21 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(657469909822192555 n^{3} + 155933499335880266205 n^{2} + 12323913629273438501492 n + 324566143955964929418732\right) a{\left(n + 78 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1284971724544319648 n^{3} + 305204197452520676769 n^{2} + 24161891741208166118647 n + 637550035739760422929092\right) a{\left(n + 79 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1296291280145732645 n^{3} + 261724048407044026581 n^{2} + 17384239260405978399316 n + 378522339274531834148916\right) a{\left(n + 75 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(3928939802927643485 n^{3} + 369814962303469439310 n^{2} + 10784380190678463178519 n + 99994938205388407294410\right) a{\left(n + 24 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(5689376438994422565 n^{3} + 1216602909735873758641 n^{2} + 86836841919020305019878 n + 2068620259439464608080356\right) a{\left(n + 70 \right)}}{2621376 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(6443585064842843054 n^{3} + 1484737573929220815573 n^{2} + 114028165679501784058843 n + 2918872933491064422932634\right) a{\left(n + 77 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(7804286130445411280 n^{3} + 479541189800862464115 n^{2} + 9598744678872876033931 n + 62047910958096958220562\right) a{\left(n + 23 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(11255283585042455939 n^{3} + 716931540517744156429 n^{2} + 13084924712313204672576 n + 51148349970485818677815\right) a{\left(n + 29 \right)}}{5242752 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(12438029878829103835 n^{3} + 3936245032301897319554 n^{2} + 208576881537429325254887 n + 3052090559633400474339648\right) a{\left(n + 31 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(13552229574461026694 n^{3} + 3099206080746766024677 n^{2} + 236222169729703132747765 n + 6000960848159058954981762\right) a{\left(n + 76 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(26567409320476986949 n^{3} + 5882975413644035271270 n^{2} + 434178869700579889741261 n + 10679820253972961784200124\right) a{\left(n + 74 \right)}}{2621376 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(26973246677678699147 n^{3} + 1841156076507688553523 n^{2} + 40207328837502609352518 n + 274418109105456245018964\right) a{\left(n + 27 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(29512709503670116412 n^{3} + 2461523486352676276755 n^{2} + 67209798719402489521183 n + 601652586526315182059184\right) a{\left(n + 26 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(29541914706131845429 n^{3} + 1934928620293491573819 n^{2} + 41092878750775971688874 n + 279630721887264436380924\right) a{\left(n + 25 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(46068150255393681986 n^{3} + 3891341629811454708087 n^{2} + 108283471898924767700821 n + 991796525238800835734954\right) a{\left(n + 28 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(80170711605903337817 n^{3} + 17627583644933911466439 n^{2} + 1291725208512283195860004 n + 31546238056729117341028296\right) a{\left(n + 73 \right)}}{7864128 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(123602778243711335215 n^{3} + 26544468064105647153183 n^{2} + 1899979657625010339108068 n + 45326554356443216213383164\right) a{\left(n + 72 \right)}}{7864128 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(155016542901857255380 n^{3} + 32985312848988743727603 n^{2} + 2339247402503386067222255 n + 55289692313515418870176488\right) a{\left(n + 71 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(291266458484372100945 n^{3} + 32923474554009249879304 n^{2} + 1234037616261382581039108 n + 15346607195998910644972378\right) a{\left(n + 35 \right)}}{3495168 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(445017375853601851787 n^{3} + 90509545067815419080094 n^{2} + 6134405220734404748833231 n + 138551192662395723694698216\right) a{\left(n + 68 \right)}}{7864128 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(453509146313525547055 n^{3} + 94092217568866247430069 n^{2} + 6506635352516429207207924 n + 149966125196900577390360608\right) a{\left(n + 69 \right)}}{5242752 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(475803448023903553611 n^{3} + 44315579509388183472909 n^{2} + 1362546016615950590378916 n + 13808277657510344672567846\right) a{\left(n + 32 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(489407191210252640521 n^{3} + 43203724978014805635954 n^{2} + 1258008978133344281759741 n + 12065210331625395598027188\right) a{\left(n + 30 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(604901920746131413998 n^{3} + 172845816094716602551485 n^{2} + 14116762108645158664415623 n + 355409018119460803416357008\right) a{\left(n + 59 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(674075838747460796041 n^{3} + 137174156492152989283511 n^{2} + 9303584543415264372271938 n + 210300504364057157548237748\right) a{\left(n + 67 \right)}}{5242752 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(1224233877269725888982 n^{3} + 140907547348999526586615 n^{2} + 5299790195673099516227395 n + 65427304323751111287430878\right) a{\left(n + 33 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1593457597715345497363 n^{3} + 222323347755534876290583 n^{2} + 9284009199101777340775754 n + 100782022949190445192066512\right) a{\left(n + 61 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(2216119576298564038501 n^{3} + 442408313943353083531233 n^{2} + 29426073557333698394629496 n + 652111723876475313895998510\right) a{\left(n + 65 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(2465372904586309329589 n^{3} + 596076527920476911685297 n^{2} + 43269626142318829060625789 n + 986748970689747007798423977\right) a{\left(n + 55 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(2682250233714155287745 n^{3} + 536017298517598232160660 n^{2} + 35699195298550818934402051 n + 792386026677501468383867028\right) a{\left(n + 66 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(2845060275064433237249 n^{3} + 297887532254515496521117 n^{2} + 10327159433004520659110856 n + 118428720586603419228099196\right) a{\left(n + 36 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(3643468506886056016316 n^{3} + 359397786192771283968375 n^{2} + 11717387551040584863469183 n + 126093059289776360943288054\right) a{\left(n + 34 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(3696633294052016141203 n^{3} + 703445522611862415238674 n^{2} + 44610360353728389769496843 n + 942801571876044989291811864\right) a{\left(n + 63 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(4090971439792808127162 n^{3} + 883717828252038368600745 n^{2} + 59263725236497986526543043 n + 1267497111368017409021646746\right) a{\left(n + 53 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(4553772513829705316281 n^{3} + 1101340370931322079699967 n^{2} + 81324139442239255098419426 n + 1900352913672994580350889022\right) a{\left(n + 57 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(5244715798458510804266 n^{3} + 1030916126863711068441291 n^{2} + 67511880870646150412977579 n + 1472977237545694016632552938\right) a{\left(n + 64 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(5753663722474788939737 n^{3} + 1105408299584065095342179 n^{2} + 70723613947796895987665840 n + 1506904962297472675901993416\right) a{\left(n + 62 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(7507118253729382374446 n^{3} + 874005598609341914647746 n^{2} + 33843049908666311942693077 n + 435914514208718005201083198\right) a{\left(n + 37 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(8504460835684780326225 n^{3} + 1577417593746233064356505 n^{2} + 97438660997698287793872486 n + 2004540279094925155193985620\right) a{\left(n + 60 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(9447905020587300876939 n^{3} + 1632229963762165450629394 n^{2} + 92793879681425116097200501 n + 1740200860294220793132259532\right) a{\left(n + 51 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(11088723094364116713068 n^{3} + 1344300671630662737878777 n^{2} + 54260943263994760066345339 n + 729247842058590013449898688\right) a{\left(n + 39 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(18807588880197228400691 n^{3} + 2091297166533533426781765 n^{2} + 77148929821534460315426572 n + 943696612836697805502016920\right) a{\left(n + 38 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(29462658015195395917647 n^{3} + 4280245280717689081149740 n^{2} + 207117299061093297106100157 n + 3338323318854135002197621806\right) a{\left(n + 47 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(29488282667546660952793 n^{3} + 4555686068174362444921200 n^{2} + 234076991362988121387012020 n + 4000725282619890149321483988\right) a{\left(n + 49 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(29646835748541097714948 n^{3} + 3753777057539145329545437 n^{2} + 158321372560740936626004830 n + 2224338960010950954999959667\right) a{\left(n + 41 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(36159082956161869565276 n^{3} + 4497041092837524823614645 n^{2} + 186076633565526754883273116 n + 2561263716258656718805824936\right) a{\left(n + 42 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(38716773053239594611187 n^{3} + 4562361102956404566918615 n^{2} + 178665387186481770994532600 n + 2324500684954925129216463528\right) a{\left(n + 40 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(39953185914486089199217 n^{3} + 6379476981500967680458097 n^{2} + 339251379561604787235484078 n + 6008194961536388166398755712\right) a{\left(n + 54 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(42761433239496123217277 n^{3} + 5659069133265260336726610 n^{2} + 249521245487148759415651330 n + 3665609714491095093045845697\right) a{\left(n + 43 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(68741756000281118677097 n^{3} + 12162909307229637910811415 n^{2} + 716979383488317144914664160 n + 14080880012992090193054213592\right) a{\left(n + 58 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(79567058605287551543083 n^{3} + 12200978978245091329094613 n^{2} + 623047612991005741225862513 n + 10594828122394943078279991984\right) a{\left(n + 52 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(82938723321614597523530 n^{3} + 11331333883332892768949220 n^{2} + 515583099071788010779212631 n + 7812574596270689498767841499\right) a{\left(n + 46 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(89515094182528772470315 n^{3} + 15014035534245162852365733 n^{2} + 838991619797153796579785114 n + 15619634042383827534734849388\right) a{\left(n + 56 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(95455423336974647246645 n^{3} + 14109387858712773857434173 n^{2} + 694597138125946481752711573 n + 11388358889722865996129591124\right) a{\left(n + 50 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(98606506820474440846331 n^{3} + 13649972875576544072424621 n^{2} + 629554664608355664067231492 n + 9674250618807423687186362454\right) a{\left(n + 45 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(118524051314236397194546 n^{3} + 15484070989291207771230093 n^{2} + 673457674062067506834360737 n + 9751091226172339544032018596\right) a{\left(n + 44 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(194768714851692730637114 n^{3} + 27720627800539432253062419 n^{2} + 1314101197158184120929178351 n + 20748391331015585137074771378\right) a{\left(n + 48 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)}, \quad n \geq 96\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 109\)
\(\displaystyle a(6) = 527\)
\(\displaystyle a(7) = 2645\)
\(\displaystyle a(8) = 13613\)
\(\displaystyle a(9) = 71395\)
\(\displaystyle a(10) = 380094\)
\(\displaystyle a(11) = 2048688\)
\(\displaystyle a(12) = 11157789\)
\(\displaystyle a(13) = 61311984\)
\(\displaystyle a(14) = 339513674\)
\(\displaystyle a(15) = 1892739265\)
\(\displaystyle a(16) = 10614437709\)
\(\displaystyle a(17) = 59839071100\)
\(\displaystyle a(18) = 338929444360\)
\(\displaystyle a(19) = 1927801353627\)
\(\displaystyle a(20) = 11006917644885\)
\(\displaystyle a(21) = 63061765711589\)
\(\displaystyle a(22) = 362435177624980\)
\(\displaystyle a(23) = 2089017682564901\)
\(\displaystyle a(24) = 12072560326983946\)
\(\displaystyle a(25) = 69937816981982519\)
\(\displaystyle a(26) = 406069428055799163\)
\(\displaystyle a(27) = 2362614568240198586\)
\(\displaystyle a(28) = 13772923925824565610\)
\(\displaystyle a(29) = 80434601561109906502\)
\(\displaystyle a(30) = 470534657972075514137\)
\(\displaystyle a(31) = 2756929227330404669066\)
\(\displaystyle a(32) = 16177171486817707031040\)
\(\displaystyle a(33) = 95056978597699910246121\)
\(\displaystyle a(34) = 559286967150081333271139\)
\(\displaystyle a(35) = 3294750098297827071932464\)
\(\displaystyle a(36) = 19432013809369619057770403\)
\(\displaystyle a(37) = 114734367063547050218002881\)
\(\displaystyle a(38) = 678148141768962504599746626\)
\(\displaystyle a(39) = 4012248548529381369041643346\)
\(\displaystyle a(40) = 23760844004259810445425423139\)
\(\displaystyle a(41) = 140840258447877684104208584791\)
\(\displaystyle a(42) = 835534177942533858148407100655\)
\(\displaystyle a(43) = 4960859174804905072463129567492\)
\(\displaystyle a(44) = 29477376560033380250373025747616\)
\(\displaystyle a(45) = 175285119620878925529190524845762\)
\(\displaystyle a(46) = 1043065460378039695660922927721240\)
\(\displaystyle a(47) = 6211196477277786226885758328315541\)
\(\displaystyle a(48) = 37010407172259953486302521055205171\)
\(\displaystyle a(49) = 220671274871484688516465187110543602\)
\(\displaystyle a(50) = 1316528396082622208798021105214516734\)
\(\displaystyle a(51) = 7858993291380979247182422272194557096\)
\(\displaystyle a(52) = 46940339506963292223470366004870227880\)
\(\displaystyle a(53) = 280516917854106700606597315477771637625\)
\(\displaystyle a(54) = 1677246209374045224609910897644063185341\)
\(\displaystyle a(55) = 10033475131564753607919901255427688954704\)
\(\displaystyle a(56) = 60050280522744636403821977009680855674470\)
\(\displaystyle a(57) = 359567566484712193868006489326242400521840\)
\(\displaystyle a(58) = 2153976052026900640832658008909542982298783\)
\(\displaystyle a(59) = 12908909325124406237858012374601355938327619\)
\(\displaystyle a(60) = 77396319258135006256185449880459989727058672\)
\(\displaystyle a(61) = 464223588705037656693573953955312202635026405\)
\(\displaystyle a(62) = 2785509154619417158047546164984382552978875307\)
\(\displaystyle a(63) = 16720416060365780859526266677892948323491057066\)
\(\displaystyle a(64) = 100403659245741279750133574135087763725016724193\)
\(\displaystyle a(65) = 603124646674632155336517285943841442876449015122\)
\(\displaystyle a(66) = 3624223812899052215266803141002860541624767762533\)
\(\displaystyle a(67) = 21785567295975991348854445874078331472962656289209\)
\(\displaystyle a(68) = 130997918955751213871311976513302212819727812703744\)
\(\displaystyle a(69) = 787947881162913751725329216543996827025579910983972\)
\(\displaystyle a(70) = 4740937693453312990098961807066038404331525635452787\)
\(\displaystyle a(71) = 28533885611184097903661797583693343688441466812527990\)
\(\displaystyle a(72) = 171784471857830234407175106237476107073382733530421981\)
\(\displaystyle a(73) = 1034498265302331398467749945652713957061215814812850640\)
\(\displaystyle a(74) = 6231537282973319294939833045898702379262538098445690758\)
\(\displaystyle a(75) = 37547153853384425605741689035840492778797538867076455405\)
\(\displaystyle a(76) = 226293557714758051047356358145836394968539531547784939424\)
\(\displaystyle a(77) = 1364199136833748932188681356579619452497833839731087505900\)
\(\displaystyle a(78) = 8226042389157823116432418637108521016737894611608488789887\)
\(\displaystyle a(79) = 49614543036088206552921168124915022557824379244703395223941\)
\(\displaystyle a(80) = 299315575502482638053085326359755668039054589058588563751601\)
\(\displaystyle a(81) = 1806131600964495142653978152917267481048474122905463777316557\)
\(\displaystyle a(82) = 10901011448171857616422104842551099459837057901460876778529075\)
\(\displaystyle a(83) = 65808076023777338175352833882793313232085609965884492951163784\)
\(\displaystyle a(84) = 397360169868338257559762836758444028434215487216618767907320279\)
\(\displaystyle a(85) = 2399827568963475894829827798175536905220619140488265916874247195\)
\(\displaystyle a(86) = 14496535121414971275087182872790257019780019287441442995535293642\)
\(\displaystyle a(87) = 87586027284911361668935314318888173971760078746095722433586152456\)
\(\displaystyle a(88) = 529285417621959783403259313334083720515728423630459316966112143482\)
\(\displaystyle a(89) = 3199098577067537879648693849282899700764811913645257518567753583140\)
\(\displaystyle a(90) = 19339537353738622693422565716990863482540042097945834062367558187005\)
\(\displaystyle a(91) = 116934734462577193287394245887420548518603594918119924124197223281345\)
\(\displaystyle a(92) = 707160950758090675742331029231554995089398380830106405745215940629387\)
\(\displaystyle a(93) = 4277289405151115220817215903722885523276676481761596024461394205722506\)
\(\displaystyle a(94) = 25875754676654321006825030460811129384009080963590889782260584720143363\)
\(\displaystyle a(95) = 156563270530676598410493494737380787134052521652874173375653431330734287\)
