Av(13452, 13524, 13542, 14352, 14532, 15324, 15342, 15432, 41352, 41532)
Counting Sequence
1, 1, 2, 6, 24, 110, 540, 2762, 14539, 78236, 428482, 2380853, 13389383, 76068459, 435937577, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(9 x^{3}-18 x^{2}+x -3\right) x^{2} F \left(x
\right)^{7}-x^{2} \left(15 x^{3}-25 x^{2}-6 x -26\right) F \left(x
\right)^{6}+\left(5 x^{5}-2 x^{4}-3 x^{3}-88 x^{2}+x -1\right) F \left(x
\right)^{5}+\left(x^{5}-3 x^{4}-18 x^{3}+127 x^{2}-3 x +10\right) F \left(x
\right)^{4}+\left(-x^{4}+6 x^{3}-60 x^{2}+4 x -36\right) F \left(x
\right)^{3}+\left(2 x^{3}+9 x^{2}-18 x +54\right) F \left(x
\right)^{2}+\left(x^{2}+7 x -27\right) F \! \left(x \right)+x = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 110\)
\(\displaystyle a(6) = 540\)
\(\displaystyle a(7) = 2762\)
\(\displaystyle a(8) = 14539\)
\(\displaystyle a(9) = 78236\)
\(\displaystyle a(10) = 428482\)
\(\displaystyle a(11) = 2380853\)
\(\displaystyle a(12) = 13389383\)
\(\displaystyle a(13) = 76068459\)
\(\displaystyle a(14) = 435937577\)
\(\displaystyle a(15) = 2517138965\)
\(\displaystyle a(16) = 14629776532\)
\(\displaystyle a(17) = 85521335684\)
\(\displaystyle a(18) = 502497519336\)
\(\displaystyle a(19) = 2966045949613\)
\(\displaystyle a(20) = 17579415924432\)
\(\displaystyle a(21) = 104578162246995\)
\(\displaystyle a(22) = 624221661932913\)
\(\displaystyle a(23) = 3737393952178107\)
\(\displaystyle a(24) = 22439771972123562\)
\(\displaystyle a(25) = 135079216108093669\)
\(\displaystyle a(26) = 815064057509979186\)
\(\displaystyle a(27) = 4928905550378813701\)
\(\displaystyle a(28) = 29867277375537968677\)
\(\displaystyle a(29) = 181328155285882444097\)
\(\displaystyle a(30) = 1102817552899617976007\)
\(\displaystyle a(31) = 6718320413669708477809\)
\(\displaystyle a(32) = 40991228005851501460835\)
\(\displaystyle a(33) = 250468464585751400087416\)
\(\displaystyle a(34) = 1532531820646166405940393\)
\(\displaystyle a(35) = 9389142727155106779110544\)
\(\displaystyle a(36) = 57593163527534475696147964\)
\(\displaystyle a(37) = 353684165190371039743887559\)
\(\displaystyle a(38) = 2174369877515346681538200603\)
\(\displaystyle a(39) = 13381347627871646523916939936\)
\(\displaystyle a(40) = 82431321244369925740793723365\)
\(\displaystyle a(41) = 508264377225517963151182197947\)
\(\displaystyle a(42) = 3136697406922114523242867803404\)
\(\displaystyle a(43) = 19374166423901236476414020616243\)
\(\displaystyle a(44) = 119763375267855785239115592240172\)
\(\displaystyle a(45) = 740900542034661496709128157527571\)
\(\displaystyle a(46) = 4586865437646708421565235050341960\)
\(\displaystyle a(47) = 28417021176248301633317477728927606\)
\(\displaystyle a(48) = 176171111330168163496800476123942396\)
\(\displaystyle a(49) = 1092879679096529271087229141792311934\)
\(\displaystyle a(50) = 6783911497839683684736717307146475996\)
\(\displaystyle a(51) = 42135435479261180274913329562389720330\)
\(\displaystyle a(52) = 261857028769954197722476962291829945270\)
\(\displaystyle a(53) = 1628249444264282887008817471679776864735\)
\(\displaystyle a(54) = 10129981314982773378963005571927464080540\)
\(\displaystyle a(55) = 63054907544723210764723156890544213673606\)
\(\displaystyle a(56) = 392684430403730039849362303067149727340042\)
\(\displaystyle a(57) = 2446670198205902966416907244515679198089330\)
\(\displaystyle a(58) = 15251303311737442845397109805538445003116627\)
\(\displaystyle a(59) = 95111152426690018961648312677504447188165030\)
\(\displaystyle a(60) = 593392995073209636922422654273105228002092335\)
\(\displaystyle a(61) = 3703682238260223376005372486832513401727651785\)
\(\displaystyle a(62) = 23125945660088255220365865348297812531454549704\)
\(\displaystyle a(63) = 144455535294460952025366038332413994152813948570\)
\(\displaystyle a(64) = 902677192723506053456726195238072113210156630412\)
\(\displaystyle a(65) = 5642730152302931668127311608592142116329913671836\)
\(\displaystyle a(66) = 35285785704288830036855001012786703461969596166114\)
\(\displaystyle a(67) = 220728995050239267962150045543901652932007101761851\)
\(\displaystyle a(68) = 1381222527630204250214007740498663963947636683905013\)
\(\displaystyle a(69) = 8645863529380118094438336751857773752925210931005359\)
\(\displaystyle a(70) = 54136418373459155280207656648742267749989464003130443\)
\(\displaystyle a(71) = 339080816237133171574974985997417776413229210556141378\)
\(\displaystyle a(72) = 2124446381055640010399896739816358403136351166000882464\)
\(\displaystyle a(73) = 13314155778089600998377230267827617250985548559270567085\)
\(\displaystyle a(74) = 83464807112673329058773172426962241372506571967046713563\)
\(\displaystyle a(75) = 523373569627739487909252259412361245592158844694467178806\)
\(\displaystyle a(76) = 3282733859501981696228991529170488309778281338308745603804\)
\(\displaystyle a(77) = 20595485874466609787808496670328060681212982799594000161724\)
\(\displaystyle a(78) = 129246261645871663429671706981008127783552455423854832224951\)
\(\displaystyle a(79) = 811279928806590801852563552610121115366030967519991148985136\)
\(\displaystyle a(80) = 5093632207520221076689115607094339439115784492290442527603161\)
\(\displaystyle a(81) = 31987917058090215488592561074233401995522657678666271475896066\)
\(\displaystyle a(82) = 200929349566690653151425614498355348251372165465971156216874459\)
\(\displaystyle a(83) = 1262401309978917389788330493273359772524349580735881683286161577\)
\(\displaystyle a(84) = 7933152885105217332723945920525214493645000041745935098012400647\)
\(\displaystyle a(85) = 49863907798766032551876835185865211479980629641504706002381670870\)
\(\displaystyle a(86) = 313484985963493469236427677005767098787048233701905490350209571661\)
\(\displaystyle a(87) = 1971219791969600184465260521774463772711870082581674408656336336073\)
\(\displaystyle a(88) = 12397645707332655754071858497492939255531098575288836828513557079736\)
\(\displaystyle a(89) = 77987916488237413599681102243647305976307228809747053239013479868433\)
\(\displaystyle a(90) = 490678996219144658964282766709799478615283068713228763854303723195049\)
\(\displaystyle a{\left(n + 91 \right)} = - \frac{330596973697832246875 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) a{\left(n \right)}}{1774558629158094 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{125 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(20227198098987163912193 n + 119230394257462523801511\right) a{\left(n + 1 \right)}}{170357628399177024 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{25 \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(7603452826760743041105422 n^{2} + 96293610652163918881624958 n + 303788461512476442736287981\right) a{\left(n + 2 \right)}}{340715256798354048 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{5 \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(129499105711344139595648468557 n^{3} + 2630272169749530530833084375545 n^{2} + 17737198503559339223730126909146 n + 39709202565131954047658409437568\right) a{\left(n + 3 \right)}}{49062996978962982912 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(n + 4\right) \left(n + 5\right) \left(32087466619041827505321025262006 n^{4} + 923138478400298288459686211279433 n^{3} + 9915288727330894866823806727613863 n^{2} + 47121202169748229860009956903016858 n + 83589245207191668029674990680824832\right) a{\left(n + 4 \right)}}{147188990936888948736 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(n + 5\right) \left(760723405211021812758109421644581 n^{5} + 28770092317311473520869625541513416 n^{4} + 433062516719026219418155983958815355 n^{3} + 3243370360799914417617882613242590420 n^{2} + 12085718704072937784602357672026442044 n + 17923828474788768314559994300227308544\right) a{\left(n + 5 \right)}}{294377981873777897472 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(21754980365769 n^{3} + 5827914091828809 n^{2} + 520405770399729884 n + 15489789408263246304\right) a{\left(n + 90 \right)}}{50087177010 \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(515132437405321867 n^{4} + 180910225571795921844 n^{3} + 23825598969304490996949 n^{2} + 1394593375720412758931164 n + 30611778919234258928509152\right) a{\left(n + 89 \right)}}{12171184013430 \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(4462405827106720818493 n^{5} + 1935073853913146786771330 n^{4} + 335632253890005514901717675 n^{3} + 29105657617874834645907912910 n^{2} + 1261939786187900447234702341752 n + 21884530576553078479435469799360\right) a{\left(n + 88 \right)}}{657243936725220 \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(2322831794269756627337209 