\(\displaystyle a{\left(n + 96 \right)} = - \frac{5 \left(n - 1\right) \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{24272 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(n + 2\right) \left(1931 n^{2} + 7019 n - 30\right) a{\left(n + 1 \right)}}{145632 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(236746 n + 22276539\right) a{\left(n + 95 \right)}}{4551 \left(n + 97\right)} - \frac{\left(17453886 n^{2} + 3266701107 n + 152847256276\right) a{\left(n + 94 \right)}}{13653 \left(n + 96\right) \left(n + 97\right)} - \frac{\left(91468 n^{3} + 842853 n^{2} + 2193686 n + 1432065\right) a{\left(n + 2 \right)}}{291264 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(1053416 n^{3} + 13846577 n^{2} + 54086644 n + 60898669\right) a{\left(n + 3 \right)}}{291264 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(10011419 n^{3} + 193037064 n^{2} + 1072041655 n + 1737800874\right) a{\left(n + 4 \right)}}{582528 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(81689498 n^{3} + 638867479 n^{2} - 171460139 n - 5398499596\right) a{\left(n + 5 \right)}}{1165056 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(5417127130 n^{3} + 99324198985 n^{2} + 597152797493 n + 1187780648738\right) a{\left(n + 6 \right)}}{3495168 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(9806420255 n^{3} + 2737611223104 n^{2} + 254740130364073 n + 7901095242961728\right) a{\left(n + 93 \right)}}{491508 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(11291843166 n^{3} + 254579830757 n^{2} + 1900078485509 n + 4694420441732\right) a{\left(n + 7 \right)}}{1165056 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(110018908019 n^{3} + 30374489802429 n^{2} + 2795199837401344 n + 85739101139026344\right) a{\left(n + 92 \right)}}{491508 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(166738322367 n^{3} + 4265009473098 n^{2} + 36895100146543 n + 107147557555108\right) a{\left(n + 8 \right)}}{6990336 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(473913395065 n^{3} + 129340965278652 n^{2} + 11766059859787727 n + 356766247908220656\right) a{\left(n + 91 \right)}}{245754 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(874220742321 n^{3} + 29962767418265 n^{2} + 309715001653608 n + 999657703731892\right) a{\left(n + 9 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(6492672978644 n^{3} + 1751079281284179 n^{2} + 157412416718272771 n + 4716532373209280976\right) a{\left(n + 90 \right)}}{491508 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(25596884273893 n^{3} + 918058933207746 n^{2} + 10502188113611531 n + 38766387879776994\right) a{\left(n + 10 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(29812758660421 n^{3} + 1238224801431879 n^{2} + 16335628016368136 n + 69379688127937320\right) a{\left(n + 11 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(34053996487537 n^{3} + 1462281598172624 n^{2} + 20119804006656373 n + 89643062751763602\right) a{\left(n + 12 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(71615042948765 n^{3} + 19082538355419054 n^{2} + 1694765279016534553 n + 50167678801924021860\right) a{\left(n + 89 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(315721570151257 n^{3} + 83106428234833416 n^{2} + 7291133804609784713 n + 213198794812202949366\right) a{\left(n + 88 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(604490781155707 n^{3} + 30962816168866551 n^{2} + 494098196261413364 n + 2515432269330453276\right) a{\left(n + 13 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(847196034423773 n^{3} + 32953968902269446 n^{2} + 420407732638213537 n + 1751882347287564864\right) a{\left(n + 14 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1078561135625707 n^{3} + 280428848702700717 n^{2} + 24300582223039374674 n + 701819355775971149904\right) a{\left(n + 87 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1112103805360769 n^{3} + 281159241498026893 n^{2} + 23685426182308532320 n + 664852789117485533678\right) a{\left(n + 85 \right)}}{327672 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1275573463419677 n^{3} + 12466104004482698 n^{2} - 584948479507778701 n - 7308963649273391958\right) a{\left(n + 16 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(2441699937680182 n^{3} + 142977972727265256 n^{2} + 2624006530730762327 n + 15414064305524467926\right) a{\left(n + 15 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(2629496670552121 n^{3} + 675038712418882788 n^{2} + 57753644941448887463 n + 1646730152090055735768\right) a{\left(n + 86 \right)}}{983016 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(3016993230978887 n^{3} + 766740494118952799 n^{2} + 64961546484714685074 n + 1834844108694192939772\right) a{\left(n + 84 \right)}}{655344 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(17044630331068036 n^{3} + 16565642331995239284 n^{2} + 692320812708310627967 n + 7381114104892067536257\right) a{\left(n + 22 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(25863716188239338 n^{3} + 5779736637648219 n^{2} - 24941364029626424159 n - 299370372848021967132\right) a{\left(n + 18 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(26741499025689065 n^{3} + 6508258401585778257 n^{2} + 527818920481360459518 n + 14264015168279555623872\right) a{\left(n + 81 \right)}}{655344 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(33745879689267748 n^{3} + 1990475566085270403 n^{2} + 38144123095380135713 n + 238774190112279666456\right) a{\left(n + 17 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(68629193630289001 n^{3} + 17099587877034870945 n^{2} + 1420098188908502792924 n + 39310359042726326212056\right) a{\left(n + 83 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(80764022359999277 n^{3} + 4586138353356016388 n^{2} + 86021738394945830849 n + 532440853983964959266\right) a{\left(n + 19 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(113741247179650309 n^{3} - 1030391536123194039 n^{2} - 175983756260484892564 n - 2192912088847826037150\right) a{\left(n + 20 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(154411263217333418 n^{3} + 37987066638217354869 n^{2} + 3114746807709077102791 n + 85121429442020146083120\right) a{\left(n + 82 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(472304447927134333 n^{3} + 113374202572992357720 n^{2} + 9071409777686877383711 n + 241938079002512710101774\right) a{\left(n + 80 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(517558520064422976 n^{3} + 29968938077491010567 n^{2} + 568769602476852371571 n + 3520017385269536815376\right) a{\left(n + 21 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(657469909822192555 n^{3} + 155933499335880266205 n^{2} + 12323913629273438501492 n + 324566143955964929418732\right) a{\left(n + 78 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1284971724544319648 n^{3} + 305204197452520676769 n^{2} + 24161891741208166118647 n + 637550035739760422929092\right) a{\left(n + 79 \right)}}{1966032 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1296291280145732645 n^{3} + 261724048407044026581 n^{2} + 17384239260405978399316 n + 378522339274531834148916\right) a{\left(n + 75 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(3928939802927643485 n^{3} + 369814962303469439310 n^{2} + 10784380190678463178519 n + 99994938205388407294410\right) a{\left(n + 24 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(5689376438994422565 n^{3} + 1216602909735873758641 n^{2} + 86836841919020305019878 n + 2068620259439464608080356\right) a{\left(n + 70 \right)}}{2621376 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(6443585064842843054 n^{3} + 1484737573929220815573 n^{2} + 114028165679501784058843 n + 2918872933491064422932634\right) a{\left(n + 77 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(7804286130445411280 n^{3} + 479541189800862464115 n^{2} + 9598744678872876033931 n + 62047910958096958220562\right) a{\left(n + 23 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(11255283585042455939 n^{3} + 716931540517744156429 n^{2} + 13084924712313204672576 n + 51148349970485818677815\right) a{\left(n + 29 \right)}}{5242752 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(12438029878829103835 n^{3} + 3936245032301897319554 n^{2} + 208576881537429325254887 n + 3052090559633400474339648\right) a{\left(n + 31 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(13552229574461026694 n^{3} + 3099206080746766024677 n^{2} + 236222169729703132747765 n + 6000960848159058954981762\right) a{\left(n + 76 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(26567409320476986949 n^{3} + 5882975413644035271270 n^{2} + 434178869700579889741261 n + 10679820253972961784200124\right) a{\left(n + 74 \right)}}{2621376 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(26973246677678699147 n^{3} + 1841156076507688553523 n^{2} + 40207328837502609352518 n + 274418109105456245018964\right) a{\left(n + 27 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(29512709503670116412 n^{3} + 2461523486352676276755 n^{2} + 67209798719402489521183 n + 601652586526315182059184\right) a{\left(n + 26 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(29541914706131845429 n^{3} + 1934928620293491573819 n^{2} + 41092878750775971688874 n + 279630721887264436380924\right) a{\left(n + 25 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(46068150255393681986 n^{3} + 3891341629811454708087 n^{2} + 108283471898924767700821 n + 991796525238800835734954\right) a{\left(n + 28 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(80170711605903337817 n^{3} + 17627583644933911466439 n^{2} + 1291725208512283195860004 n + 31546238056729117341028296\right) a{\left(n + 73 \right)}}{7864128 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(123602778243711335215 n^{3} + 26544468064105647153183 n^{2} + 1899979657625010339108068 n + 45326554356443216213383164\right) a{\left(n + 72 \right)}}{7864128 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(155016542901857255380 n^{3} + 32985312848988743727603 n^{2} + 2339247402503386067222255 n + 55289692313515418870176488\right) a{\left(n + 71 \right)}}{3932064 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(291266458484372100945 n^{3} + 32923474554009249879304 n^{2} + 1234037616261382581039108 n + 15346607195998910644972378\right) a{\left(n + 35 \right)}}{3495168 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(445017375853601851787 n^{3} + 90509545067815419080094 n^{2} + 6134405220734404748833231 n + 138551192662395723694698216\right) a{\left(n + 68 \right)}}{7864128 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(453509146313525547055 n^{3} + 94092217568866247430069 n^{2} + 6506635352516429207207924 n + 149966125196900577390360608\right) a{\left(n + 69 \right)}}{5242752 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(475803448023903553611 n^{3} + 44315579509388183472909 n^{2} + 1362546016615950590378916 n + 13808277657510344672567846\right) a{\left(n + 32 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(489407191210252640521 n^{3} + 43203724978014805635954 n^{2} + 1258008978133344281759741 n + 12065210331625395598027188\right) a{\left(n + 30 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(604901920746131413998 n^{3} + 172845816094716602551485 n^{2} + 14116762108645158664415623 n + 355409018119460803416357008\right) a{\left(n + 59 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(674075838747460796041 n^{3} + 137174156492152989283511 n^{2} + 9303584543415264372271938 n + 210300504364057157548237748\right) a{\left(n + 67 \right)}}{5242752 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(1224233877269725888982 n^{3} + 140907547348999526586615 n^{2} + 5299790195673099516227395 n + 65427304323751111287430878\right) a{\left(n + 33 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(1593457597715345497363 n^{3} + 222323347755534876290583 n^{2} + 9284009199101777340775754 n + 100782022949190445192066512\right) a{\left(n + 61 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(2216119576298564038501 n^{3} + 442408313943353083531233 n^{2} + 29426073557333698394629496 n + 652111723876475313895998510\right) a{\left(n + 65 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(2465372904586309329589 n^{3} + 596076527920476911685297 n^{2} + 43269626142318829060625789 n + 986748970689747007798423977\right) a{\left(n + 55 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(2682250233714155287745 n^{3} + 536017298517598232160660 n^{2} + 35699195298550818934402051 n + 792386026677501468383867028\right) a{\left(n + 66 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(2845060275064433237249 n^{3} + 297887532254515496521117 n^{2} + 10327159433004520659110856 n + 118428720586603419228099196\right) a{\left(n + 36 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(3643468506886056016316 n^{3} + 359397786192771283968375 n^{2} + 11717387551040584863469183 n + 126093059289776360943288054\right) a{\left(n + 34 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(3696633294052016141203 n^{3} + 703445522611862415238674 n^{2} + 44610360353728389769496843 n + 942801571876044989291811864\right) a{\left(n + 63 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(4090971439792808127162 n^{3} + 883717828252038368600745 n^{2} + 59263725236497986526543043 n + 1267497111368017409021646746\right) a{\left(n + 53 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(4553772513829705316281 n^{3} + 1101340370931322079699967 n^{2} + 81324139442239255098419426 n + 1900352913672994580350889022\right) a{\left(n + 57 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(5244715798458510804266 n^{3} + 1030916126863711068441291 n^{2} + 67511880870646150412977579 n + 1472977237545694016632552938\right) a{\left(n + 64 \right)}}{15728256 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(5753663722474788939737 n^{3} + 1105408299584065095342179 n^{2} + 70723613947796895987665840 n + 1506904962297472675901993416\right) a{\left(n + 62 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(7507118253729382374446 n^{3} + 874005598609341914647746 n^{2} + 33843049908666311942693077 n + 435914514208718005201083198\right) a{\left(n + 37 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(8504460835684780326225 n^{3} + 1577417593746233064356505 n^{2} + 97438660997698287793872486 n + 2004540279094925155193985620\right) a{\left(n + 60 \right)}}{10485504 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(9447905020587300876939 n^{3} + 1632229963762165450629394 n^{2} + 92793879681425116097200501 n + 1740200860294220793132259532\right) a{\left(n + 51 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(11088723094364116713068 n^{3} + 1344300671630662737878777 n^{2} + 54260943263994760066345339 n + 729247842058590013449898688\right) a{\left(n + 39 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(18807588880197228400691 n^{3} + 2091297166533533426781765 n^{2} + 77148929821534460315426572 n + 943696612836697805502016920\right) a{\left(n + 38 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(29462658015195395917647 n^{3} + 4280245280717689081149740 n^{2} + 207117299061093297106100157 n + 3338323318854135002197621806\right) a{\left(n + 47 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(29488282667546660952793 n^{3} + 4555686068174362444921200 n^{2} + 234076991362988121387012020 n + 4000725282619890149321483988\right) a{\left(n + 49 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(29646835748541097714948 n^{3} + 3753777057539145329545437 n^{2} + 158321372560740936626004830 n + 2224338960010950954999959667\right) a{\left(n + 41 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(36159082956161869565276 n^{3} + 4497041092837524823614645 n^{2} + 186076633565526754883273116 n + 2561263716258656718805824936\right) a{\left(n + 42 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(38716773053239594611187 n^{3} + 4562361102956404566918615 n^{2} + 178665387186481770994532600 n + 2324500684954925129216463528\right) a{\left(n + 40 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(39953185914486089199217 n^{3} + 6379476981500967680458097 n^{2} + 339251379561604787235484078 n + 6008194961536388166398755712\right) a{\left(n + 54 \right)}}{20971008 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(42761433239496123217277 n^{3} + 5659069133265260336726610 n^{2} + 249521245487148759415651330 n + 3665609714491095093045845697\right) a{\left(n + 43 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(68741756000281118677097 n^{3} + 12162909307229637910811415 n^{2} + 716979383488317144914664160 n + 14080880012992090193054213592\right) a{\left(n + 58 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(79567058605287551543083 n^{3} + 12200978978245091329094613 n^{2} + 623047612991005741225862513 n + 10594828122394943078279991984\right) a{\left(n + 52 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(82938723321614597523530 n^{3} + 11331333883332892768949220 n^{2} + 515583099071788010779212631 n + 7812574596270689498767841499\right) a{\left(n + 46 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(89515094182528772470315 n^{3} + 15014035534245162852365733 n^{2} + 838991619797153796579785114 n + 15619634042383827534734849388\right) a{\left(n + 56 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} + \frac{\left(95455423336974647246645 n^{3} + 14109387858712773857434173 n^{2} + 694597138125946481752711573 n + 11388358889722865996129591124\right) a{\left(n + 50 \right)}}{31456512 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(98606506820474440846331 n^{3} + 13649972875576544072424621 n^{2} + 629554664608355664067231492 n + 9674250618807423687186362454\right) a{\left(n + 45 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(118524051314236397194546 n^{3} + 15484070989291207771230093 n^{2} + 673457674062067506834360737 n + 9751091226172339544032018596\right) a{\left(n + 44 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)} - \frac{\left(194768714851692730637114 n^{3} + 27720627800539432253062419 n^{2} + 1314101197158184120929178351 n + 20748391331015585137074771378\right) a{\left(n + 48 \right)}}{62913024 \left(n + 95\right) \left(n + 96\right) \left(n + 97\right)}, \quad n \geq 96\)
This specification was found using the strategy pack "Point And Row Placements Req Corrob" and has 109 rules.
Finding the specification took 62628 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_{13}\! \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_{13}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{13}\! \left(x \right) &= x\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{11}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{20}\! \left(x \right) &= 0\\
F_{21}\! \left(x \right) &= F_{13}\! \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_{19}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{24}\! \left(x \right) &= 2 F_{20}\! \left(x \right)+F_{25}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{13}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= \frac{F_{28}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{28}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{32}\! \left(x \right) &= -F_{20}\! \left(x \right)-F_{33}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{13}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{4} \left(x \right)^{2}\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{13}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{13}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{13}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{13}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{45}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{10}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{13}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{65}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{13}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{13}\! \left(x \right) F_{27}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{13}\! \left(x \right) F_{73}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{73}\! \left(x \right) &= \frac{F_{74}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{74}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{13}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= x^{2}\\
F_{86}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{13}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{13}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{4}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{13}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{45}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{60}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{13}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{64}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 1163 rules.
Finding the specification took 70869 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_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{13}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{1125}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{1039}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{13}\! \left(x \right) &= x\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{13}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{13}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{13}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{13}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{13}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{41}\! \left(x \right) &= 0\\
F_{42}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{13}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{13}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{1029}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{1027}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{26}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{13}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{964}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{2}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{13}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{63}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{13}\! \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_{16}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{63}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{13}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{70}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{13}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{13}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{13}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{13}\! \left(x \right) F_{78}\! \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_{81}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{13}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{90}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{13}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{1026}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{1015}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{49}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= -F_{103}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{1014}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{0}\! \left(x \right) F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{13}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{13}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{116}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{117}\! \left(x \right) &= -F_{120}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= \frac{F_{119}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{119}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= -F_{960}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{142}\! \left(x \right)}\\
F_{124}\! \left(x \right) &= -F_{131}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= \frac{F_{126}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{126}\! \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_{13}\! \left(x \right)}\\
F_{129}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{2}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{958}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{13}\! \left(x \right) F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{13}\! \left(x \right) F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{13}\! \left(x \right) F_{136}\! \left(x \right)\\
F_{142}\! \left(x \right) &= \frac{F_{143}\! \left(x \right)}{F_{56}\! \left(x \right)}\\
F_{143}\! \left(x \right) &= -F_{925}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= \frac{F_{145}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{149}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= \frac{F_{148}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{148}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{149}\! \left(x \right) &= -F_{152}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= \frac{F_{151}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{151}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{13}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{916}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{904}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{197}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{163}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{13}\! \left(x \right) F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{13}\! \left(x \right) F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{13}\! \left(x \right) F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= x^{2}\\
F_{172}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{173}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{13}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{13}\! \left(x \right) F_{169}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{13}\! \left(x \right) F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{13}\! \left(x \right) F_{176}\! \left(x \right)\\
F_{183}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{184}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{13}\! \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_{172}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{188}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{184}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{13}\! \left(x \right) F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{188}\! \left(x \right)\\
F_{191}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{192}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{13}\! \left(x \right) F_{188}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{13}\! \left(x \right) F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{13}\! \left(x \right) F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{13}\! \left(x \right) F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{903}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{132}\! \left(x \right) F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= \frac{F_{202}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{202}\! \left(x \right) &= -F_{841}\! \left(x \right)+F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= \frac{F_{204}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{13}\! \left(x \right) F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{841}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{0}\! \left(x \right) F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= -F_{839}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= \frac{F_{210}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\
F_{211}\! \left(x \right) &= -F_{666}\! \left(x \right)+F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= \frac{F_{213}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{13}\! \left(x \right) F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{655}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{384}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{255}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{13}\! \left(x \right) F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{13}\! \left(x \right) F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{13}\! \left(x \right) F_{227}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{231}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{232}\! \left(x \right)+F_{233}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{13}\! \left(x \right) F_{228}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{13}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{13}\! \left(x \right) F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{13}\! \left(x \right) F_{235}\! \left(x \right)\\
F_{241}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{242}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{13}\! \left(x \right) F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{228}\! \left(x \right)+F_{231}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{246}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{242}\! \left(x \right)+F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{13}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{249}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{250}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{13}\! \left(x \right) F_{246}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{13}\! \left(x \right) F_{252}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{13}\! \left(x \right) F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{252}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{344}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{41}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{13}\! \left(x \right) F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)+F_{287}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{261}\! \left(x \right)+F_{41}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{13}\! \left(x \right) F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{274}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{38}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{13}\! \left(x \right) F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{270}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{269}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{269}\! \left(x \right) &= x^{2}\\
F_{270}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{271}\! \left(x \right)\\
F_{271}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{272}\! \left(x \right)+F_{273}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{13}\! \left(x \right) F_{264}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{13}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)+F_{286}\! \left(x \right)+F_{41}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{13}\! \left(x \right) F_{276}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{281}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{279}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{279}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{173}\! \left(x \right)+F_{280}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{13}\! \left(x \right) F_{278}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{282}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{275}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{283}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{284}\! \left(x \right)+F_{285}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{13}\! \left(x \right) F_{282}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{13}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{13}\! \left(x \right) F_{263}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{311}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{289}\! \left(x \right)+F_{306}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{13}\! \left(x \right) F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right)+F_{298}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)+F_{294}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{13}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{296}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{13}\! \left(x \right) F_{292}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{13}\! \left(x \right) F_{297}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{268}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)+F_{302}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{289}\! \left(x \right)+F_{300}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{13}\! \left(x \right) F_{301}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{302}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{303}\! \left(x \right)+F_{304}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{13}\! \left(x \right) F_{299}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{13}\! \left(x \right) F_{305}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{13}\! \left(x \right) F_{307}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{301}\! \left(x \right)+F_{308}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{309}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{13}\! \left(x \right) F_{288}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{330}\! \left(x \right)+F_{342}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{13}\! \left(x \right) F_{313}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{322}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{318}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{13}\! \left(x \right) F_{317}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{278}\! \left(x \right)\\
F_{318}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{319}\! \left(x \right)+F_{320}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{13}\! \left(x \right) F_{315}\! \left(x \right)\\
F_{320}\! \left(x \right) &= F_{13}\! \left(x \right) F_{321}\! \left(x \right)\\
F_{321}\! \left(x \right) &= F_{279}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{326}\! \left(x \right)\\
F_{323}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{312}\! \left(x \right)+F_{324}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{13}\! \left(x \right) F_{325}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{282}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{326}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{327}\! \left(x \right)+F_{328}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{13}\! \left(x \right) F_{323}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{13}\! \left(x \right) F_{329}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{283}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{13}\! \left(x \right) F_{331}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)+F_{333}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{274}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{334}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{330}\! \left(x \right)+F_{335}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{13}\! \left(x \right) F_{336}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{334}\! \left(x \right)\\