n^{6} + 1201513401490884922148463551 n^{5} + 258943843711829033116780968025 n^{4} + 29761756359426380508732146190425 n^{3} + 1924027301985396351603833597141566 n^{2} + 66334540197324320125769974789885304 n + 952870709231781504093536680234246080\right) a{\left(n + 87 \right)}}{7886927240702640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(2277492536530962214800938531 n^{6} + 1171773531612550130596280698621 n^{5} + 251186402509463482112614540251795 n^{4} + 28716022640687441029640470025620715 n^{3} + 1846511405085511309215821238490033114 n^{2} + 63322124613349461818553657789065666664 n + 904742095352691461719099938356671387200\right) a{\left(n + 86 \right)}}{425894070997942560 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(100574538584915415889524031287 n^{6} + 52442933726549937060442909944803 n^{5} + 11385743661358202961674030957397385 n^{4} + 1317457168957104570216931521575298025 n^{3} + 85693952881224305357527719265579839128 n^{2} + 2970924993414573273051373451577825149052 n + 42890708010545635751098492789719193273200\right) a{\left(n + 85 \right)}}{2555364425987655360 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(11852410857682977156021168130055 n^{6} + 5508040940315617668645944072992953 n^{5} + 1059173637424803111339645954448985195 n^{4} + 107735307250151743690378005081620410695 n^{3} + 6103037219807870764693698131646098297990 n^{2} + 182136344141082945346135551000583928172792 n + 2229904299680371305117288714717817849068480\right) a{\left(n + 84 \right)}}{45996559667777796480 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(1494468428214128265060793563412165 n^{6} + 733660958336570769659619785501946576 n^{5} + 150010761702036601923193997566698495640 n^{4} + 16352065102211516642324175158947546775190 n^{3} + 1002222947527051169536060453786144435048075 n^{2} + 32746738322422428878483771535603095377964634 n + 445623028697479625220646815208980150871713240\right) a{\left(n + 83 \right)}}{137989679003333389440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(73908881175760153438410061097714858 n^{6} + 36266011736770456716483435552326033343 n^{5} + 7413628283288388568525745306902997295950 n^{4} + 808163519963548571079498905357438431288905 n^{3} + 49548269434385678550411049708530177099360092 n^{2} + 1619922751917148078154887186953220559862395772 n + 22064101005860139168249622286642192734303896720\right) a{\left(n + 82 \right)}}{413969037010000168320 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(272683130830233492943043355014006791 n^{6} + 12697022585415363813882393465083925981 n^{5} + 244555105260198958750805327942516138185 n^{4} + 2494645845803249393330819226590115061335 n^{3} + 14217592314859739241385498743852264964984 n^{2} + 42933851683254070771162193413137671948724 n + 53679616494928231996838506310935513400880\right) a{\left(n + 6 \right)}}{13247009184320005386240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(4971654618186113923025707819063073185 n^{6} + 188388940424222306453470835814741525357 n^{5} + 2398116211547876702154493947128770423225 n^{4} + 6693332746306602924593623711629371350515 n^{3} - 100786262185213177196708836685987371252130 n^{2} - 866656815357373666156533527109294250190712 n - 2008792032952489046010492819115903791644160\right) a{\left(n + 7 \right)}}{79482055105920032317440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(28104076034282220256067156179015435261 n^{6} + 13533740490845495687512717443634556368929 n^{5} + 2715717700047142650435401029913102140692895 n^{4} + 290656502575393576929381748703218889779021755 n^{3} + 17499607285548226556711966763648651896293431364 n^{2} + 561960729670125694299613657329560171734088885316 n + 7519750002305822431239897081074045968617746500800\right) a{\left(n + 81 \right)}}{9935256888240004039680 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(91821215166802133578190922613929397177 n^{6} + 6816376339301091635293886242942530134243 n^{5} + 202727261157367631886915513150004248984945 n^{4} + 3121807046275326552772942598126668467782605 n^{3} + 26410524988399913425454882526323469099570398 n^{2} + 116855485667642183508243842694978128578575192 n + 211853271614969394776509853735058793725543840\right) a{\left(n + 8 \right)}}{79482055105920032317440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(3121862826098550677403976198702451459821 n^{6} + 1473032940192949275799391640096253510022295 n^{5} + 289596821785601550475440593728012534974416725 n^{4} + 30364707524528201014119668590586971453638664545 n^{3} + 1790867889227953095206255989588350399132075036574 n^{2} + 56331943378586547538345450938280922132248649391720 n + 738302141184827351417114795760815419246617405870720\right) a{\left(n + 80 \right)}}{59611541329440024238080 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(18332595245190196722411122558289360129695 n^{6} + 1350088374653246299746524838846489221513907 n^{5} + 40887814810917769397723831892297120970513775 n^{4} + 652709847384159627294916647013093122694834365 n^{3} + 5798703282709404308456552060302777267164665450 n^{2} + 27206622363785004122754188328691474409633728248 n + 52703836882370336877847011510448110497270814240\right) a{\left(n + 9 \right)}}{715338495953280290856960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(161507454269181484694624322304828523560598 n^{6} + 75305180430556325304715135496687167520707317 n^{5} + 14628890858586158931652928783526252448436969255 n^{4} + 1515522335764731067164998487616404565379540703405 n^{3} + 88308326134410552596265435685859343451849561014467 n^{2} + 2744136605292756946904014648448754014139621576345918 n + 35527512649989707425499386085513623741739937260398560\right) a{\left(n + 79 \right)}}{178834623988320072714240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(678078500281086373100965400215328154687323 n^{6} + 52856833201669985491426964280692510308358163 n^{5} + 1702917218360029683665005864260984612834015185 n^{4} + 29039411913348494719854768644579677096940781585 n^{3} + 276563834900940843195694640838970919451197376812 n^{2} + 1395250404472112301794167312425070180847576900052 n + 2913965106656557830015433494657661219608118518240\right) a{\left(n + 10 \right)}}{2146015487859840872570880 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - 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\frac{\left(27837561363719906321037483496149983641453658918151184580 n^{6} + 9480904249457429386403114238828736420409760846543954820779 n^{5} + 1345193020416563195267522399650271899374037710686744884721378 n^{4} + 101775712237091874750237936759708017692330602626797275301530147 n^{3} + 4330624407070931686460125231027406109356025045243948151587025820 n^{2} + 98260304479113318190635429159029098641165761044189154538540179532 n + 928784589221735252256718944525609094638604878802498486833623445912\right) a{\left(n + 56 \right)}}{965706969536928392656896 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(28858684746738588687679591510731905093693297899959289237 n^{6} + 6228946654439036435407724655490616575815772642643466720007 n^{5} + 560357851476204401307228669333306073751099460064511831308425 n^{4} + 26894843122053547552274610277937942235246046066269581728894305 n^{3} + 726409492030986885322984659220031419287370904163099366832576058 n^{2} + 10469212669967561222030615492942043062457100103457773394774035168 n + 62906251357437146125127588889255697352003894455157177430744697680\right) a{\left(n + 36 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(36375148941242025396848741444609882726743020562896274535 n^{6} + 8714791112751952755994580831446873614062528949685300399943 n^{5} + 869907813956167147471710692429073657756560035057921378828391 n^{4} + 46309628020014009310810445487500271547551956193206199571785201 n^{3} + 1386704213756129986929460930628409604444333849270989243023805602 n^{2} + 22146090332225955032614746968573202787292767796553293104658576776 n + 147371060625091261533283825968556062964130409163599851987649768144\right) a{\left(n + 40 \right)}}{1287609292715904523542528 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(45528355744949750768617587652242934757899375947107653637 n^{6} + 16287604858550408301775271724557951380446258020822706170523 n^{5} + 2427151582247959201819125529101764263636979139861578646894365 n^{4} + 192842587754094953997725772734904759628530473924397979493198685 n^{3} + 8615700643667711575739069171786641756844449033013262062021129558 n^{2} + 205223395633059560109310981279727142902703026321689813450778541072 n + 2036066442007234028658723319626715874027046027824120816231160958800\right) a{\left(n + 60 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(74300718647488873447929962754033396655700484558627103330 n^{6} + 16464742789145412411409954635333001135031755835609292647913 n^{5} + 1520405568627131779904442665975261576018549684664272060879140 n^{4} + 74892752752118365577486028734408043073108828946711816645541435 n^{3} + 2075608087060750829545995661257321962782880982140131464924854110 n^{2} + 30688822263650604531402471608595686720493627649043511875458461192 n + 189131836254305060725943496774495046278417934019290408973692034160\right) a{\left(n + 37 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(92289097161040256744272205154834499307789992503380353880 n^{6} + 31868568927973917536746095374206318781030581797866260597587 n^{5} + 4584722975623126025588340678350614428154332135221700247780385 n^{4} + 351730106280008534421809132222758612048224609146439919132299105 n^{3} + 15176552506921136099640957679415592012251286369531433595866164695 n^{2} + 349202516508443088176398939406500354483815017478251396061743507328 n + 3347414242298099792417228208239441790452797846444123746139843441380\right) a{\left(n + 57 \right)}}{4828534847684641963284480 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(120711527274023702045184202339861608356680843999610988758 n^{6} + 27459665966522790314786496456352975023098636264037234998067 n^{5} + 2602806322786951435225840553969373551452155486393158553728345 n^{4} + 131587890327517650760071629908394029432756428538397719798717995 n^{3} + 3742489255278922511977818038823048018099736789317000686426530697 n^{2} + 56777103595742589326438795182993861872632190190340504695384217298 n + 358977521378596008182386297353576980674654146766233003913009443240\right) a{\left(n + 38 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(127127655488031445781856576963575414712071489183184233023 n^{6} + 36811337380466862884458811640376978243606071857445477801873 n^{5} + 4439660516689289345092848802069493728301605403514888979724585 n^{4} + 285460429036821658547168309982966473384312878412869709422845155 n^{3} + 10320126388159666504070381571327221549918048523660717315267408112 n^{2} + 198899724880784724756650029331956504834344606562268588482713871412 n + 1596518992353372763790797974600869355657897815706010515900994574960\right) a{\left(n + 49 \right)}}{2146015487859840872570880 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(213841040990926341933481944848889604755236995925258648795 n^{6} + 74828432121972754743161389894804870584342868962420126898887 n^{5} + 10909035882629765334267718350401080782513272112849579559194755 n^{4} + 848119492904158407232398061186138930031431077768246266616943665 n^{3} + 37085074043150937827752808865943022514525248541229337492349731450 n^{2} + 864739716069030957628981747558080111251399883412003492051502988048 n + 8400443039757396507156634474660879925106859068441062365466306195520\right) a{\left(n + 58 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(237401411906423596415448820220210287196060484624353091299 n^{6} + 66804205320129657403837056914645233531551023474741072500977 n^{5} + 7832038652062484738128693778206881132479196999156708254185820 n^{4} + 489668443041364757723945593718184391765239083887454303335229610 n^{3} + 17218895545068190686056688695174818231263454877538919237506357461 n^{2} + 322891322205352664845856411785546814153435807610287742437451229653 n + 2522558443452464898596921805638404818088337914539163301173256671620\right) a{\left(n + 47 \right)}}{2414267423842320981642240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(254882269574199906044520979565906280152494238178806206363 n^{6} + 62637748771472625154384689187655498967827221783902676632813 n^{5} + 6413436758896121979006767535700432437666989932665840185118545 n^{4} + 350201190244854304584561326818748378451687722701572486744301895 n^{3} + 10755858285515456801025806119827721427406266291499407527207899012 n^{2} + 176179299608700737476124230990821313812483132748270810530220536892 n + 1202384531550065440675048961669639174096088223977983448586603670640\right) a{\left(n + 41 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(277173846050633425312966722432041571787783179974145459119 n^{6} + 79598819178919904730108894066999589191251800999972156484040 n^{5} + 9502866472887443803799694855192343461715883335615069797681320 n^{4} + 603537326784025635491836925019642981668580253836772476147595710 n^{3} + 21501120903056442840624648997909612265070231059259344373559617821 n^{2} + 407253263301661078372252819192594278597878486109218351745396725070 n + 3202900947840709540089607874218576244514949607947813728921749957160\right) a{\left(n + 50 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(341994715585959523925253931459271351056429105902491240853 n^{6} + 86168158369125077455527414726948189852914255206196067057475 n^{5} + 9045437771907496495891707533109929754938371146410829938243765 n^{4} + 506382417136838678983531986312172658959941237538382581316556645 n^{3} + 15944799769076854542520298669220012182644309003122472795115580622 n^{2} + 267749712876459288196305962844723775316230900958126338100379426800 n + 1873272062272532382010467543797440566312372959926610097671131303200\right) a{\left(n + 42 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(372002706040063365251520311850217331710638502895496924947 n^{6} + 86856184602236096292953851341384675983317771262166807241443 n^{5} + 8449513542939727470774603270114464132805653175106190788988345 n^{4} + 438390565480027157253591972873578758382248103344992242532817305 n^{3} + 12794601420404133895728416462029044218367896222795566611625942028 n^{2} + 199168144086640330093476372587101371401172446901428661802226121132 n + 1291955233856950837912724058752180720427444170364269875604258199360\right) a{\left(n + 39 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(492676164893151809297665688965405819285064836212273149561 n^{6} + 162436534916893944288295190222159200190565432888240789260241 n^{5} + 22255737126897294528595564056901675176849028615147349296570355 n^{4} + 1622372665007598788919365802820611765158874662926115000804820555 n^{3} + 66377827538086196187801240726155869968314141813974396555798761644 n^{2} + 1445482636529489447450050060329516925309355669096571056797805210604 n + 13091140823703572112576188380878252917695315999673396131531243412400\right) a{\left(n + 52 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(654147888887471606909063420661045364609119975122085345237 n^{6} + 180536092428350507477834849388574865088562214847054775561357 n^{5} + 20759002104667754977565351454840811876507661893431863676562355 n^{4} + 1272943346929848116516060514848024411019518745112766900571475775 n^{3} + 43902731241088345857753423219854142478233831103205908094986078768 n^{2} + 807469256539403465638252458833666281788364518649104569656047030108 n + 6187261143687950369200825117155599492439559744526638904351485074240\right) a{\left(n + 46 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(658159438745396397838104076121336448790272753611766163984 n^{6} + 169902198367888828770549893476328972751652347955407459992772 n^{5} + 18273464903753692774041918285798513411479311200297008767362745 n^{4} + 1048106496441542300599325222537751210456044651615163510167364090 n^{3} + 33812338702613902191676668685682342867283062702388053647136129551 n^{2} + 581708846582904977655343195541107194455049677862137183784204815298 n + 4169522156734194163662288365342060809432272478170201093304007542440\right) a{\left(n + 43 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(731648123264671060526237183059558359593191185819687670237 n^{6} + 245769417270028948673160576379681529207410554806439991421097 n^{5} + 34389661116351273764454397014994806111943622502619901389127245 n^{4} + 2565739370136304499907530511828855034966542243821865278696476935 n^{3} + 107647883267183301097855534673297955711506338656950139452312332678 n^{2} + 2408145351469577054600163271366457118464024994866308218946731410208 n + 22440561202008100845425980772701966596541411011284487232725856849920\right) a{\left(n + 55 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(760247517305745932343298590504172997839477999530540832139 n^{6} + 249650507826614077011632950840499577209988693983286382426401 n^{5} + 34128658929450154639889521594415311317841992288588656957841425 n^{4} + 2486235899084241842609452390992146634218134533990880334994975195 n^{3} + 101798396178489746940802388435138351096158866979466235004580812796 n^{2} + 2221289006763184699905950610835728429965739553698709395590974032444 n + 20180746281240125839745641182568740149651118060330108051738620399280\right) a{\left(n + 53 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(802815862237377675445793409037761125186341091506893503168 n^{6} + 212153135858399825230305456615723012578361014216828074192296 n^{5} + 23358052094269324477984910552002182158230574663102736811711805 n^{4} + 1371464270749277428043205858983680710860419421724245171779352430 n^{3} + 45291229483889220679503259483337361638584428885108569051967808967 n^{2} + 797625530283068876091416045138701211650929853317177320338911910134 n + 5852304080712886374949443053458003542854303491619194465778554661040\right) a{\left(n + 44 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(824212114035625307421314371241458045675714764694639387141 n^{6} + 273307113781658583572753222598102459336332670335487619282719 n^{5} + 37744905817491017730044542725076069547341480074817929183774355 n^{4} + 2778915233374430143643735529241744063797288124584135498921337845 n^{3} + 115034796036933330335505327794650840588798866062405131465749271264 n^{2} + 2538630642614116308384230391213273826945375260772486635626058065076 n + 23333451087528637728075758742196799718355895633781076256682852656160\right) a{\left(n + 54 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(1619494044634060637837160036515139626464999731902355308531 n^{6} + 463493693710682225466033752635681749255138481244151306679677 n^{5} + 55263374492163412182418768824424429128030090910844305205976365 n^{4} + 3513707023456582405465117367743878445358906194265956372609207935 n^{3} + 125645685224409426019700689245993955105700097278232189872843898344 n^{2} + 2395825669233247454623667974607746378715088957680136819373305495948 n + 19031543018479865501147885546145432126839135827087253929101649571520\right) a{\left(n + 48 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(1843186730798695890180903285268164489160537880272951445455 n^{6} + 498090943976794473817810359796597235032787617840339534252071 n^{5} + 56079231996435332573824842374002275661604914748491861917944155 n^{4} + 3367098007313613812516885540883773889576030997470828068854730865 n^{3} + 113707690654699220947213722392972373557096925880875543442819684870 n^{2} + 2047749720710225991570642103299960881810160728299031499427757665704 n + 15363966426452863501909677577629095210793720194851676294404442715360\right) a{\left(n + 45 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)}, \quad n \geq 91\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 110\)
\(\displaystyle a(6) = 540\)
\(\displaystyle a(7) = 2762\)
\(\displaystyle a(8) = 14539\)
\(\displaystyle a(9) = 78236\)
\(\displaystyle a(10) = 428482\)
\(\displaystyle a(11) = 2380853\)
\(\displaystyle a(12) = 13389383\)
\(\displaystyle a(13) = 76068459\)
\(\displaystyle a(14) = 435937577\)
\(\displaystyle a(15) = 2517138965\)
\(\displaystyle a(16) = 14629776532\)
\(\displaystyle a(17) = 85521335684\)
\(\displaystyle a(18) = 502497519336\)
\(\displaystyle a(19) = 2966045949613\)
\(\displaystyle a(20) = 17579415924432\)
\(\displaystyle a(21) = 104578162246995\)
\(\displaystyle a(22) = 624221661932913\)
\(\displaystyle a(23) = 3737393952178107\)
\(\displaystyle a(24) = 22439771972123562\)
\(\displaystyle a(25) = 135079216108093669\)
\(\displaystyle a(26) = 815064057509979186\)
\(\displaystyle a(27) = 4928905550378813701\)
\(\displaystyle a(28) = 29867277375537968677\)
\(\displaystyle a(29) = 181328155285882444097\)
\(\displaystyle a(30) = 1102817552899617976007\)
\(\displaystyle a(31) = 6718320413669708477809\)
\(\displaystyle a(32) = 40991228005851501460835\)
\(\displaystyle a(33) = 250468464585751400087416\)
\(\displaystyle a(34) = 1532531820646166405940393\)
\(\displaystyle a(35) = 9389142727155106779110544\)
\(\displaystyle a(36) = 57593163527534475696147964\)
\(\displaystyle a(37) = 353684165190371039743887559\)
\(\displaystyle a(38) = 2174369877515346681538200603\)
\(\displaystyle a(39) = 13381347627871646523916939936\)
\(\displaystyle a(40) = 82431321244369925740793723365\)
\(\displaystyle a(41) = 508264377225517963151182197947\)
\(\displaystyle a(42) = 3136697406922114523242867803404\)
\(\displaystyle a(43) = 19374166423901236476414020616243\)
\(\displaystyle a(44) = 119763375267855785239115592240172\)
\(\displaystyle a(45) = 740900542034661496709128157527571\)
\(\displaystyle a(46) = 4586865437646708421565235050341960\)
\(\displaystyle a(47) = 28417021176248301633317477728927606\)
\(\displaystyle a(48) = 176171111330168163496800476123942396\)
\(\displaystyle a(49) = 1092879679096529271087229141792311934\)
\(\displaystyle a(50) = 6783911497839683684736717307146475996\)
\(\displaystyle a(51) = 42135435479261180274913329562389720330\)
\(\displaystyle a(52) = 261857028769954197722476962291829945270\)
\(\displaystyle a(53) = 1628249444264282887008817471679776864735\)
\(\displaystyle a(54) = 10129981314982773378963005571927464080540\)
\(\displaystyle a(55) = 63054907544723210764723156890544213673606\)
\(\displaystyle a(56) = 392684430403730039849362303067149727340042\)
\(\displaystyle a(57) = 2446670198205902966416907244515679198089330\)
\(\displaystyle a(58) = 15251303311737442845397109805538445003116627\)
\(\displaystyle a(59) = 95111152426690018961648312677504447188165030\)
\(\displaystyle a(60) = 593392995073209636922422654273105228002092335\)
\(\displaystyle a(61) = 3703682238260223376005372486832513401727651785\)
\(\displaystyle a(62) = 23125945660088255220365865348297812531454549704\)
\(\displaystyle a(63) = 144455535294460952025366038332413994152813948570\)
\(\displaystyle a(64) = 902677192723506053456726195238072113210156630412\)
\(\displaystyle a(65) = 5642730152302931668127311608592142116329913671836\)
\(\displaystyle a(66) = 35285785704288830036855001012786703461969596166114\)
\(\displaystyle a(67) = 220728995050239267962150045543901652932007101761851\)
\(\displaystyle a(68) = 1381222527630204250214007740498663963947636683905013\)
\(\displaystyle a(69) = 8645863529380118094438336751857773752925210931005359\)
\(\displaystyle a(70) = 54136418373459155280207656648742267749989464003130443\)
\(\displaystyle a(71) = 339080816237133171574974985997417776413229210556141378\)
\(\displaystyle a(72) = 2124446381055640010399896739816358403136351166000882464\)
\(\displaystyle a(73) = 13314155778089600998377230267827617250985548559270567085\)
\(\displaystyle a(74) = 83464807112673329058773172426962241372506571967046713563\)
\(\displaystyle a(75) = 523373569627739487909252259412361245592158844694467178806\)
\(\displaystyle a(76) = 3282733859501981696228991529170488309778281338308745603804\)
\(\displaystyle a(77) = 20595485874466609787808496670328060681212982799594000161724\)
\(\displaystyle a(78) = 129246261645871663429671706981008127783552455423854832224951\)
\(\displaystyle a(79) = 811279928806590801852563552610121115366030967519991148985136\)
\(\displaystyle a(80) = 5093632207520221076689115607094339439115784492290442527603161\)
\(\displaystyle a(81) = 31987917058090215488592561074233401995522657678666271475896066\)
\(\displaystyle a(82) = 200929349566690653151425614498355348251372165465971156216874459\)
\(\displaystyle a(83) = 1262401309978917389788330493273359772524349580735881683286161577\)
\(\displaystyle a(84) = 7933152885105217332723945920525214493645000041745935098012400647\)
\(\displaystyle a(85) = 49863907798766032551876835185865211479980629641504706002381670870\)
\(\displaystyle a(86) = 313484985963493469236427677005767098787048233701905490350209571661\)
\(\displaystyle a(87) = 1971219791969600184465260521774463772711870082581674408656336336073\)
\(\displaystyle a(88) = 12397645707332655754071858497492939255531098575288836828513557079736\)
\(\displaystyle a(89) = 77987916488237413599681102243647305976307228809747053239013479868433\)
\(\displaystyle a(90) = 490678996219144658964282766709799478615283068713228763854303723195049\)