F_{337}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{338}\! \left(x \right)+F_{339}\! \left(x \right)+F_{340}\! \left(x \right)\\
F_{338}\! \left(x \right) &= 0\\
F_{339}\! \left(x \right) &= F_{13}\! \left(x \right) F_{334}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{13}\! \left(x \right) F_{341}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{309}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{13}\! \left(x \right) F_{343}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{336}\! \left(x \right)+F_{341}\! \left(x \right)\\
F_{344}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{345}\! \left(x \right)+F_{347}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{13}\! \left(x \right) F_{346}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{13}\! \left(x \right) F_{348}\! \left(x \right)\\
F_{348}\! \left(x \right) &= F_{349}\! \left(x \right)+F_{362}\! \left(x \right)\\
F_{349}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{350}\! \left(x \right)\\
F_{350}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{232}\! \left(x \right)+F_{351}\! \left(x \right)\\
F_{351}\! \left(x \right) &= F_{13}\! \left(x \right) F_{352}\! \left(x \right)\\
F_{352}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{356}\! \left(x \right)\\
F_{353}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{354}\! \left(x \right)\\
F_{354}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{232}\! \left(x \right)+F_{355}\! \left(x \right)\\
F_{355}\! \left(x \right) &= F_{13}\! \left(x \right) F_{353}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{357}\! \left(x \right)+F_{359}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{358}\! \left(x \right)\\
F_{358}\! \left(x \right) &= F_{13}\! \left(x \right) F_{264}\! \left(x \right)\\
F_{359}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{360}\! \left(x \right)+F_{361}\! \left(x \right)\\
F_{360}\! \left(x \right) &= F_{13}\! \left(x \right) F_{354}\! \left(x \right)\\
F_{361}\! \left(x \right) &= F_{13}\! \left(x \right) F_{356}\! \left(x \right)\\
F_{362}\! \left(x \right) &= F_{363}\! \left(x \right)+F_{370}\! \left(x \right)\\
F_{363}\! \left(x \right) &= F_{364}\! \left(x \right)\\
F_{364}\! \left(x \right) &= F_{13}\! \left(x \right) F_{365}\! \left(x \right)\\
F_{365}\! \left(x \right) &= F_{366}\! \left(x \right)+F_{367}\! \left(x \right)\\
F_{366}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{357}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{363}\! \left(x \right)+F_{368}\! \left(x \right)\\
F_{368}\! \left(x \right) &= F_{369}\! \left(x \right)\\
F_{369}\! \left(x \right) &= F_{13}\! \left(x \right) F_{363}\! \left(x \right)\\
F_{370}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{371}\! \left(x \right)+F_{382}\! \left(x \right)\\
F_{371}\! \left(x \right) &= F_{13}\! \left(x \right) F_{372}\! \left(x \right)\\
F_{372}\! \left(x \right) &= F_{373}\! \left(x \right)+F_{374}\! \left(x \right)\\
F_{373}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{359}\! \left(x \right)\\
F_{374}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{375}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{371}\! \left(x \right)+F_{376}\! \left(x \right)\\
F_{376}\! \left(x \right) &= F_{13}\! \left(x \right) F_{377}\! \left(x \right)\\
F_{377}\! \left(x \right) &= F_{363}\! \left(x \right)+F_{375}\! \left(x \right)\\
F_{378}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{379}\! \left(x \right)+F_{380}\! \left(x \right)\\
F_{379}\! \left(x \right) &= F_{13}\! \left(x \right) F_{375}\! \left(x \right)\\
F_{380}\! \left(x \right) &= F_{13}\! \left(x \right) F_{381}\! \left(x \right)\\
F_{381}\! \left(x \right) &= F_{368}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{382}\! \left(x \right) &= F_{13}\! \left(x \right) F_{383}\! \left(x \right)\\
F_{383}\! \left(x \right) &= F_{377}\! \left(x \right)+F_{381}\! \left(x \right)\\
F_{384}\! \left(x \right) &= F_{385}\! \left(x \right)\\
F_{385}\! \left(x \right) &= F_{13}\! \left(x \right) F_{386}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{386}\! \left(x \right) &= F_{387}\! \left(x \right)+F_{388}\! \left(x \right)\\
F_{387}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{218}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{389}\! \left(x \right)+F_{493}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{390}\! \left(x \right)+F_{420}\! \left(x \right)\\
F_{390}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{391}\! \left(x \right)\\
F_{391}\! \left(x \right) &= F_{392}\! \left(x \right)\\
F_{392}\! \left(x \right) &= F_{13}\! \left(x \right) F_{393}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{394}\! \left(x \right)+F_{405}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{395}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{396}\! \left(x \right)\\
F_{396}\! \left(x \right) &= F_{13}\! \left(x \right) F_{397}\! \left(x \right)\\
F_{397}\! \left(x \right) &= F_{398}\! \left(x \right)+F_{401}\! \left(x \right)\\
F_{398}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{399}\! \left(x \right)\\
F_{399}\! \left(x \right) &= F_{400}\! \left(x \right)\\
F_{400}\! \left(x \right) &= F_{13}\! \left(x \right) F_{398}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{402}\! \left(x \right)\\
F_{402}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{403}\! \left(x \right)+F_{404}\! \left(x \right)\\
F_{403}\! \left(x \right) &= F_{13}\! \left(x \right) F_{399}\! \left(x \right)\\
F_{404}\! \left(x \right) &= F_{13}\! \left(x \right) F_{401}\! \left(x \right)\\
F_{405}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{406}\! \left(x \right)\\
F_{406}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{407}\! \left(x \right)+F_{418}\! \left(x \right)\\
F_{407}\! \left(x \right) &= F_{13}\! \left(x \right) F_{408}\! \left(x \right)\\
F_{408}\! \left(x \right) &= F_{409}\! \left(x \right)+F_{410}\! \left(x \right)\\
F_{409}\! \left(x \right) &= F_{399}\! \left(x \right)+F_{402}\! \left(x \right)\\
F_{410}\! \left(x \right) &= F_{411}\! \left(x \right)+F_{414}\! \left(x \right)\\
F_{411}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{407}\! \left(x \right)+F_{412}\! \left(x \right)\\
F_{412}\! \left(x \right) &= F_{13}\! \left(x \right) F_{413}\! \left(x \right)\\
F_{413}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{411}\! \left(x \right)\\
F_{414}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{415}\! \left(x \right)+F_{416}\! \left(x \right)\\
F_{415}\! \left(x \right) &= F_{13}\! \left(x \right) F_{411}\! \left(x \right)\\
F_{416}\! \left(x \right) &= F_{13}\! \left(x \right) F_{417}\! \left(x \right)\\
F_{417}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{414}\! \left(x \right)\\
F_{418}\! \left(x \right) &= F_{13}\! \left(x \right) F_{419}\! \left(x \right)\\
F_{419}\! \left(x \right) &= F_{413}\! \left(x \right)+F_{417}\! \left(x \right)\\
F_{420}\! \left(x \right) &= F_{421}\! \left(x \right)+F_{453}\! \left(x \right)\\
F_{421}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{422}\! \left(x \right)\\
F_{422}\! \left(x \right) &= F_{13}\! \left(x \right) F_{423}\! \left(x \right)\\
F_{423}\! \left(x \right) &= F_{424}\! \left(x \right)+F_{431}\! \left(x \right)\\
F_{424}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{425}\! \left(x \right)\\
F_{425}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{426}\! \left(x \right)\\
F_{426}\! \left(x \right) &= F_{13}\! \left(x \right) F_{427}\! \left(x \right)\\
F_{427}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{428}\! \left(x \right)\\
F_{428}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{429}\! \left(x \right)\\
F_{429}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{280}\! \left(x \right)+F_{41}\! \left(x \right)+F_{430}\! \left(x \right)\\
F_{430}\! \left(x \right) &= F_{13}\! \left(x \right) F_{428}\! \left(x \right)\\
F_{431}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{438}\! \left(x \right)\\
F_{432}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{41}\! \left(x \right)+F_{433}\! \left(x \right)\\
F_{433}\! \left(x \right) &= F_{13}\! \left(x \right) F_{434}\! \left(x \right)\\
F_{434}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{435}\! \left(x \right)\\
F_{435}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{436}\! \left(x \right)\\
F_{436}\! \left(x \right) &= F_{437}\! \left(x \right)\\
F_{437}\! \left(x \right) &= F_{13}\! \left(x \right) F_{432}\! \left(x \right)\\
F_{438}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{41}\! \left(x \right)+F_{439}\! \left(x \right)+F_{451}\! \left(x \right)\\
F_{439}\! \left(x \right) &= F_{13}\! \left(x \right) F_{440}\! \left(x \right)\\
F_{440}\! \left(x \right) &= F_{441}\! \left(x \right)+F_{442}\! \left(x \right)\\
F_{441}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{429}\! \left(x \right)\\
F_{442}\! \left(x \right) &= F_{443}\! \left(x \right)+F_{446}\! \left(x \right)\\
F_{443}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{41}\! \left(x \right)+F_{439}\! \left(x \right)+F_{444}\! \left(x \right)\\
F_{444}\! \left(x \right) &= F_{13}\! \left(x \right) F_{445}\! \left(x \right)\\
F_{445}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{443}\! \left(x \right)\\
F_{446}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{447}\! \left(x \right)+F_{448}\! \left(x \right)+F_{449}\! \left(x \right)\\
F_{447}\! \left(x \right) &= 0\\
F_{448}\! \left(x \right) &= F_{13}\! \left(x \right) F_{443}\! \left(x \right)\\
F_{449}\! \left(x \right) &= F_{13}\! \left(x \right) F_{450}\! \left(x \right)\\
F_{450}\! \left(x \right) &= F_{436}\! \left(x \right)+F_{446}\! \left(x \right)\\
F_{451}\! \left(x \right) &= F_{13}\! \left(x \right) F_{452}\! \left(x \right)\\
F_{452}\! \left(x \right) &= F_{445}\! \left(x \right)+F_{450}\! \left(x \right)\\
F_{453}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{454}\! \left(x \right)+F_{456}\! \left(x \right)\\
F_{454}\! \left(x \right) &= F_{13}\! \left(x \right) F_{455}\! \left(x \right)\\
F_{455}\! \left(x \right) &= F_{399}\! \left(x \right)\\
F_{456}\! \left(x \right) &= F_{13}\! \left(x \right) F_{457}\! \left(x \right)\\
F_{457}\! \left(x \right) &= F_{458}\! \left(x \right)+F_{471}\! \left(x \right)\\
F_{458}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{459}\! \left(x \right)\\
F_{459}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{403}\! \left(x \right)+F_{460}\! \left(x \right)\\
F_{460}\! \left(x \right) &= F_{13}\! \left(x \right) F_{461}\! \left(x \right)\\
F_{461}\! \left(x \right) &= F_{462}\! \left(x \right)+F_{465}\! \left(x \right)\\
F_{462}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{463}\! \left(x \right)\\
F_{463}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{403}\! \left(x \right)+F_{464}\! \left(x \right)\\
F_{464}\! \left(x \right) &= F_{13}\! \left(x \right) F_{462}\! \left(x \right)\\
F_{465}\! \left(x \right) &= F_{466}\! \left(x \right)+F_{468}\! \left(x \right)\\
F_{466}\! \left(x \right) &= F_{467}\! \left(x \right)\\
F_{467}\! \left(x \right) &= F_{13}\! \left(x \right) F_{268}\! \left(x \right)\\
F_{468}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{469}\! \left(x \right)+F_{470}\! \left(x \right)\\
F_{469}\! \left(x \right) &= F_{13}\! \left(x \right) F_{463}\! \left(x \right)\\
F_{470}\! \left(x \right) &= F_{13}\! \left(x \right) F_{465}\! \left(x \right)\\
F_{471}\! \left(x \right) &= F_{472}\! \left(x \right)+F_{479}\! \left(x \right)\\
F_{472}\! \left(x \right) &= F_{473}\! \left(x \right)\\
F_{473}\! \left(x \right) &= F_{13}\! \left(x \right) F_{474}\! \left(x \right)\\
F_{474}\! \left(x \right) &= F_{475}\! \left(x \right)+F_{476}\! \left(x \right)\\
F_{475}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{466}\! \left(x \right)\\
F_{476}\! \left(x \right) &= F_{472}\! \left(x \right)+F_{477}\! \left(x \right)\\
F_{477}\! \left(x \right) &= F_{478}\! \left(x \right)\\
F_{478}\! \left(x \right) &= F_{13}\! \left(x \right) F_{472}\! \left(x \right)\\
F_{479}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{480}\! \left(x \right)+F_{491}\! \left(x \right)\\
F_{480}\! \left(x \right) &= F_{13}\! \left(x \right) F_{481}\! \left(x \right)\\
F_{481}\! \left(x \right) &= F_{482}\! \left(x \right)+F_{483}\! \left(x \right)\\
F_{482}\! \left(x \right) &= F_{463}\! \left(x \right)+F_{468}\! \left(x \right)\\
F_{483}\! \left(x \right) &= F_{484}\! \left(x \right)+F_{487}\! \left(x \right)\\
F_{484}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{480}\! \left(x \right)+F_{485}\! \left(x \right)\\
F_{485}\! \left(x \right) &= F_{13}\! \left(x \right) F_{486}\! \left(x \right)\\
F_{486}\! \left(x \right) &= F_{472}\! \left(x \right)+F_{484}\! \left(x \right)\\
F_{487}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{488}\! \left(x \right)+F_{489}\! \left(x \right)\\
F_{488}\! \left(x \right) &= F_{13}\! \left(x \right) F_{484}\! \left(x \right)\\
F_{489}\! \left(x \right) &= F_{13}\! \left(x \right) F_{490}\! \left(x \right)\\
F_{490}\! \left(x \right) &= F_{477}\! \left(x \right)+F_{487}\! \left(x \right)\\
F_{491}\! \left(x \right) &= F_{13}\! \left(x \right) F_{492}\! \left(x \right)\\
F_{492}\! \left(x \right) &= F_{486}\! \left(x \right)+F_{490}\! \left(x \right)\\
F_{493}\! \left(x \right) &= F_{494}\! \left(x \right)+F_{530}\! \left(x \right)\\
F_{494}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{495}\! \left(x \right)\\
F_{495}\! \left(x \right) &= F_{496}\! \left(x \right)\\
F_{496}\! \left(x \right) &= F_{13}\! \left(x \right) F_{497}\! \left(x \right)\\
F_{497}\! \left(x \right) &= F_{498}\! \left(x \right)+F_{509}\! \left(x \right)\\
F_{498}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{499}\! \left(x \right)\\
F_{499}\! \left(x \right) &= F_{500}\! \left(x \right)\\
F_{500}\! \left(x \right) &= F_{13}\! \left(x \right) F_{501}\! \left(x \right)\\
F_{501}\! \left(x \right) &= F_{502}\! \left(x \right)+F_{505}\! \left(x \right)\\
F_{502}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{503}\! \left(x \right)\\
F_{503}\! \left(x \right) &= F_{504}\! \left(x \right)\\
F_{504}\! \left(x \right) &= F_{13}\! \left(x \right) F_{502}\! \left(x \right)\\
F_{505}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{506}\! \left(x \right)\\
F_{506}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{507}\! \left(x \right)+F_{508}\! \left(x \right)\\
F_{507}\! \left(x \right) &= F_{13}\! \left(x \right) F_{503}\! \left(x \right)\\
F_{508}\! \left(x \right) &= F_{13}\! \left(x \right) F_{505}\! \left(x \right)\\
F_{509}\! \left(x \right) &= F_{510}\! \left(x \right)+F_{516}\! \left(x \right)\\
F_{510}\! \left(x \right) &= F_{511}\! \left(x \right)\\
F_{511}\! \left(x \right) &= F_{13}\! \left(x \right) F_{512}\! \left(x \right)\\
F_{512}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{513}\! \left(x \right)\\
F_{513}\! \left(x \right) &= F_{510}\! \left(x \right)+F_{514}\! \left(x \right)\\
F_{514}\! \left(x \right) &= F_{515}\! \left(x \right)\\
F_{515}\! \left(x \right) &= F_{13}\! \left(x \right) F_{510}\! \left(x \right)\\
F_{516}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{517}\! \left(x \right)+F_{528}\! \left(x \right)\\
F_{517}\! \left(x \right) &= F_{13}\! \left(x \right) F_{518}\! \left(x \right)\\
F_{518}\! \left(x \right) &= F_{519}\! \left(x \right)+F_{520}\! \left(x \right)\\
F_{519}\! \left(x \right) &= F_{503}\! \left(x \right)+F_{506}\! \left(x \right)\\
F_{520}\! \left(x \right) &= F_{521}\! \left(x \right)+F_{524}\! \left(x \right)\\
F_{521}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{517}\! \left(x \right)+F_{522}\! \left(x \right)\\
F_{522}\! \left(x \right) &= F_{13}\! \left(x \right) F_{523}\! \left(x \right)\\
F_{523}\! \left(x \right) &= F_{510}\! \left(x \right)+F_{521}\! \left(x \right)\\
F_{524}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{525}\! \left(x \right)+F_{526}\! \left(x \right)\\
F_{525}\! \left(x \right) &= F_{13}\! \left(x \right) F_{521}\! \left(x \right)\\
F_{526}\! \left(x \right) &= F_{13}\! \left(x \right) F_{527}\! \left(x \right)\\
F_{527}\! \left(x \right) &= F_{514}\! \left(x \right)+F_{524}\! \left(x \right)\\
F_{528}\! \left(x \right) &= F_{13}\! \left(x \right) F_{529}\! \left(x \right)\\
F_{529}\! \left(x \right) &= F_{523}\! \left(x \right)+F_{527}\! \left(x \right)\\
F_{530}\! \left(x \right) &= F_{531}\! \left(x \right)+F_{615}\! \left(x \right)\\
F_{531}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{184}\! \left(x \right)+F_{532}\! \left(x \right)\\
F_{532}\! \left(x \right) &= F_{13}\! \left(x \right) F_{533}\! \left(x \right)\\
F_{533}\! \left(x \right) &= F_{534}\! \left(x \right)+F_{563}\! \left(x \right)\\
F_{534}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{535}\! \left(x \right)\\
F_{535}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{184}\! \left(x \right)+F_{536}\! \left(x \right)\\
F_{536}\! \left(x \right) &= F_{13}\! \left(x \right) F_{537}\! \left(x \right)\\
F_{537}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{538}\! \left(x \right)\\
F_{538}\! \left(x \right) &= F_{539}\! \left(x \right)+F_{550}\! \left(x \right)\\
F_{539}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{182}\! \left(x \right)+F_{540}\! \left(x \right)\\
F_{540}\! \left(x \right) &= F_{13}\! \left(x \right) F_{541}\! \left(x \right)\\
F_{541}\! \left(x \right) &= F_{542}\! \left(x \right)+F_{546}\! \left(x \right)\\
F_{542}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{543}\! \left(x \right)\\
F_{543}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{544}\! \left(x \right)+F_{545}\! \left(x \right)\\
F_{544}\! \left(x \right) &= F_{13}\! \left(x \right) F_{268}\! \left(x \right)\\
F_{545}\! \left(x \right) &= F_{13}\! \left(x \right) F_{170}\! \left(x \right)\\
F_{546}\! \left(x \right) &= F_{539}\! \left(x \right)+F_{547}\! \left(x \right)\\
F_{547}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{548}\! \left(x \right)+F_{549}\! \left(x \right)\\
F_{548}\! \left(x \right) &= F_{13}\! \left(x \right) F_{539}\! \left(x \right)\\
F_{549}\! \left(x \right) &= F_{13}\! \left(x \right) F_{181}\! \left(x \right)\\
F_{550}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{192}\! \left(x \right)+F_{551}\! \left(x \right)+F_{562}\! \left(x \right)\\
F_{551}\! \left(x \right) &= F_{13}\! \left(x \right) F_{552}\! \left(x \right)\\
F_{552}\! \left(x \right) &= F_{553}\! \left(x \right)+F_{557}\! \left(x \right)\\
F_{553}\! \left(x \right) &= F_{279}\! \left(x \right)+F_{554}\! \left(x \right)\\
F_{554}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{555}\! \left(x \right)+F_{556}\! \left(x \right)\\
F_{555}\! \left(x \right) &= F_{13}\! \left(x \right) F_{279}\! \left(x \right)\\
F_{556}\! \left(x \right) &= F_{13}\! \left(x \right) F_{172}\! \left(x \right)\\
F_{557}\! \left(x \right) &= F_{558}\! \left(x \right)+F_{559}\! \left(x \right)\\
F_{558}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{192}\! \left(x \right)+F_{551}\! \left(x \right)\\
F_{559}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{560}\! \left(x \right)+F_{561}\! \left(x \right)\\
F_{560}\! \left(x \right) &= F_{13}\! \left(x \right) F_{558}\! \left(x \right)\\
F_{561}\! \left(x \right) &= F_{13}\! \left(x \right) F_{191}\! \left(x \right)\\
F_{562}\! \left(x \right) &= F_{13}\! \left(x \right) F_{538}\! \left(x \right)\\
F_{563}\! \left(x \right) &= F_{564}\! \left(x \right)+F_{585}\! \left(x \right)\\
F_{564}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{565}\! \left(x \right)+F_{580}\! \left(x \right)\\
F_{565}\! \left(x \right) &= F_{13}\! \left(x \right) F_{566}\! \left(x \right)\\
F_{566}\! \left(x \right) &= F_{567}\! \left(x \right)+F_{572}\! \left(x \right)\\
F_{567}\! \left(x \right) &= F_{294}\! \left(x \right)+F_{568}\! \left(x \right)\\
F_{568}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{569}\! \left(x \right)+F_{570}\! \left(x \right)\\
F_{569}\! \left(x \right) &= F_{13}\! \left(x \right) F_{294}\! \left(x \right)\\
F_{570}\! \left(x \right) &= F_{13}\! \left(x \right) F_{571}\! \left(x \right)\\
F_{571}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{543}\! \left(x \right)\\
F_{572}\! \left(x \right) &= F_{573}\! \left(x \right)+F_{576}\! \left(x \right)\\
F_{573}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{565}\! \left(x \right)+F_{574}\! \left(x \right)\\
F_{574}\! \left(x \right) &= F_{13}\! \left(x \right) F_{575}\! \left(x \right)\\
F_{575}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{539}\! \left(x \right)\\
F_{576}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{577}\! \left(x \right)+F_{578}\! \left(x \right)\\
F_{577}\! \left(x \right) &= F_{13}\! \left(x \right) F_{573}\! \left(x \right)\\
F_{578}\! \left(x \right) &= F_{13}\! \left(x \right) F_{579}\! \left(x \right)\\
F_{579}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{547}\! \left(x \right)\\
F_{580}\! \left(x \right) &= F_{13}\! \left(x \right) F_{581}\! \left(x \right)\\
F_{581}\! \left(x \right) &= F_{575}\! \left(x \right)+F_{582}\! \left(x \right)\\
F_{582}\! \left(x \right) &= F_{564}\! \left(x \right)+F_{583}\! \left(x \right)\\
F_{583}\! \left(x \right) &= F_{584}\! \left(x \right)\\
F_{584}\! \left(x \right) &= F_{13}\! \left(x \right) F_{564}\! \left(x \right)\\
F_{585}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{586}\! \left(x \right)+F_{601}\! \left(x \right)+F_{613}\! \left(x \right)\\
F_{586}\! \left(x \right) &= F_{13}\! \left(x \right) F_{587}\! \left(x \right)\\
F_{587}\! \left(x \right) &= F_{588}\! \left(x \right)+F_{593}\! \left(x \right)\\
F_{588}\! \left(x \right) &= F_{318}\! \left(x \right)+F_{589}\! \left(x \right)\\
F_{589}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{590}\! \left(x \right)+F_{591}\! \left(x \right)\\
F_{590}\! \left(x \right) &= F_{13}\! \left(x \right) F_{318}\! \left(x \right)\\
F_{591}\! \left(x \right) &= F_{13}\! \left(x \right) F_{592}\! \left(x \right)\\
F_{592}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{554}\! \left(x \right)\\
F_{593}\! \left(x \right) &= F_{594}\! \left(x \right)+F_{597}\! \left(x \right)\\
F_{594}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{586}\! \left(x \right)+F_{595}\! \left(x \right)\\
F_{595}\! \left(x \right) &= F_{13}\! \left(x \right) F_{596}\! \left(x \right)\\
F_{596}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{558}\! \left(x \right)\\
F_{597}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{598}\! \left(x \right)+F_{599}\! \left(x \right)\\
F_{598}\! \left(x \right) &= F_{13}\! \left(x \right) F_{594}\! \left(x \right)\\
F_{599}\! \left(x \right) &= F_{13}\! \left(x \right) F_{600}\! \left(x \right)\\
F_{600}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{559}\! \left(x \right)\\
F_{601}\! \left(x \right) &= F_{13}\! \left(x \right) F_{602}\! \left(x \right)\\
F_{602}\! \left(x \right) &= F_{603}\! \left(x \right)+F_{604}\! \left(x \right)\\
F_{603}\! \left(x \right) &= F_{188}\! \left(x \right)+F_{550}\! \left(x \right)\\
F_{604}\! \left(x \right) &= F_{605}\! \left(x \right)+F_{608}\! \left(x \right)\\
F_{605}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{586}\! \left(x \right)+F_{601}\! \left(x \right)+F_{606}\! \left(x \right)\\
F_{606}\! \left(x \right) &= F_{13}\! \left(x \right) F_{607}\! \left(x \right)\\
F_{607}\! \left(x \right) &= F_{564}\! \left(x \right)+F_{605}\! \left(x \right)\\
F_{608}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{609}\! \left(x \right)+F_{610}\! \left(x \right)+F_{611}\! \left(x \right)\\
F_{609}\! \left(x \right) &= 0\\
F_{610}\! \left(x \right) &= F_{13}\! \left(x \right) F_{605}\! \left(x \right)\\
F_{611}\! \left(x \right) &= F_{13}\! \left(x \right) F_{612}\! \left(x \right)\\
F_{612}\! \left(x \right) &= F_{583}\! \left(x \right)+F_{608}\! \left(x \right)\\
F_{613}\! \left(x \right) &= F_{13}\! \left(x \right) F_{614}\! \left(x \right)\\
F_{614}\! \left(x \right) &= F_{607}\! \left(x \right)+F_{612}\! \left(x \right)\\
F_{615}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{616}\! \left(x \right)+F_{618}\! \left(x \right)\\
F_{616}\! \left(x \right) &= F_{13}\! \left(x \right) F_{617}\! \left(x \right)\\
F_{617}\! \left(x \right) &= F_{503}\! \left(x \right)\\
F_{618}\! \left(x \right) &= F_{13}\! \left(x \right) F_{619}\! \left(x \right)\\
F_{619}\! \left(x \right) &= F_{620}\! \left(x \right)+F_{633}\! \left(x \right)\\
F_{620}\! \left(x \right) &= F_{539}\! \left(x \right)+F_{621}\! \left(x \right)\\
F_{621}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{507}\! \left(x \right)+F_{622}\! \left(x \right)\\
F_{622}\! \left(x \right) &= F_{13}\! \left(x \right) F_{623}\! \left(x \right)\\
F_{623}\! \left(x \right) &= F_{624}\! \left(x \right)+F_{627}\! \left(x \right)\\
F_{624}\! \left(x \right) &= F_{539}\! \left(x \right)+F_{625}\! \left(x \right)\\
F_{625}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{507}\! \left(x \right)+F_{626}\! \left(x \right)\\
F_{626}\! \left(x \right) &= F_{13}\! \left(x \right) F_{624}\! \left(x \right)\\
F_{627}\! \left(x \right) &= F_{628}\! \left(x \right)+F_{630}\! \left(x \right)\\
F_{628}\! \left(x \right) &= F_{629}\! \left(x \right)\\
F_{629}\! \left(x \right) &= F_{13}\! \left(x \right) F_{539}\! \left(x \right)\\
F_{630}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{631}\! \left(x \right)+F_{632}\! \left(x \right)\\
F_{631}\! \left(x \right) &= F_{13}\! \left(x \right) F_{625}\! \left(x \right)\\
F_{632}\! \left(x \right) &= F_{13}\! \left(x \right) F_{627}\! \left(x \right)\\
F_{633}\! \left(x \right) &= F_{634}\! \left(x \right)+F_{641}\! \left(x \right)\\
F_{634}\! \left(x \right) &= F_{635}\! \left(x \right)\\
F_{635}\! \left(x \right) &= F_{13}\! \left(x \right) F_{636}\! \left(x \right)\\
F_{636}\! \left(x \right) &= F_{637}\! \left(x \right)+F_{638}\! \left(x \right)\\
F_{637}\! \left(x \right) &= F_{539}\! \left(x \right)+F_{628}\! \left(x \right)\\
F_{638}\! \left(x \right) &= F_{634}\! \left(x \right)+F_{639}\! \left(x \right)\\
F_{639}\! \left(x \right) &= F_{640}\! \left(x \right)\\
F_{640}\! \left(x \right) &= F_{13}\! \left(x \right) F_{634}\! \left(x \right)\\
F_{641}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{642}\! \left(x \right)+F_{653}\! \left(x \right)\\
F_{642}\! \left(x \right) &= F_{13}\! \left(x \right) F_{643}\! \left(x \right)\\
F_{643}\! \left(x \right) &= F_{644}\! \left(x \right)+F_{645}\! \left(x \right)\\
F_{644}\! \left(x \right) &= F_{625}\! \left(x \right)+F_{630}\! \left(x \right)\\
F_{645}\! \left(x \right) &= F_{646}\! \left(x \right)+F_{649}\! \left(x \right)\\
F_{646}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{642}\! \left(x \right)+F_{647}\! \left(x \right)\\
F_{647}\! \left(x \right) &= F_{13}\! \left(x \right) F_{648}\! \left(x \right)\\
F_{648}\! \left(x \right) &= F_{634}\! \left(x \right)+F_{646}\! \left(x \right)\\
F_{649}\! \left(x \right) &= 5 F_{41}\! \left(x \right)+F_{650}\! \left(x \right)+F_{651}\! \left(x \right)\\
F_{650}\! \left(x \right) &= F_{13}\! \left(x \right) F_{646}\! \left(x \right)\\
F_{651}\! \left(x \right) &= F_{13}\! \left(x \right) F_{652}\! \left(x \right)\\
F_{652}\! \left(x \right) &= F_{639}\! \left(x \right)+F_{649}\! \left(x \right)\\
F_{653}\! \left(x \right) &= F_{13}\! \left(x \right) F_{654}\! \left(x \right)\\
F_{654}\! \left(x \right) &= F_{648}\! \left(x \right)+F_{652}\! \left(x \right)\\
F_{655}\! \left(x \right) &= F_{13}\! \left(x \right) F_{656}\! \left(x \right)\\
F_{656}\! \left(x \right) &= F_{657}\! \left(x \right)+F_{658}\! \left(x \right)\\
F_{657}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{658}\! \left(x \right) &= F_{659}\! \left(x \right)\\
F_{659}\! \left(x \right) &= F_{13}\! \left(x \right) F_{660}\! \left(x \right) F_{665}\! \left(x \right)\\
F_{660}\! \left(x \right) &= F_{661}\! \left(x \right)+F_{663}\! \left(x \right)\\
F_{661}\! \left(x \right) &= F_{0}\! \left(x \right) F_{662}\! \left(x \right)\\
F_{662}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{663}\! \left(x \right) &= F_{15}\! \left(x \right) F_{664}\! \left(x \right)\\
F_{664}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{665}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{666}\! \left(x \right) &= F_{667}\! \left(x \right)\\
F_{667}\! \left(x \right) &= F_{13}\! \left(x \right) F_{668}\! \left(x \right)\\
F_{668}\! \left(x \right) &= F_{669}\! \left(x \right)+F_{833}\! \left(x \right)\\
F_{669}\! \left(x \right) &= -F_{831}\! \left(x \right)+F_{670}\! \left(x \right)\\
F_{670}\! \left(x \right) &= -F_{817}\! \left(x \right)+F_{671}\! \left(x \right)\\
F_{671}\! \left(x \right) &= \frac{F_{672}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{672}\! \left(x \right) &= F_{673}\! \left(x \right)\\
F_{673}\! \left(x \right) &= -F_{798}\! \left(x \right)+F_{674}\! \left(x \right)\\
F_{674}\! \left(x \right) &= -F_{796}\! \left(x \right)+F_{675}\! \left(x \right)\\
F_{675}\! \left(x \right) &= \frac{F_{676}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{676}\! \left(x \right) &= F_{677}\! \left(x \right)\\
F_{677}\! \left(x \right) &= F_{678}\! \left(x \right)\\
F_{678}\! \left(x \right) &= F_{13}\! \left(x \right) F_{679}\! \left(x \right)\\
F_{679}\! \left(x \right) &= F_{680}\! \left(x \right)+F_{792}\! \left(x \right)\\
F_{680}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{681}\! \left(x \right)\\
F_{681}\! \left(x \right) &= F_{682}\! \left(x \right)\\
F_{682}\! \left(x \right) &= F_{683}\! \left(x \right)+F_{717}\! \left(x \right)\\
F_{683}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{684}\! \left(x \right)\\
F_{684}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{685}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{685}\! \left(x \right) &= F_{13}\! \left(x \right) F_{686}\! \left(x \right)\\
F_{686}\! \left(x \right) &= F_{687}\! \left(x \right)+F_{695}\! \left(x \right)\\
F_{687}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{688}\! \left(x \right)\\
F_{688}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{689}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{689}\! \left(x \right) &= F_{13}\! \left(x \right) F_{690}\! \left(x \right)\\
F_{690}\! \left(x \right) &= F_{691}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{691}\! \left(x \right) &= F_{692}\! \left(x \right)+F_{693}\! \left(x \right)\\
F_{692}\! \left(x \right) &= F_{273}\! \left(x \right)\\
F_{693}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{285}\! \left(x \right)+F_{694}\! \left(x \right)\\
F_{694}\! \left(x \right) &= F_{13}\! \left(x \right) F_{691}\! \left(x \right)\\
F_{695}\! \left(x \right) &= F_{696}\! \left(x \right)+F_{703}\! \left(x \right)\\
F_{696}\! \left(x \right) &= F_{697}\! \left(x \right)\\
F_{697}\! \left(x \right) &= F_{13}\! \left(x \right) F_{698}\! \left(x \right)\\
F_{698}\! \left(x \right) &= F_{699}\! \left(x \right)+F_{700}\! \left(x \right)\\
F_{699}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{692}\! \left(x \right)\\
F_{700}\! \left(x \right) &= F_{696}\! \left(x \right)+F_{701}\! \left(x \right)\\
F_{701}\! \left(x \right) &= F_{702}\! \left(x \right)\\
F_{702}\! \left(x \right) &= F_{13}\! \left(x \right) F_{696}\! \left(x \right)\\
F_{703}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{704}\! \left(x \right)+F_{715}\! \left(x \right)\\
F_{704}\! \left(x \right) &= F_{13}\! \left(x \right) F_{705}\! \left(x \right)\\
F_{705}\! \left(x \right) &= F_{706}\! \left(x \right)+F_{707}\! \left(x \right)\\
F_{706}\! \left(x \right) &= F_{693}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{707}\! \left(x \right) &= F_{708}\! \left(x \right)+F_{711}\! \left(x \right)\\
F_{708}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{704}\! \left(x \right)+F_{709}\! \left(x \right)\\
F_{709}\! \left(x \right) &= F_{13}\! \left(x \right) F_{710}\! \left(x \right)\\
F_{710}\! \left(x \right) &= F_{696}\! \left(x \right)+F_{708}\! \left(x \right)\\
F_{711}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{712}\! \left(x \right)+F_{713}\! \left(x \right)\\
F_{712}\! \left(x \right) &= F_{13}\! \left(x \right) F_{708}\! \left(x \right)\\
F_{713}\! \left(x \right) &= F_{13}\! \left(x \right) F_{714}\! \left(x \right)\\
F_{714}\! \left(x \right) &= F_{701}\! \left(x \right)+F_{711}\! \left(x \right)\\
F_{715}\! \left(x \right) &= F_{13}\! \left(x \right) F_{716}\! \left(x \right)\\
F_{716}\! \left(x \right) &= F_{710}\! \left(x \right)+F_{714}\! \left(x \right)\\
F_{717}\! \left(x \right) &= F_{718}\! \left(x \right)\\
F_{718}\! \left(x \right) &= F_{13}\! \left(x \right) F_{719}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{719}\! \left(x \right) &= F_{720}\! \left(x \right)+F_{723}\! \left(x \right)\\
F_{720}\! \left(x \right) &= F_{683}\! \left(x \right)+F_{721}\! \left(x \right)\\