\(\displaystyle a{\left(n + 91 \right)} = - \frac{330596973697832246875 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) a{\left(n \right)}}{1774558629158094 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{125 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(20227198098987163912193 n + 119230394257462523801511\right) a{\left(n + 1 \right)}}{170357628399177024 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{25 \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(7603452826760743041105422 n^{2} + 96293610652163918881624958 n + 303788461512476442736287981\right) a{\left(n + 2 \right)}}{340715256798354048 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{5 \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(129499105711344139595648468557 n^{3} + 2630272169749530530833084375545 n^{2} + 17737198503559339223730126909146 n + 39709202565131954047658409437568\right) a{\left(n + 3 \right)}}{49062996978962982912 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(n + 4\right) \left(n + 5\right) \left(32087466619041827505321025262006 n^{4} + 923138478400298288459686211279433 n^{3} + 9915288727330894866823806727613863 n^{2} + 47121202169748229860009956903016858 n + 83589245207191668029674990680824832\right) a{\left(n + 4 \right)}}{147188990936888948736 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(n + 5\right) \left(760723405211021812758109421644581 n^{5} + 28770092317311473520869625541513416 n^{4} + 433062516719026219418155983958815355 n^{3} + 3243370360799914417617882613242590420 n^{2} + 12085718704072937784602357672026442044 n + 17923828474788768314559994300227308544\right) a{\left(n + 5 \right)}}{294377981873777897472 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(21754980365769 n^{3} + 5827914091828809 n^{2} + 520405770399729884 n + 15489789408263246304\right) a{\left(n + 90 \right)}}{50087177010 \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(515132437405321867 n^{4} + 180910225571795921844 n^{3} + 23825598969304490996949 n^{2} + 1394593375720412758931164 n + 30611778919234258928509152\right) a{\left(n + 89 \right)}}{12171184013430 \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(4462405827106720818493 n^{5} + 1935073853913146786771330 n^{4} + 335632253890005514901717675 n^{3} + 29105657617874834645907912910 n^{2} + 1261939786187900447234702341752 n + 21884530576553078479435469799360\right) a{\left(n + 88 \right)}}{657243936725220 \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(2322831794269756627337209 n^{6} + 1201513401490884922148463551 n^{5} + 258943843711829033116780968025 n^{4} + 29761756359426380508732146190425 n^{3} + 1924027301985396351603833597141566 n^{2} + 66334540197324320125769974789885304 n + 952870709231781504093536680234246080\right) a{\left(n + 87 \right)}}{7886927240702640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(2277492536530962214800938531 n^{6} + 1171773531612550130596280698621 n^{5} + 251186402509463482112614540251795 n^{4} + 28716022640687441029640470025620715 n^{3} + 1846511405085511309215821238490033114 n^{2} + 63322124613349461818553657789065666664 n + 904742095352691461719099938356671387200\right) a{\left(n + 86 \right)}}{425894070997942560 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(100574538584915415889524031287 n^{6} + 52442933726549937060442909944803 n^{5} + 11385743661358202961674030957397385 n^{4} + 1317457168957104570216931521575298025 n^{3} + 85693952881224305357527719265579839128 n^{2} + 2970924993414573273051373451577825149052 n + 42890708010545635751098492789719193273200\right) a{\left(n + 85 \right)}}{2555364425987655360 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(11852410857682977156021168130055 n^{6} + 5508040940315617668645944072992953 n^{5} + 1059173637424803111339645954448985195 n^{4} + 107735307250151743690378005081620410695 n^{3} + 6103037219807870764693698131646098297990 n^{2} + 182136344141082945346135551000583928172792 n + 2229904299680371305117288714717817849068480\right) a{\left(n + 84 \right)}}{45996559667777796480 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(1494468428214128265060793563412165 n^{6} + 733660958336570769659619785501946576 n^{5} + 150010761702036601923193997566698495640 n^{4} + 16352065102211516642324175158947546775190 n^{3} + 1002222947527051169536060453786144435048075 n^{2} + 32746738322422428878483771535603095377964634 n + 445623028697479625220646815208980150871713240\right) a{\left(n + 83 \right)}}{137989679003333389440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(73908881175760153438410061097714858 n^{6} + 36266011736770456716483435552326033343 n^{5} + 7413628283288388568525745306902997295950 n^{4} + 808163519963548571079498905357438431288905 n^{3} + 49548269434385678550411049708530177099360092 n^{2} + 1619922751917148078154887186953220559862395772 n + 22064101005860139168249622286642192734303896720\right) a{\left(n + 82 \right)}}{413969037010000168320 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(272683130830233492943043355014006791 n^{6} + 12697022585415363813882393465083925981 n^{5} + 244555105260198958750805327942516138185 n^{4} + 2494645845803249393330819226590115061335 n^{3} + 14217592314859739241385498743852264964984 n^{2} + 42933851683254070771162193413137671948724 n + 53679616494928231996838506310935513400880\right) a{\left(n + 6 \right)}}{13247009184320005386240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(4971654618186113923025707819063073185 n^{6} + 188388940424222306453470835814741525357 n^{5} + 2398116211547876702154493947128770423225 n^{4} + 6693332746306602924593623711629371350515 n^{3} - 100786262185213177196708836685987371252130 n^{2} - 866656815357373666156533527109294250190712 n - 2008792032952489046010492819115903791644160\right) a{\left(n + 7 \right)}}{79482055105920032317440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(28104076034282220256067156179015435261 n^{6} + 13533740490845495687512717443634556368929 n^{5} + 2715717700047142650435401029913102140692895 n^{4} + 290656502575393576929381748703218889779021755 n^{3} + 17499607285548226556711966763648651896293431364 n^{2} + 561960729670125694299613657329560171734088885316 n + 7519750002305822431239897081074045968617746500800\right) a{\left(n + 81 \right)}}{9935256888240004039680 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(91821215166802133578190922613929397177 n^{6} + 6816376339301091635293886242942530134243 n^{5} + 202727261157367631886915513150004248984945 n^{4} + 3121807046275326552772942598126668467782605 n^{3} + 26410524988399913425454882526323469099570398 n^{2} + 116855485667642183508243842694978128578575192 n + 211853271614969394776509853735058793725543840\right) a{\left(n + 8 \right)}}{79482055105920032317440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(3121862826098550677403976198702451459821 n^{6} + 1473032940192949275799391640096253510022295 n^{5} + 289596821785601550475440593728012534974416725 n^{4} + 30364707524528201014119668590586971453638664545 n^{3} + 1790867889227953095206255989588350399132075036574 n^{2} + 56331943378586547538345450938280922132248649391720 n + 738302141184827351417114795760815419246617405870720\right) a{\left(n + 80 \right)}}{59611541329440024238080 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(18332595245190196722411122558289360129695 n^{6} + 1350088374653246299746524838846489221513907 n^{5} + 40887814810917769397723831892297120970513775 n^{4} + 652709847384159627294916647013093122694834365 n^{3} + 5798703282709404308456552060302777267164665450 n^{2} + 27206622363785004122754188328691474409633728248 n + 52703836882370336877847011510448110497270814240\right) a{\left(n + 9 \right)}}{715338495953280290856960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(161507454269181484694624322304828523560598 n^{6} + 75305180430556325304715135496687167520707317 n^{5} + 14628890858586158931652928783526252448436969255 n^{4} + 1515522335764731067164998487616404565379540703405 n^{3} + 88308326134410552596265435685859343451849561014467 n^{2} + 2744136605292756946904014648448754014139621576345918 n + 35527512649989707425499386085513623741739937260398560\right) a{\left(n + 79 \right)}}{178834623988320072714240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(678078500281086373100965400215328154687323 n^{6} + 52856833201669985491426964280692510308358163 n^{5} + 1702917218360029683665005864260984612834015185 n^{4} + 29039411913348494719854768644579677096940781585 n^{3} + 276563834900940843195694640838970919451197376812 n^{2} + 1395250404472112301794167312425070180847576900052 n + 2913965106656557830015433494657661219608118518240\right) a{\left(n + 10 \right)}}{2146015487859840872570880 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(3178673919787449549085759213703996337623158 n^{6} + 264223189510760127670420833961609537395295701 n^{5} + 9096971896442109848848550996334117612334675570 n^{4} + 166094006034376459303058487519980347049267238015 n^{3} + 1696570191335169738540843184006937191508698254952 n^{2} + 9194316650619460914333120721549456184963657060964 n + 20657040660667052353337260250815600664910237495840\right) a{\left(n + 11 \right)}}{1073007743929920436285440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(13043468314280512353935665163485439199504823 n^{6} + 6032263175180331815053598976243100190089929969 n^{5} + 1162304252619439207400906664529818780665117500255 n^{4} + 119432200655192099763828001898478169341137990463735 n^{3} + 6902535369223355983657139275877210166267124367084842 n^{2} + 212744030167163922314410279595638880028833145308034936 n + 2731853616503075920482029085382772426441392055460867360\right) a{\left(n + 78 \right)}}{1073007743929920436285440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(24613180641497695213828802221214462239199165 n^{6} + 2180771122370123427713155327007992670955520557 n^{5} + 80128030214601948199260239125791201733449094610 n^{4} + 1563078434753960382495417827966419775737823067045 n^{3} + 17076329353299345138479598451179109261940010054965 n^{2} + 99075430388333479412971431328019612875510329191178 n + 238529514980262740296809006540825064752565955401920\right) a{\left(n + 12 \right)}}{1073007743929920436285440 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(193392036814791929079534948848974258572483130 n^{6} + 88820437298289857403873488925521469627092829399 n^{5} + 16995291680508673745140141825534789734517285714885 n^{4} + 1734185593951916241817661121356396031109196041084995 n^{3} + 99526201287276981227577337086372589389472105261906345 n^{2} + 3046002462063897250643934555783089405164181116398453366 n + 38838632552115707422223499809499205896591636166512095880\right) a{\left(n + 77 \right)}}{1609511615894880654428160 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - 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\frac{\left(12537522147855576708838741428784241254132439948386534999 n^{6} + 2501822730797771061674640672412099443347529493662250452669 n^{5} + 208295416781337027509861075292009434423438590345188443515375 n^{4} + 9262678025647508191185857709201641430688536356286486415355115 n^{3} + 232057474605355334769944156870639867584973022568453679315322706 n^{2} + 3105819139863904755064459703519736713997749343834085455020336736 n + 17350400413239333776715469792417462506480712631785647533749092480\right) a{\left(n + 33 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(13414549483262914064094261709953542879346266046796481372 n^{6} + 4751524516246417470619838833011217698435067455776330616873 n^{5} + 701160816001969051861581685531927922156130739650766322779790 n^{4} + 55174154882299172122125619098997677035991823096049345571914490 n^{3} + 2441778787645391861676100455293876135359937497278932083550187023 n^{2} + 57623660733359185481352566401878656729354349669337457505621189282 n + 566505530674597482748675121743848734630481582545846083320261312480\right) a{\left(n + 59 \right)}}{2414267423842320981642240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(27837561363719906321037483496149983641453658918151184580 n^{6} + 9480904249457429386403114238828736420409760846543954820779 n^{5} + 1345193020416563195267522399650271899374037710686744884721378 n^{4} + 101775712237091874750237936759708017692330602626797275301530147 n^{3} + 4330624407070931686460125231027406109356025045243948151587025820 n^{2} + 98260304479113318190635429159029098641165761044189154538540179532 n + 928784589221735252256718944525609094638604878802498486833623445912\right) a{\left(n + 56 \right)}}{965706969536928392656896 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(28858684746738588687679591510731905093693297899959289237 n^{6} + 6228946654439036435407724655490616575815772642643466720007 n^{5} + 560357851476204401307228669333306073751099460064511831308425 n^{4} + 26894843122053547552274610277937942235246046066269581728894305 n^{3} + 726409492030986885322984659220031419287370904163099366832576058 n^{2} + 10469212669967561222030615492942043062457100103457773394774035168 n + 62906251357437146125127588889255697352003894455157177430744697680\right) a{\left(n + 36 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(36375148941242025396848741444609882726743020562896274535 n^{6} + 8714791112751952755994580831446873614062528949685300399943 n^{5} + 869907813956167147471710692429073657756560035057921378828391 n^{4} + 46309628020014009310810445487500271547551956193206199571785201 n^{3} + 1386704213756129986929460930628409604444333849270989243023805602 n^{2} + 22146090332225955032614746968573202787292767796553293104658576776 n + 147371060625091261533283825968556062964130409163599851987649768144\right) a{\left(n + 40 \right)}}{1287609292715904523542528 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(45528355744949750768617587652242934757899375947107653637 n^{6} + 16287604858550408301775271724557951380446258020822706170523 n^{5} + 2427151582247959201819125529101764263636979139861578646894365 n^{4} + 192842587754094953997725772734904759628530473924397979493198685 n^{3} + 8615700643667711575739069171786641756844449033013262062021129558 n^{2} + 205223395633059560109310981279727142902703026321689813450778541072 n + 2036066442007234028658723319626715874027046027824120816231160958800\right) a{\left(n + 60 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(74300718647488873447929962754033396655700484558627103330 n^{6} + 16464742789145412411409954635333001135031755835609292647913 n^{5} + 1520405568627131779904442665975261576018549684664272060879140 n^{4} + 74892752752118365577486028734408043073108828946711816645541435 n^{3} + 2075608087060750829545995661257321962782880982140131464924854110 n^{2} + 30688822263650604531402471608595686720493627649043511875458461192 n + 189131836254305060725943496774495046278417934019290408973692034160\right) a{\left(n + 37 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(92289097161040256744272205154834499307789992503380353880 n^{6} + 31868568927973917536746095374206318781030581797866260597587 n^{5} + 4584722975623126025588340678350614428154332135221700247780385 n^{4} + 351730106280008534421809132222758612048224609146439919132299105 n^{3} + 15176552506921136099640957679415592012251286369531433595866164695 n^{2} + 349202516508443088176398939406500354483815017478251396061743507328 n + 3347414242298099792417228208239441790452797846444123746139843441380\right) a{\left(n + 57 \right)}}{4828534847684641963284480 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(120711527274023702045184202339861608356680843999610988758 n^{6} + 27459665966522790314786496456352975023098636264037234998067 n^{5} + 2602806322786951435225840553969373551452155486393158553728345 n^{4} + 131587890327517650760071629908394029432756428538397719798717995 n^{3} + 3742489255278922511977818038823048018099736789317000686426530697 n^{2} + 56777103595742589326438795182993861872632190190340504695384217298 n + 358977521378596008182386297353576980674654146766233003913009443240\right) a{\left(n + 38 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(127127655488031445781856576963575414712071489183184233023 n^{6} + 36811337380466862884458811640376978243606071857445477801873 n^{5} + 4439660516689289345092848802069493728301605403514888979724585 n^{4} + 285460429036821658547168309982966473384312878412869709422845155 n^{3} + 10320126388159666504070381571327221549918048523660717315267408112 n^{2} + 198899724880784724756650029331956504834344606562268588482713871412 n + 1596518992353372763790797974600869355657897815706010515900994574960\right) a{\left(n + 49 \right)}}{2146015487859840872570880 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(213841040990926341933481944848889604755236995925258648795 n^{6} + 74828432121972754743161389894804870584342868962420126898887 n^{5} + 10909035882629765334267718350401080782513272112849579559194755 n^{4} + 848119492904158407232398061186138930031431077768246266616943665 n^{3} + 37085074043150937827752808865943022514525248541229337492349731450 n^{2} + 864739716069030957628981747558080111251399883412003492051502988048 n + 8400443039757396507156634474660879925106859068441062365466306195520\right) a{\left(n + 58 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(237401411906423596415448820220210287196060484624353091299 n^{6} + 66804205320129657403837056914645233531551023474741072500977 n^{5} + 7832038652062484738128693778206881132479196999156708254185820 n^{4} + 489668443041364757723945593718184391765239083887454303335229610 n^{3} + 17218895545068190686056688695174818231263454877538919237506357461 n^{2} + 322891322205352664845856411785546814153435807610287742437451229653 n + 2522558443452464898596921805638404818088337914539163301173256671620\right) a{\left(n + 47 \right)}}{2414267423842320981642240 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(254882269574199906044520979565906280152494238178806206363 n^{6} + 62637748771472625154384689187655498967827221783902676632813 n^{5} + 