F_{721}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{722}\! \left(x \right)\\
F_{722}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{723}\! \left(x \right) &= F_{724}\! \left(x \right)+F_{758}\! \left(x \right)\\
F_{724}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{725}\! \left(x \right)\\
F_{725}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{173}\! \left(x \right)+F_{726}\! \left(x \right)\\
F_{726}\! \left(x \right) &= F_{13}\! \left(x \right) F_{727}\! \left(x \right)\\
F_{727}\! \left(x \right) &= F_{728}\! \left(x \right)+F_{736}\! \left(x \right)\\
F_{728}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{729}\! \left(x \right)\\
F_{729}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{173}\! \left(x \right)+F_{730}\! \left(x \right)\\
F_{730}\! \left(x \right) &= F_{13}\! \left(x \right) F_{731}\! \left(x \right)\\
F_{731}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{732}\! \left(x \right)\\
F_{732}\! \left(x \right) &= F_{733}\! \left(x \right)+F_{734}\! \left(x \right)\\
F_{733}\! \left(x \right) &= F_{545}\! \left(x \right)\\
F_{734}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{556}\! \left(x \right)+F_{735}\! \left(x \right)\\
F_{735}\! \left(x \right) &= F_{13}\! \left(x \right) F_{732}\! \left(x \right)\\
F_{736}\! \left(x \right) &= F_{737}\! \left(x \right)+F_{744}\! \left(x \right)\\
F_{737}\! \left(x \right) &= F_{738}\! \left(x \right)\\
F_{738}\! \left(x \right) &= F_{13}\! \left(x \right) F_{739}\! \left(x \right)\\
F_{739}\! \left(x \right) &= F_{740}\! \left(x \right)+F_{741}\! \left(x \right)\\
F_{740}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{733}\! \left(x \right)\\
F_{741}\! \left(x \right) &= F_{737}\! \left(x \right)+F_{742}\! \left(x \right)\\
F_{742}\! \left(x \right) &= F_{743}\! \left(x \right)\\
F_{743}\! \left(x \right) &= F_{13}\! \left(x \right) F_{737}\! \left(x \right)\\
F_{744}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{745}\! \left(x \right)+F_{756}\! \left(x \right)\\
F_{745}\! \left(x \right) &= F_{13}\! \left(x \right) F_{746}\! \left(x \right)\\
F_{746}\! \left(x \right) &= F_{747}\! \left(x \right)+F_{748}\! \left(x \right)\\
F_{747}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{734}\! \left(x \right)\\
F_{748}\! \left(x \right) &= F_{749}\! \left(x \right)+F_{752}\! \left(x \right)\\
F_{749}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{745}\! \left(x \right)+F_{750}\! \left(x \right)\\
F_{750}\! \left(x \right) &= F_{13}\! \left(x \right) F_{751}\! \left(x \right)\\
F_{751}\! \left(x \right) &= F_{737}\! \left(x \right)+F_{749}\! \left(x \right)\\
F_{752}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{753}\! \left(x \right)+F_{754}\! \left(x \right)\\
F_{753}\! \left(x \right) &= F_{13}\! \left(x \right) F_{749}\! \left(x \right)\\
F_{754}\! \left(x \right) &= F_{13}\! \left(x \right) F_{755}\! \left(x \right)\\
F_{755}\! \left(x \right) &= F_{742}\! \left(x \right)+F_{752}\! \left(x \right)\\
F_{756}\! \left(x \right) &= F_{13}\! \left(x \right) F_{757}\! \left(x \right)\\
F_{757}\! \left(x \right) &= F_{751}\! \left(x \right)+F_{755}\! \left(x \right)\\
F_{758}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{759}\! \left(x \right)\\
F_{759}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{192}\! \left(x \right)+F_{760}\! \left(x \right)\\
F_{760}\! \left(x \right) &= F_{13}\! \left(x \right) F_{761}\! \left(x \right)\\
F_{761}\! \left(x \right) &= F_{762}\! \left(x \right)+F_{770}\! \left(x \right)\\
F_{762}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{763}\! \left(x \right)\\
F_{763}\! \left(x \right) &= 3 F_{41}\! \left(x \right)+F_{192}\! \left(x \right)+F_{764}\! \left(x \right)\\
F_{764}\! \left(x \right) &= F_{13}\! \left(x \right) F_{765}\! \left(x \right)\\
F_{765}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{766}\! \left(x \right)\\
F_{766}\! \left(x \right) &= F_{767}\! \left(x \right)+F_{768}\! \left(x \right)\\
F_{767}\! \left(x \right) &= F_{549}\! \left(x \right)\\
F_{768}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{561}\! \left(x \right)+F_{769}\! \left(x \right)\\
F_{769}\! \left(x \right) &= F_{13}\! \left(x \right) F_{766}\! \left(x \right)\\
F_{770}\! \left(x \right) &= F_{771}\! \left(x \right)+F_{778}\! \left(x \right)\\
F_{771}\! \left(x \right) &= F_{772}\! \left(x \right)\\
F_{772}\! \left(x \right) &= F_{13}\! \left(x \right) F_{773}\! \left(x \right)\\
F_{773}\! \left(x \right) &= F_{774}\! \left(x \right)+F_{775}\! \left(x \right)\\
F_{774}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{767}\! \left(x \right)\\
F_{775}\! \left(x \right) &= F_{771}\! \left(x \right)+F_{776}\! \left(x \right)\\
F_{776}\! \left(x \right) &= F_{777}\! \left(x \right)\\
F_{777}\! \left(x \right) &= F_{13}\! \left(x \right) F_{771}\! \left(x \right)\\
F_{778}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{779}\! \left(x \right)+F_{790}\! \left(x \right)\\
F_{779}\! \left(x \right) &= F_{13}\! \left(x \right) F_{780}\! \left(x \right)\\
F_{780}\! \left(x \right) &= F_{781}\! \left(x \right)+F_{782}\! \left(x \right)\\
F_{781}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{768}\! \left(x \right)\\
F_{782}\! \left(x \right) &= F_{783}\! \left(x \right)+F_{786}\! \left(x \right)\\
F_{783}\! \left(x \right) &= 4 F_{41}\! \left(x \right)+F_{779}\! \left(x \right)+F_{784}\! \left(x \right)\\
F_{784}\! \left(x \right) &= F_{13}\! \left(x \right) F_{785}\! \left(x \right)\\
F_{785}\! \left(x \right) &= F_{771}\! \left(x \right)+F_{783}\! \left(x \right)\\
F_{786}\! \left(x \right) &= 5 F_{41}\! \left(x \right)+F_{787}\! \left(x \right)+F_{788}\! \left(x \right)\\
F_{787}\! \left(x \right) &= F_{13}\! \left(x \right) F_{783}\! \left(x \right)\\
F_{788}\! \left(x \right) &= F_{13}\! \left(x \right) F_{789}\! \left(x \right)\\
F_{789}\! \left(x \right) &= F_{776}\! \left(x \right)+F_{786}\! \left(x \right)\\
F_{790}\! \left(x \right) &= F_{13}\! \left(x \right) F_{791}\! \left(x \right)\\
F_{791}\! \left(x \right) &= F_{785}\! \left(x \right)+F_{789}\! \left(x \right)\\
F_{792}\! \left(x \right) &= F_{158}\! \left(x \right) F_{793}\! \left(x \right)\\
F_{793}\! \left(x \right) &= F_{794}\! \left(x \right)\\
F_{794}\! \left(x \right) &= F_{13}\! \left(x \right) F_{795}\! \left(x \right)\\
F_{795}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{796}\! \left(x \right) &= F_{797}\! \left(x \right)\\
F_{797}\! \left(x \right) &= F_{13}\! \left(x \right) F_{57}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{798}\! \left(x \right) &= -F_{806}\! \left(x \right)+F_{799}\! \left(x \right)\\
F_{799}\! \left(x \right) &= \frac{F_{800}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{800}\! \left(x \right) &= F_{801}\! \left(x \right)\\
F_{801}\! \left(x \right) &= F_{677}\! \left(x \right)+F_{802}\! \left(x \right)\\
F_{802}\! \left(x \right) &= F_{803}\! \left(x \right)\\
F_{803}\! \left(x \right) &= F_{13}\! \left(x \right) F_{804}\! \left(x \right)\\
F_{804}\! \left(x \right) &= \frac{F_{805}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{805}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{806}\! \left(x \right) &= -F_{810}\! \left(x \right)+F_{807}\! \left(x \right)\\
F_{807}\! \left(x \right) &= \frac{F_{808}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{808}\! \left(x \right) &= F_{809}\! \left(x \right)\\
F_{809}\! \left(x \right) &= F_{13}\! \left(x \right) F_{799}\! \left(x \right)\\
F_{810}\! \left(x \right) &= \frac{F_{811}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{811}\! \left(x \right) &= F_{812}\! \left(x \right)\\
F_{812}\! \left(x \right) &= F_{13}\! \left(x \right) F_{813}\! \left(x \right)\\
F_{813}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{814}\! \left(x \right)\\
F_{814}\! \left(x \right) &= F_{815}\! \left(x \right)+F_{816}\! \left(x \right)\\
F_{815}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{816}\! \left(x \right) &= F_{684}\! \left(x \right)\\
F_{817}\! \left(x \right) &= -F_{829}\! \left(x \right)+F_{818}\! \left(x \right)\\
F_{818}\! \left(x \right) &= \frac{F_{819}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{819}\! \left(x \right) &= F_{820}\! \left(x \right)\\
F_{820}\! \left(x \right) &= F_{821}\! \left(x \right)\\
F_{821}\! \left(x \right) &= F_{13}\! \left(x \right) F_{795}\! \left(x \right) F_{822}\! \left(x \right)\\
F_{822}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{823}\! \left(x \right)\\
F_{823}\! \left(x \right) &= F_{824}\! \left(x \right)\\
F_{824}\! \left(x \right) &= F_{13}\! \left(x \right) F_{825}\! \left(x \right) F_{826}\! \left(x \right)\\
F_{825}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{826}\! \left(x \right) &= F_{827}\! \left(x \right)+F_{828}\! \left(x \right)\\
F_{827}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{721}\! \left(x \right)\\
F_{828}\! \left(x \right) &= F_{13}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{829}\! \left(x \right) &= F_{830}\! \left(x \right)\\
F_{830}\! \left(x \right) &= F_{13}\! \left(x \right) F_{81}\! \left(x \right) F_{822}\! \left(x \right)\\
F_{831}\! \left(x \right) &= \frac{F_{832}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{832}\! \left(x \right) &= F_{717}\! \left(x \right)\\
F_{833}\! \left(x \right) &= F_{13}\! \left(x \right) F_{834}\! \left(x \right)\\
F_{834}\! \left(x \right) &= \frac{F_{835}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{835}\! \left(x \right) &= F_{836}\! \left(x \right)\\
F_{836}\! \left(x \right) &= F_{13}\! \left(x \right) F_{837}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{837}\! \left(x \right) &= F_{665}\! \left(x \right)+F_{838}\! \left(x \right)\\
F_{838}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{839}\! \left(x \right) &= F_{840}\! \left(x \right)\\
F_{840}\! \left(x \right) &= F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{837}\! \left(x \right)\\
F_{841}\! \left(x \right) &= F_{664}\! \left(x \right) F_{842}\! \left(x \right)\\
F_{842}\! \left(x \right) &= -F_{892}\! \left(x \right)+F_{843}\! \left(x \right)\\
F_{843}\! \left(x \right) &= \frac{F_{844}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{844}\! \left(x \right) &= F_{845}\! \left(x \right)\\
F_{845}\! \left(x \right) &= -F_{887}\! \left(x \right)+F_{846}\! \left(x \right)\\
F_{846}\! \left(x \right) &= \frac{F_{847}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{847}\! \left(x \right) &= F_{848}\! \left(x \right)\\
F_{848}\! \left(x \right) &= F_{849}\! \left(x \right)\\
F_{849}\! \left(x \right) &= F_{13}\! \left(x \right) F_{850}\! \left(x \right)\\
F_{850}\! \left(x \right) &= F_{851}\! \left(x \right)+F_{858}\! \left(x \right)\\
F_{851}\! \left(x \right) &= F_{852}\! \left(x \right)+F_{853}\! \left(x \right)\\
F_{852}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{853}\! \left(x \right) &= F_{854}\! \left(x \right)\\
F_{854}\! \left(x \right) &= F_{15} \left(x \right)^{2} F_{13}\! \left(x \right) F_{855}\! \left(x \right)\\
F_{855}\! \left(x \right) &= F_{827}\! \left(x \right)+F_{856}\! \left(x \right)\\
F_{856}\! \left(x \right) &= F_{683}\! \left(x \right)+F_{857}\! \left(x \right)\\
F_{857}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{858}\! \left(x \right) &= F_{859}\! \left(x \right)\\
F_{859}\! \left(x \right) &= F_{13}\! \left(x \right) F_{860}\! \left(x \right)\\
F_{860}\! \left(x \right) &= F_{861}\! \left(x \right)+F_{883}\! \left(x \right)\\
F_{861}\! \left(x \right) &= F_{862}\! \left(x \right)+F_{878}\! \left(x \right)\\
F_{862}\! \left(x \right) &= F_{15}\! \left(x \right) F_{863}\! \left(x \right)\\
F_{863}\! \left(x \right) &= F_{864}\! \left(x \right)+F_{876}\! \left(x \right)\\
F_{864}\! \left(x \right) &= F_{865}\! \left(x \right)+F_{873}\! \left(x \right)\\
F_{865}\! \left(x \right) &= -F_{870}\! \left(x \right)+F_{866}\! \left(x \right)\\
F_{866}\! \left(x \right) &= \frac{F_{867}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{867}\! \left(x \right) &= F_{868}\! \left(x \right)\\
F_{868}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{869}\! \left(x \right)\\
F_{869}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{870}\! \left(x \right) &= F_{13}\! \left(x \right) F_{871}\! \left(x \right)\\
F_{871}\! \left(x \right) &= F_{658}\! \left(x \right)+F_{872}\! \left(x \right)\\
F_{872}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{873}\! \left(x \right) &= F_{820}\! \left(x \right)+F_{874}\! \left(x \right)\\
F_{874}\! \left(x \right) &= F_{875}\! \left(x \right)\\
F_{875}\! \left(x \right) &= F_{13}\! \left(x \right) F_{822}\! \left(x \right)\\
F_{876}\! \left(x \right) &= F_{877}\! \left(x \right)\\
F_{877}\! \left(x \right) &= F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{822}\! \left(x \right)\\
F_{878}\! \left(x \right) &= F_{879}\! \left(x \right)\\
F_{879}\! \left(x \right) &= F_{39}\! \left(x \right) F_{822}\! \left(x \right) F_{880}\! \left(x \right)\\
F_{880}\! \left(x \right) &= F_{881}\! \left(x \right)+F_{882}\! \left(x \right)\\
F_{881}\! \left(x \right) &= F_{35}\! \left(x \right) F_{825}\! \left(x \right)\\
F_{882}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{264}\! \left(x \right)\\
F_{883}\! \left(x \right) &= F_{884}\! \left(x \right)+F_{886}\! \left(x \right)\\
F_{884}\! \left(x \right) &= F_{15}\! \left(x \right) F_{885}\! \left(x \right)\\
F_{885}\! \left(x \right) &= F_{717}\! \left(x \right)+F_{720}\! \left(x \right)\\
F_{886}\! \left(x \right) &= F_{39}\! \left(x \right) F_{721}\! \left(x \right) F_{825}\! \left(x \right)\\
F_{887}\! \left(x \right) &= F_{888}\! \left(x \right)+F_{889}\! \left(x \right)\\
F_{888}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{801}\! \left(x \right)\\
F_{889}\! \left(x \right) &= F_{848}\! \left(x \right)+F_{890}\! \left(x \right)\\
F_{890}\! \left(x \right) &= F_{891}\! \left(x \right)\\
F_{891}\! \left(x \right) &= F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{892}\! \left(x \right) &= F_{893}\! \left(x \right)\\
F_{893}\! \left(x \right) &= \frac{F_{894}\! \left(x \right)}{F_{664}\! \left(x \right)}\\
F_{894}\! \left(x \right) &= -F_{898}\! \left(x \right)+F_{895}\! \left(x \right)\\
F_{895}\! \left(x \right) &= \frac{F_{896}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{896}\! \left(x \right) &= F_{897}\! \left(x \right)\\
F_{897}\! \left(x \right) &= F_{13}\! \left(x \right) F_{56}\! \left(x \right) F_{658}\! \left(x \right)\\
F_{898}\! \left(x \right) &= F_{0}\! \left(x \right) F_{899}\! \left(x \right)\\
F_{899}\! \left(x \right) &= F_{900}\! \left(x \right)\\
F_{900}\! \left(x \right) &= -F_{208}\! \left(x \right)+F_{901}\! \left(x \right)\\
F_{901}\! \left(x \right) &= \frac{F_{902}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{902}\! \left(x \right) &= F_{798}\! \left(x \right)\\
F_{903}\! \left(x \right) &= F_{142}\! \left(x \right) F_{842}\! \left(x \right)\\
F_{904}\! \left(x \right) &= F_{905}\! \left(x \right)\\
F_{905}\! \left(x \right) &= F_{906}\! \left(x \right)+F_{907}\! \left(x \right)\\
F_{906}\! \left(x \right) &= F_{721}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{907}\! \left(x \right) &= F_{908}\! \left(x \right)\\
F_{908}\! \left(x \right) &= F_{13}\! \left(x \right) F_{909}\! \left(x \right)\\
F_{909}\! \left(x \right) &= F_{910}\! \left(x \right)+F_{915}\! \left(x \right)\\
F_{910}\! \left(x \right) &= F_{132}\! \left(x \right) F_{911}\! \left(x \right)\\
F_{911}\! \left(x \right) &= \frac{F_{912}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{912}\! \left(x \right) &= -F_{894}\! \left(x \right)+F_{913}\! \left(x \right)\\
F_{913}\! \left(x \right) &= \frac{F_{914}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{914}\! \left(x \right) &= F_{897}\! \left(x \right)\\
F_{915}\! \left(x \right) &= F_{142}\! \left(x \right) F_{893}\! \left(x \right)\\
F_{916}\! \left(x \right) &= F_{158}\! \left(x \right) F_{917}\! \left(x \right)\\
F_{917}\! \left(x \right) &= F_{918}\! \left(x \right)\\
F_{918}\! \left(x \right) &= F_{13}\! \left(x \right) F_{919}\! \left(x \right)\\
F_{919}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{920}\! \left(x \right)\\
F_{920}\! \left(x \right) &= -F_{923}\! \left(x \right)+F_{921}\! \left(x \right)\\
F_{921}\! \left(x \right) &= \frac{F_{922}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{922}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{923}\! \left(x \right) &= F_{924}\! \left(x \right)\\
F_{924}\! \left(x \right) &= F_{13}\! \left(x \right) F_{139}\! \left(x \right)\\
F_{925}\! \left(x \right) &= F_{1012}\! \left(x \right)+F_{926}\! \left(x \right)\\