6413436758896121979006767535700432437666989932665840185118545 n^{4} + 350201190244854304584561326818748378451687722701572486744301895 n^{3} + 10755858285515456801025806119827721427406266291499407527207899012 n^{2} + 176179299608700737476124230990821313812483132748270810530220536892 n + 1202384531550065440675048961669639174096088223977983448586603670640\right) a{\left(n + 41 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(277173846050633425312966722432041571787783179974145459119 n^{6} + 79598819178919904730108894066999589191251800999972156484040 n^{5} + 9502866472887443803799694855192343461715883335615069797681320 n^{4} + 603537326784025635491836925019642981668580253836772476147595710 n^{3} + 21501120903056442840624648997909612265070231059259344373559617821 n^{2} + 407253263301661078372252819192594278597878486109218351745396725070 n + 3202900947840709540089607874218576244514949607947813728921749957160\right) a{\left(n + 50 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(341994715585959523925253931459271351056429105902491240853 n^{6} + 86168158369125077455527414726948189852914255206196067057475 n^{5} + 9045437771907496495891707533109929754938371146410829938243765 n^{4} + 506382417136838678983531986312172658959941237538382581316556645 n^{3} + 15944799769076854542520298669220012182644309003122472795115580622 n^{2} + 267749712876459288196305962844723775316230900958126338100379426800 n + 1873272062272532382010467543797440566312372959926610097671131303200\right) a{\left(n + 42 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(372002706040063365251520311850217331710638502895496924947 n^{6} + 86856184602236096292953851341384675983317771262166807241443 n^{5} + 8449513542939727470774603270114464132805653175106190788988345 n^{4} + 438390565480027157253591972873578758382248103344992242532817305 n^{3} + 12794601420404133895728416462029044218367896222795566611625942028 n^{2} + 199168144086640330093476372587101371401172446901428661802226121132 n + 1291955233856950837912724058752180720427444170364269875604258199360\right) a{\left(n + 39 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(492676164893151809297665688965405819285064836212273149561 n^{6} + 162436534916893944288295190222159200190565432888240789260241 n^{5} + 22255737126897294528595564056901675176849028615147349296570355 n^{4} + 1622372665007598788919365802820611765158874662926115000804820555 n^{3} + 66377827538086196187801240726155869968314141813974396555798761644 n^{2} + 1445482636529489447450050060329516925309355669096571056797805210604 n + 13091140823703572112576188380878252917695315999673396131531243412400\right) a{\left(n + 52 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(654147888887471606909063420661045364609119975122085345237 n^{6} + 180536092428350507477834849388574865088562214847054775561357 n^{5} + 20759002104667754977565351454840811876507661893431863676562355 n^{4} + 1272943346929848116516060514848024411019518745112766900571475775 n^{3} + 43902731241088345857753423219854142478233831103205908094986078768 n^{2} + 807469256539403465638252458833666281788364518649104569656047030108 n + 6187261143687950369200825117155599492439559744526638904351485074240\right) a{\left(n + 46 \right)}}{6438046463579522617712640 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(658159438745396397838104076121336448790272753611766163984 n^{6} + 169902198367888828770549893476328972751652347955407459992772 n^{5} + 18273464903753692774041918285798513411479311200297008767362745 n^{4} + 1048106496441542300599325222537751210456044651615163510167364090 n^{3} + 33812338702613902191676668685682342867283062702388053647136129551 n^{2} + 581708846582904977655343195541107194455049677862137183784204815298 n + 4169522156734194163662288365342060809432272478170201093304007542440\right) a{\left(n + 43 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(731648123264671060526237183059558359593191185819687670237 n^{6} + 245769417270028948673160576379681529207410554806439991421097 n^{5} + 34389661116351273764454397014994806111943622502619901389127245 n^{4} + 2565739370136304499907530511828855034966542243821865278696476935 n^{3} + 107647883267183301097855534673297955711506338656950139452312332678 n^{2} + 2408145351469577054600163271366457118464024994866308218946731410208 n + 22440561202008100845425980772701966596541411011284487232725856849920\right) a{\left(n + 55 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(760247517305745932343298590504172997839477999530540832139 n^{6} + 249650507826614077011632950840499577209988693983286382426401 n^{5} + 34128658929450154639889521594415311317841992288588656957841425 n^{4} + 2486235899084241842609452390992146634218134533990880334994975195 n^{3} + 101798396178489746940802388435138351096158866979466235004580812796 n^{2} + 2221289006763184699905950610835728429965739553698709395590974032444 n + 20180746281240125839745641182568740149651118060330108051738620399280\right) a{\left(n + 53 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(802815862237377675445793409037761125186341091506893503168 n^{6} + 212153135858399825230305456615723012578361014216828074192296 n^{5} + 23358052094269324477984910552002182158230574663102736811711805 n^{4} + 1371464270749277428043205858983680710860419421724245171779352430 n^{3} + 45291229483889220679503259483337361638584428885108569051967808967 n^{2} + 797625530283068876091416045138701211650929853317177320338911910134 n + 5852304080712886374949443053458003542854303491619194465778554661040\right) a{\left(n + 44 \right)}}{9657069695369283926568960 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(824212114035625307421314371241458045675714764694639387141 n^{6} + 273307113781658583572753222598102459336332670335487619282719 n^{5} + 37744905817491017730044542725076069547341480074817929183774355 n^{4} + 2778915233374430143643735529241744063797288124584135498921337845 n^{3} + 115034796036933330335505327794650840588798866062405131465749271264 n^{2} + 2538630642614116308384230391213273826945375260772486635626058065076 n + 23333451087528637728075758742196799718355895633781076256682852656160\right) a{\left(n + 54 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} + \frac{\left(1619494044634060637837160036515139626464999731902355308531 n^{6} + 463493693710682225466033752635681749255138481244151306679677 n^{5} + 55263374492163412182418768824424429128030090910844305205976365 n^{4} + 3513707023456582405465117367743878445358906194265956372609207935 n^{3} + 125645685224409426019700689245993955105700097278232189872843898344 n^{2} + 2395825669233247454623667974607746378715088957680136819373305495948 n + 19031543018479865501147885546145432126839135827087253929101649571520\right) a{\left(n + 48 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)} - \frac{\left(1843186730798695890180903285268164489160537880272951445455 n^{6} + 498090943976794473817810359796597235032787617840339534252071 n^{5} + 56079231996435332573824842374002275661604914748491861917944155 n^{4} + 3367098007313613812516885540883773889576030997470828068854730865 n^{3} + 113707690654699220947213722392972373557096925880875543442819684870 n^{2} + 2047749720710225991570642103299960881810160728299031499427757665704 n + 15363966426452863501909677577629095210793720194851676294404442715360\right) a{\left(n + 45 \right)}}{19314139390738567853137920 \left(n + 89\right) \left(n + 90\right) \left(n + 91\right) \left(n + 92\right) \left(3 n + 271\right) \left(3 n + 272\right)}, \quad n \geq 91\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 291 rules.
Finding the specification took 14539 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_{15}\! \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_{15}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{257}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{15}\! \left(x \right) &= x\\