F_{926}\! \left(x \right) &= F_{927}\! \left(x \right)+F_{928}\! \left(x \right)\\
F_{927}\! \left(x \right) &= F_{132}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{928}\! \left(x \right) &= F_{929}\! \left(x \right)\\
F_{929}\! \left(x \right) &= F_{13}\! \left(x \right) F_{930}\! \left(x \right)\\
F_{930}\! \left(x \right) &= F_{931}\! \left(x \right)+F_{994}\! \left(x \right)\\
F_{931}\! \left(x \right) &= F_{132}\! \left(x \right) F_{932}\! \left(x \right)\\
F_{932}\! \left(x \right) &= \frac{F_{933}\! \left(x \right)}{F_{13}\! \left(x \right) F_{939}\! \left(x \right)}\\
F_{933}\! \left(x \right) &= F_{934}\! \left(x \right)\\
F_{934}\! \left(x \right) &= F_{935}\! \left(x \right)+F_{948}\! \left(x \right)\\
F_{935}\! \left(x \right) &= F_{936}\! \left(x \right)\\
F_{936}\! \left(x \right) &= F_{13}\! \left(x \right) F_{937}\! \left(x \right)\\
F_{937}\! \left(x \right) &= F_{938}\! \left(x \right)+F_{943}\! \left(x \right)\\
F_{938}\! \left(x \right) &= F_{935}\! \left(x \right)+F_{939}\! \left(x \right)\\
F_{939}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{940}\! \left(x \right)\\
F_{940}\! \left(x \right) &= F_{941}\! \left(x \right)\\
F_{941}\! \left(x \right) &= F_{13}\! \left(x \right) F_{942}\! \left(x \right)\\
F_{942}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{943}\! \left(x \right) &= F_{944}\! \left(x \right)+F_{946}\! \left(x \right)\\
F_{944}\! \left(x \right) &= F_{945}\! \left(x \right)\\
F_{945}\! \left(x \right) &= F_{13}\! \left(x \right) F_{939}\! \left(x \right)\\
F_{946}\! \left(x \right) &= F_{947}\! \left(x \right)\\
F_{947}\! \left(x \right) &= F_{13}\! \left(x \right) F_{935}\! \left(x \right)\\
F_{948}\! \left(x \right) &= -F_{993}\! \left(x \right)+F_{949}\! \left(x \right)\\
F_{949}\! \left(x \right) &= -F_{987}\! \left(x \right)+F_{950}\! \left(x \right)\\
F_{950}\! \left(x \right) &= -F_{969}\! \left(x \right)+F_{951}\! \left(x \right)\\
F_{951}\! \left(x \right) &= F_{952}\! \left(x \right)+F_{954}\! \left(x \right)\\
F_{952}\! \left(x \right) &= F_{953}\! \left(x \right)\\
F_{953}\! \left(x \right) &= F_{2}\! \left(x \right) F_{35}\! \left(x \right) F_{938}\! \left(x \right)\\
F_{954}\! \left(x \right) &= -F_{967}\! \left(x \right)+F_{955}\! \left(x \right)\\
F_{955}\! \left(x \right) &= \frac{F_{956}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{956}\! \left(x \right) &= F_{957}\! \left(x \right)\\
F_{957}\! \left(x \right) &= F_{13}\! \left(x \right) F_{939}\! \left(x \right) F_{958}\! \left(x \right)\\
F_{958}\! \left(x \right) &= F_{959}\! \left(x \right)+F_{963}\! \left(x \right)\\
F_{959}\! \left(x \right) &= F_{35}\! \left(x \right) F_{960}\! \left(x \right)\\
F_{960}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{961}\! \left(x \right)\\
F_{961}\! \left(x \right) &= F_{962}\! \left(x \right)\\
F_{962}\! \left(x \right) &= F_{13}\! \left(x \right) F_{958}\! \left(x \right)\\
F_{963}\! \left(x \right) &= F_{964}\! \left(x \right)\\
F_{964}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{965}\! \left(x \right)\\
F_{965}\! \left(x \right) &= \frac{F_{966}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{966}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{967}\! \left(x \right) &= F_{968}\! \left(x \right)\\
F_{968}\! \left(x \right) &= F_{0}\! \left(x \right) F_{35}\! \left(x \right) F_{938}\! \left(x \right)\\
F_{969}\! \left(x \right) &= -F_{970}\! \left(x \right)+F_{955}\! \left(x \right)\\
F_{970}\! \left(x \right) &= F_{971}\! \left(x \right)+F_{972}\! \left(x \right)\\
F_{971}\! \left(x \right) &= F_{827}\! \left(x \right) F_{939}\! \left(x \right)\\
F_{972}\! \left(x \right) &= \frac{F_{973}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{973}\! \left(x \right) &= F_{974}\! \left(x \right)\\
F_{974}\! \left(x \right) &= F_{13}\! \left(x \right) F_{939}\! \left(x \right) F_{975}\! \left(x \right)\\
F_{975}\! \left(x \right) &= F_{976}\! \left(x \right)\\
F_{976}\! \left(x \right) &= -F_{804}\! \left(x \right)+F_{977}\! \left(x \right)\\
F_{977}\! \left(x \right) &= \frac{F_{978}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{978}\! \left(x \right) &= F_{979}\! \left(x \right)\\
F_{979}\! \left(x \right) &= F_{980}\! \left(x \right)+F_{982}\! \left(x \right)\\
F_{980}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{981}\! \left(x \right)\\
F_{981}\! \left(x \right) &= F_{13}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{982}\! \left(x \right) &= F_{983}\! \left(x \right)+F_{984}\! \left(x \right)\\
F_{983}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{802}\! \left(x \right)\\
F_{984}\! \left(x \right) &= F_{985}\! \left(x \right)\\
F_{985}\! \left(x \right) &= F_{13}\! \left(x \right) F_{986}\! \left(x \right)\\
F_{986}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{683}\! \left(x \right)\\
F_{987}\! \left(x \right) &= F_{988}\! \left(x \right)+F_{989}\! \left(x \right)\\
F_{988}\! \left(x \right) &= F_{722}\! \left(x \right) F_{939}\! \left(x \right)\\
F_{989}\! \left(x \right) &= -F_{992}\! \left(x \right)+F_{990}\! \left(x \right)\\
F_{990}\! \left(x \right) &= F_{991}\! \left(x \right)\\
F_{991}\! \left(x \right) &= F_{13}\! \left(x \right) F_{911}\! \left(x \right) F_{939}\! \left(x \right)\\
F_{992}\! \left(x \right) &= F_{947}\! \left(x \right)\\
F_{993}\! \left(x \right) &= F_{57}\! \left(x \right) F_{939}\! \left(x \right)\\
F_{994}\! \left(x \right) &= F_{142}\! \left(x \right) F_{995}\! \left(x \right)\\
F_{995}\! \left(x \right) &= \frac{F_{996}\! \left(x \right)}{F_{664}\! \left(x \right)}\\
F_{996}\! \left(x \right) &= -F_{1011}\! \left(x \right)+F_{997}\! \left(x \right)\\
F_{997}\! \left(x \right) &= \frac{F_{998}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{998}\! \left(x \right) &= F_{999}\! \left(x \right)\\
F_{999}\! \left(x \right) &= -F_{1000}\! \left(x \right)+F_{865}\! \left(x \right)\\
F_{1000}\! \left(x \right) &= F_{1001}\! \left(x \right)+F_{1002}\! \left(x \right)\\
F_{1001}\! \left(x \right) &= F_{0}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{1002}\! \left(x \right) &= -F_{1003}\! \left(x \right)+F_{865}\! \left(x \right)\\
F_{1003}\! \left(x \right) &= F_{1004}\! \left(x \right)+F_{1005}\! \left(x \right)\\
F_{1004}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{857}\! \left(x \right)\\
F_{1005}\! \left(x \right) &= F_{1006}\! \left(x \right)\\
F_{1006}\! \left(x \right) &= F_{1007}\! \left(x \right) F_{13}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{1007}\! \left(x \right) &= F_{1004}\! \left(x \right)+F_{1008}\! \left(x \right)\\
F_{1008}\! \left(x \right) &= F_{1009}\! \left(x \right)+F_{1010}\! \left(x \right)\\
F_{1009}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{421}\! \left(x \right)\\
F_{1010}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{531}\! \left(x \right)\\
F_{1011}\! \left(x \right) &= F_{0}\! \left(x \right) F_{932}\! \left(x \right)\\
F_{1012}\! \left(x \right) &= F_{1013}\! \left(x \right)+F_{907}\! \left(x \right)\\
F_{1013}\! \left(x \right) &= F_{132}\! \left(x \right) F_{721}\! \left(x \right)\\
F_{1014}\! \left(x \right) &= F_{0}\! \left(x \right) F_{114}\! \left(x \right)\\
F_{1015}\! \left(x \right) &= F_{1016}\! \left(x \right) F_{116}\! \left(x \right)\\
F_{1016}\! \left(x \right) &= -F_{1019}\! \left(x \right)+F_{1017}\! \left(x \right)\\
F_{1017}\! \left(x \right) &= \frac{F_{1018}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1018}\! \left(x \right) &= F_{793}\! \left(x \right)\\
F_{1019}\! \left(x \right) &= F_{1020}\! \left(x \right)\\
F_{1020}\! \left(x \right) &= F_{1021}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1021}\! \left(x \right) &= F_{1022}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{1022}\! \left(x \right) &= F_{1023}\! \left(x \right)\\
F_{1023}\! \left(x \right) &= F_{1024}\! \left(x \right) F_{13}\! \left(x \right) F_{825}\! \left(x \right)\\
F_{1024}\! \left(x \right) &= F_{1025}\! \left(x \right)+F_{958}\! \left(x \right)\\
F_{1025}\! \left(x \right) &= F_{123}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1026}\! \left(x \right) &= F_{1019}\! \left(x \right) F_{116}\! \left(x \right)\\
F_{1027}\! \left(x \right) &= F_{1028}\! \left(x \right)\\
F_{1028}\! \left(x \right) &= F_{27}\! \left(x \right) F_{35}\! \left(x \right) F_{825}\! \left(x \right)\\
F_{1029}\! \left(x \right) &= F_{1030}\! \left(x \right)\\
F_{1030}\! \left(x \right) &= F_{1031}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1031}\! \left(x \right) &= F_{1032}\! \left(x \right)+F_{1123}\! \left(x \right)\\
F_{1032}\! \left(x \right) &= F_{1033}\! \left(x \right)+F_{1122}\! \left(x \right)\\
F_{1033}\! \left(x \right) &= F_{1034}\! \left(x \right)+F_{1120}\! \left(x \right)\\
F_{1034}\! \left(x \right) &= F_{1035}\! \left(x \right) F_{958}\! \left(x \right)\\
F_{1035}\! \left(x \right) &= F_{1036}\! \left(x \right)+F_{1118}\! \left(x \right)\\
F_{1036}\! \left(x \right) &= F_{1037}\! \left(x \right)+F_{1115}\! \left(x \right)\\
F_{1037}\! \left(x \right) &= F_{1038}\! \left(x \right)+F_{1039}\! \left(x \right)\\
F_{1038}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{1039}\! \left(x \right) &= -F_{1040}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{1040}\! \left(x \right) &= F_{1041}\! \left(x \right)\\
F_{1041}\! \left(x \right) &= F_{1042}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1042}\! \left(x \right) &= F_{1043}\! \left(x \right)\\
F_{1043}\! \left(x \right) &= F_{1044}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1044}\! \left(x \right) &= F_{1045}\! \left(x \right)+F_{1075}\! \left(x \right)\\
F_{1045}\! \left(x \right) &= \frac{F_{1046}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1046}\! \left(x \right) &= F_{1047}\! \left(x \right)\\
F_{1047}\! \left(x \right) &= F_{1048}\! \left(x \right)\\
F_{1048}\! \left(x \right) &= F_{1049}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1049}\! \left(x \right) &= F_{1050}\! \left(x \right)+F_{1053}\! \left(x \right)\\
F_{1050}\! \left(x \right) &= F_{1035}\! \left(x \right)+F_{1051}\! \left(x \right)\\
F_{1051}\! \left(x \right) &= F_{1052}\! \left(x \right)\\
F_{1052}\! \left(x \right) &= F_{1044}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1053}\! \left(x \right) &= F_{1054}\! \left(x \right)\\
F_{1054}\! \left(x \right) &= F_{1055}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{1055}\! \left(x \right) &= F_{1056}\! \left(x \right)+F_{1085}\! \left(x \right)\\
F_{1056}\! \left(x \right) &= F_{1057}\! \left(x \right)+F_{1058}\! \left(x \right)\\
F_{1057}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{1058}\! \left(x \right) &= F_{1059}\! \left(x \right)\\
F_{1059}\! \left(x \right) &= F_{1060}\! \left(x \right)\\
F_{1060}\! \left(x \right) &= F_{1061}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1061}\! \left(x \right) &= \frac{F_{1062}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1062}\! \left(x \right) &= F_{1063}\! \left(x \right)\\
F_{1063}\! \left(x \right) &= -F_{1084}\! \left(x \right)+F_{1064}\! \left(x \right)\\
F_{1064}\! \left(x \right) &= F_{1065}\! \left(x \right)+F_{1082}\! \left(x \right)\\
F_{1065}\! \left(x \right) &= F_{1066}\! \left(x \right)\\
F_{1066}\! \left(x \right) &= F_{1067}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1067}\! \left(x \right) &= -F_{1053}\! \left(x \right)+F_{1068}\! \left(x \right)\\
F_{1068}\! \left(x \right) &= \frac{F_{1069}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1069}\! \left(x \right) &= F_{1070}\! \left(x \right)\\
F_{1070}\! \left(x \right) &= F_{1071}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1071}\! \left(x \right) &= F_{1072}\! \left(x \right)+F_{1076}\! \left(x \right)\\
F_{1072}\! \left(x \right) &= F_{1073}\! \left(x \right)+F_{1075}\! \left(x \right)\\
F_{1073}\! \left(x \right) &= F_{1053}\! \left(x \right)+F_{1074}\! \left(x \right)\\
F_{1074}\! \left(x \right) &= F_{1050}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{1075}\! \left(x \right) &= F_{1050}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1076}\! \left(x \right) &= F_{1077}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{1077}\! \left(x \right) &= -F_{1080}\! \left(x \right)+F_{1078}\! \left(x \right)\\
F_{1078}\! \left(x \right) &= \frac{F_{1079}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1079}\! \left(x \right) &= F_{1051}\! \left(x \right)\\
F_{1080}\! \left(x \right) &= F_{1050}\! \left(x \right)+F_{1081}\! \left(x \right)\\
F_{1081}\! \left(x \right) &= -F_{1045}\! \left(x \right)+F_{1078}\! \left(x \right)\\
F_{1082}\! \left(x \right) &= F_{1083}\! \left(x \right)\\
F_{1083}\! \left(x \right) &= F_{1055}\! \left(x \right) F_{13}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{1084}\! \left(x \right) &= F_{1051}\! \left(x \right)+F_{1082}\! \left(x \right)\\
F_{1085}\! \left(x \right) &= F_{1086}\! \left(x \right)\\
F_{1086}\! \left(x \right) &= F_{1087}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1087}\! \left(x \right) &= \frac{F_{1088}\! \left(x \right)}{F_{822}\! \left(x \right)}\\
F_{1088}\! \left(x \right) &= -F_{1111}\! \left(x \right)+F_{1089}\! \left(x \right)\\
F_{1089}\! \left(x \right) &= \frac{F_{1090}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1090}\! \left(x \right) &= F_{1091}\! \left(x \right)\\
F_{1091}\! \left(x \right) &= -F_{1106}\! \left(x \right)+F_{1092}\! \left(x \right)\\
F_{1092}\! \left(x \right) &= \frac{F_{1093}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1093}\! \left(x \right) &= F_{1094}\! \left(x \right)\\
F_{1094}\! \left(x \right) &= -F_{1105}\! \left(x \right)+F_{1095}\! \left(x \right)\\
F_{1095}\! \left(x \right) &= -F_{1098}\! \left(x \right)+F_{1096}\! \left(x \right)\\
F_{1096}\! \left(x \right) &= \frac{F_{1097}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1097}\! \left(x \right) &= F_{983}\! \left(x \right)\\
F_{1098}\! \left(x \right) &= F_{1099}\! \left(x \right)\\
F_{1099}\! \left(x \right) &= F_{1100}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1100}\! \left(x \right) &= F_{1101}\! \left(x \right)+F_{1103}\! \left(x \right)\\
F_{1101}\! \left(x \right) &= \frac{F_{1102}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1102}\! \left(x \right) &= F_{1039}\! \left(x \right)\\
F_{1103}\! \left(x \right) &= F_{1104}\! \left(x \right)\\
F_{1104}\! \left(x \right) &= F_{1044}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1105}\! \left(x \right) &= F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{1106}\! \left(x \right) &= F_{1107}\! \left(x \right)\\
F_{1107}\! \left(x \right) &= F_{1108}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1108}\! \left(x \right) &= F_{1109}\! \left(x \right)+F_{1110}\! \left(x \right)\\
F_{1109}\! \left(x \right) &= F_{1101}\! \left(x \right) F_{822}\! \left(x \right)\\
F_{1110}\! \left(x \right) &= F_{1042}\! \left(x \right)\\
F_{1111}\! \left(x \right) &= F_{1112}\! \left(x \right) F_{1113}\! \left(x \right)\\
F_{1112}\! \left(x \right) &= F_{1100}\! \left(x \right)+F_{1110}\! \left(x \right)\\
F_{1113}\! \left(x \right) &= \frac{F_{1114}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1114}\! \left(x \right) &= F_{823}\! \left(x \right)\\
F_{1115}\! \left(x \right) &= F_{1116}\! \left(x \right)\\
F_{1116}\! \left(x \right) &= F_{1117}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1117}\! \left(x \right) &= F_{1036}\! \left(x \right)+F_{1051}\! \left(x \right)\\
F_{1118}\! \left(x \right) &= F_{1119}\! \left(x \right)\\
F_{1119}\! \left(x \right) &= F_{1047}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{1120}\! \left(x \right) &= F_{1121}\! \left(x \right)\\
F_{1121}\! \left(x \right) &= F_{1055}\! \left(x \right) F_{15}\! \left(x \right) F_{825}\! \left(x \right)\\
F_{1122}\! \left(x \right) &= F_{1077}\! \left(x \right) F_{123}\! \left(x \right)\\
F_{1123}\! \left(x \right) &= F_{1124}\! \left(x \right)\\
F_{1124}\! \left(x \right) &= F_{1061}\! \left(x \right) F_{35}\! \left(x \right) F_{825}\! \left(x \right)\\
F_{1125}\! \left(x \right) &= F_{1126}\! \left(x \right)\\
F_{1126}\! \left(x \right) &= F_{1127}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1127}\! \left(x \right) &= F_{1128}\! \left(x \right)+F_{1161}\! \left(x \right)\\
F_{1128}\! \left(x \right) &= F_{1129}\! \left(x \right)+F_{1130}\! \left(x \right)\\
F_{1129}\! \left(x \right) &= F_{1037}\! \left(x \right) F_{158}\! \left(x \right)\\
F_{1130}\! \left(x \right) &= F_{1131}\! \left(x \right)\\
F_{1131}\! \left(x \right) &= F_{1132}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1132}\! \left(x \right) &= F_{1133}\! \left(x \right)+F_{1137}\! \left(x \right)\\
F_{1133}\! \left(x \right) &= F_{1134}\! \left(x \right) F_{201}\! \left(x \right)\\
F_{1134}\! \left(x \right) &= -F_{1135}\! \left(x \right)+F_{1035}\! \left(x \right)\\
F_{1135}\! \left(x \right) &= F_{1136}\! \left(x \right)\\
F_{1136}\! \left(x \right) &= F_{1050}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1137}\! \left(x \right) &= F_{1138}\! \left(x \right) F_{842}\! \left(x \right)\\
F_{1138}\! \left(x \right) &= F_{1139}\! \left(x \right)\\
F_{1139}\! \left(x \right) &= F_{1140}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{1140}\! \left(x \right) &= F_{1141}\! \left(x \right)+F_{1146}\! \left(x \right)\\
F_{1141}\! \left(x \right) &= -F_{1145}\! \left(x \right)+F_{1142}\! \left(x \right)\\
F_{1142}\! \left(x \right) &= \frac{F_{1143}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1143}\! \left(x \right) &= F_{1144}\! \left(x \right)\\
F_{1144}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{1145}\! \left(x \right) &= F_{1040}\! \left(x \right)+F_{1057}\! \left(x \right)\\
F_{1146}\! \left(x \right) &= -F_{1154}\! \left(x \right)+F_{1147}\! \left(x \right)\\
F_{1147}\! \left(x \right) &= -F_{1059}\! \left(x \right)+F_{1148}\! \left(x \right)\\
F_{1148}\! \left(x \right) &= \frac{F_{1149}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1149}\! \left(x \right) &= F_{1150}\! \left(x \right)\\
F_{1150}\! \left(x \right) &= -F_{133}\! \left(x \right)+F_{1151}\! \left(x \right)\\
F_{1151}\! \left(x \right) &= -F_{8}\! \left(x \right)+F_{1152}\! \left(x \right)\\
F_{1152}\! \left(x \right) &= \frac{F_{1153}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1153}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{1154}\! \left(x \right) &= F_{1155}\! \left(x \right)\\
F_{1155}\! \left(x \right) &= -F_{1159}\! \left(x \right)+F_{1156}\! \left(x \right)\\
F_{1156}\! \left(x \right) &= \frac{F_{1157}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1157}\! \left(x \right) &= F_{1158}\! \left(x \right)\\
F_{1158}\! \left(x \right) &= F_{1144}\! \left(x \right)+F_{1150}\! \left(x \right)\\
F_{1159}\! \left(x \right) &= \frac{F_{1160}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{1160}\! \left(x \right) &= F_{1055}\! \left(x \right)\\
F_{1161}\! \left(x \right) &= F_{1162}\! \left(x \right) F_{158}\! \left(x \right)\\
F_{1162}\! \left(x \right) &= F_{1144}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 353 rules.
Finding the specification took 51136 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_{48}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{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_{21}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{17}\! \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_{12}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{12}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{30}\! \left(x \right) &= 0\\
F_{31}\! \left(x \right) &= F_{12}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{35}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{12}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{12}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{12}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{42}\! \left(x \right) &= 2 F_{30}\! \left(x \right)+F_{43}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{12}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{12}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{12}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{12}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{12}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{4}\! \left(x \right) F_{6}\! \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_{300}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{12}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x , 1\right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right) F_{76}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{6}\! \left(x \right)+F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{76}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= y x\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{14}\! \left(x \right) F_{5}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x , 1\right)\\
F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{282}\! \left(x \right)+F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{25}\! \left(x \right) F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{278}\! \left(x , y\right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{298}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{295}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{12}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{14}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{22}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{235}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{216}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{107}\! \left(x \right) F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{122}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \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_{234}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{220}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{107}\! \left(x \right) F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= \frac{F_{132}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= -F_{138}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{12}\! \left(x \right) F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{219}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{0}\! \left(x \right) F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{12}\! \left(x \right) F_{131}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{119}\! \left(x \right) F_{12}\! \left(x \right) F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{149}\! \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_{152}\! \left(x \right)+F_{131}\! \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_{12}\! \left(x \right)}\\
F_{154}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{155}\! \left(x \right) &= \frac{F_{156}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= -F_{212}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= \frac{F_{159}\! \left(x \right)}{F_{178}\! \left(x \right)}\\
F_{159}\! \left(x \right) &= -F_{166}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= \frac{F_{161}\! \left(x \right)}{F_{12}\! \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_{12}\! \left(x \right)}\\
F_{164}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{107}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{12}\! \left(x \right) F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{208}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{12}\! \left(x \right) F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{12}\! \left(x \right) F_{171}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{12}\! \left(x \right) F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= -F_{185}\! \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_{122}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{12}\! \left(x \right) F_{174}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x , 1\right)\\
F_{188}\! \left(x , y\right) &= -\frac{-y F_{189}\! \left(x , y\right)+F_{189}\! \left(x , 1\right)}{-1+y}\\
F_{189}\! \left(x , y\right) &= F_{190}\! \left(x , y\right)\\
F_{190}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{191}\! \left(x , y\right)\\
F_{191}\! \left(x , y\right) &= F_{192}\! \left(x , y\right)+F_{208}\! \left(x \right)\\
F_{192}\! \left(x , y\right) &= F_{167}\! \left(x \right)+F_{193}\! \left(x , y\right)\\
F_{193}\! \left(x , y\right) &= F_{194}\! \left(x , y\right)\\
F_{194}\! \left(x , y\right) &= F_{195}\! \left(x , y\right) F_{200}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{195}\! \left(x , y\right) &= F_{196}\! \left(x \right)+F_{197}\! \left(x , y\right)\\
F_{196}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{197}\! \left(x , y\right) &= y F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{12}\! \left(x \right) F_{167}\! \left(x \right)\\
F_{200}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{201}\! \left(x , y\right)\\
F_{201}\! \left(x , y\right) &= F_{202}\! \left(x , y\right)\\
F_{202}\! \left(x , y\right) &= F_{203}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{203}\! \left(x , y\right) &= F_{204}\! \left(x , y\right)+F_{205}\! \left(x , y\right)\\
F_{204}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{78}\! \left(x , y\right)\\
F_{205}\! \left(x , y\right) &= F_{201}\! \left(x , y\right)+F_{206}\! \left(x , y\right)\\
F_{206}\! \left(x , y\right) &= F_{207}\! \left(x , y\right)\\
F_{207}\! \left(x , y\right) &= F_{201}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{12}\! \left(x \right) F_{180}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{215}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{12}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= -F_{112}\! \left(x \right)+F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= \frac{F_{218}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{218}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{0}\! \left(x \right) F_{149}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{151}\! \left(x \right) F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= -F_{226}\! \left(x \right)+F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= \frac{F_{223}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{12}\! \left(x \right) F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{12}\! \left(x \right) F_{228}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{12}\! \left(x \right) F_{231}\! \left(x \right) F_{232}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{12}\! \left(x \right) F_{158}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{151}\! \left(x \right) F_{226}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x , 1\right)\\
F_{237}\! \left(x , y\right) &= F_{200}\! \left(x , y\right) F_{204}\! \left(x , y\right) F_{97}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{12}\! \left(x \right) F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{290}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{210}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{14}\! \left(x \right) F_{231}\! \left(x \right) F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{12}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)+F_{287}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{261}\! \left(x \right)\\
F_{250}\! \left(x \right) &= -F_{259}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= \frac{F_{252}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{256}\! \left(x \right) &= -F_{257}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{12}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)+F_{274}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{12}\! \left(x \right) F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{12}\! \left(x \right) F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)+F_{271}\! \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_{262}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{12}\! \left(x \right) F_{265}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{14}\! \left(x \right) F_{246}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x , 1\right)\\
F_{275}\! \left(x , y\right) &= -\frac{y \left(F_{276}\! \left(x , 1\right)-F_{276}\! \left(x , y\right)\right)}{-1+y}\\
F_{276}\! \left(x , y\right) &= F_{277}\! \left(x , y\right)\\
F_{277}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{278}\! \left(x , y\right)\\
F_{278}\! \left(x , y\right) &= F_{279}\! \left(x , y\right)\\
F_{279}\! \left(x , y\right) &= F_{200}\! \left(x , y\right) F_{280}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{280}\! \left(x , y\right) &= F_{281}\! \left(x , y\right)+F_{282}\! \left(x \right)\\
F_{281}\! \left(x , y\right) &= F_{204}\! \left(x , y\right) F_{87}\! \left(x \right)\\
F_{282}\! \left(x \right) &= -F_{285}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= \frac{F_{284}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{284}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= -F_{269}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{12}\! \left(x \right) F_{265}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{158}\! \left(x \right) F_{282}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{231}\! \left(x \right) F_{25}\! \left(x \right) F_{292}\! \left(x \right)\\
F_{292}\! \left(x \right) &= \frac{F_{293}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{262}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{12}\! \left(x \right) F_{297}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{14}\! \left(x \right) F_{262}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{301}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{12}\! \left(x \right) F_{302}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{347}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{304}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{305}\! \left(x , 1\right)\\
F_{305}\! \left(x , y\right) &= F_{306}\! \left(x \right)+F_{346}\! \left(x , y\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_{5}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{12}\! \left(x \right) F_{304}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{311}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{312}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{12}\! \left(x \right) F_{313}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{324}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{315}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{316}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{12}\! \left(x \right) F_{317}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{318}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{321}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{320}\! \left(x \right)\\
F_{320}\! \left(x \right) &= x^{2}\\
F_{321}\! \left(x \right) &= 2 F_{30}\! \left(x \right)+F_{322}\! \left(x \right)+F_{323}\! \left(x \right)\\
F_{322}\! \left(x \right) &= F_{12}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{323}\! \left(x \right) &= F_{12}\! \left(x \right) F_{318}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{332}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{12}\! \left(x \right) F_{327}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{329}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{319}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{330}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{331}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{12}\! \left(x \right) F_{325}\! \left(x \right)\\
F_{332}\! \left(x \right) &= 2 F_{30}\! \left(x \right)+F_{333}\! \left(x \right)+F_{344}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{12}\! \left(x \right) F_{334}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right)+F_{336}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{321}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{337}\! \left(x \right)+F_{340}\! \left(x \right)\\
F_{337}\! \left(x \right) &= 2 F_{30}\! \left(x \right)+F_{333}\! \left(x \right)+F_{338}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{12}\! \left(x \right) F_{339}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{340}\! \left(x \right) &= 3 F_{30}\! \left(x \right)+F_{341}\! \left(x \right)+F_{342}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{12}\! \left(x \right) F_{337}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{12}\! \left(x \right) F_{343}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{340}\! \left(x \right)\\
F_{344}\! \left(x \right) &= F_{12}\! \left(x \right) F_{345}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{339}\! \left(x \right)+F_{343}\! \left(x \right)\\
F_{346}\! \left(x , y\right) &= F_{307}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{347}\! \left(x \right) &= F_{307}\! \left(x \right) F_{348}\! \left(x \right)\\
F_{348}\! \left(x \right) &= \frac{F_{349}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{349}\! \left(x \right) &= F_{350}\! \left(x \right)\\
F_{350}\! \left(x \right) &= -F_{351}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{351}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{352}\! \left(x \right)\\
F_{352}\! \left(x \right) &= F_{294}\! \left(x \right)\\
\end{align*}\)