F_{16}\! \left(x \right) &= F_{17}\! \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_{252}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{15}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{23}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{33}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{15}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{0}\! \left(x \right) F_{15}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{2}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{249}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= -F_{247}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= -F_{65}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= -F_{239}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= \frac{F_{72}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{72}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{0}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{15}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{59}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{0}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{15}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{59}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{0}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{15}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= -F_{28}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= -F_{101}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= -F_{106}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{129}\! \left(x \right)\\
F_{120}\! \left(x \right) &= -F_{126}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= \frac{F_{123}\! \left(x \right)}{F_{0}\! \left(x \right) F_{15}\! \left(x \right)}\\
F_{123}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{129}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{120}\! \left(x \right) F_{134}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{15}\! \left(x \right) F_{160}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{223}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{129}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{0}\! \left(x \right) F_{134}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{221}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= -F_{164}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= \frac{F_{150}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= -F_{160}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{15}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{15}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{15}\! \left(x \right) F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{164}\! \left(x \right) &= \frac{F_{165}\! \left(x \right)}{F_{129}\! \left(x \right)}\\
F_{165}\! \left(x \right) &= -F_{179}\! \left(x \right)+F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{171}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{129}\! \left(x \right) F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= \frac{F_{169}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{174}\! \left(x \right)\\
F_{172}\! \left(x \right) &= \frac{F_{173}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{173}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{177}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{176}\! \left(x \right) &= 0\\
F_{177}\! \left(x \right) &= F_{15}\! \left(x \right) F_{174}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{130}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{172}\! \left(x \right) F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= -F_{220}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= -F_{197}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= \frac{F_{188}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{15}\! \left(x \right) F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{129}\! \left(x \right) F_{151}\! \left(x \right)\\
F_{197}\! \left(x \right) &= -F_{217}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= \frac{F_{199}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= -F_{208}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= \frac{F_{202}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{15}\! \left(x \right) F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{130}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{192}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{130}\! \left(x \right) F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{211}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{0}\! \left(x \right) F_{129}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= \frac{F_{214}\! \left(x \right)}{F_{15}\! \left(x \right) F_{23}\! \left(x \right)}\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= -F_{216}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{129}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{181}\! \left(x \right) F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= \frac{F_{219}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{219}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{191}\! \left(x \right) F_{218}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{15}\! \left(x \right) F_{222}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{129}\! \left(x \right) F_{161}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{15}\! \left(x \right) F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{154}\! \left(x \right) F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{15}\! \left(x \right) F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{233}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{2}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{121}\! \left(x \right) F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{121}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{0} \left(x \right)^{2}\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{15}\! \left(x \right) F_{244}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{15}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{15}\! \left(x \right) F_{19}\! \left(x \right) F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{254}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{15}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{276}\! \left(x \right)\\
F_{260}\! \left(x \right) &= -F_{261}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{15}\! \left(x \right) F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{274}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{265}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{15}\! \left(x \right) F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)+F_{270}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{12}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{152}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{152}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{15}\! \left(x \right) F_{254}\! \left(x \right) F_{260}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{15}\! \left(x \right) F_{280}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{281}\! \left(x \right)+F_{282}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{23}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{15}\! \left(x \right) F_{284}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{286}\! \left(x \right)+F_{287}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{11}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{121}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{121}\! \left(x \right) F_{259}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 280 rules.
Finding the specification took 40566 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_{15}\! \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_{15}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{13}\! \left(x \right) &= \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{14}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{15}\! \left(x \right) &= x\\
F_{16}\! \left(x \right) &= F_{17}\! \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_{241}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{15}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{23}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{33}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{15}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{0}\! \left(x \right) F_{15}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{51}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{2}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= -F_{234}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{65}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{0}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{15}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{64}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{15}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{15}\! \left(x \right) F_{23}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{15}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{0}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{15}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{73}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{0}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{15}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= \frac{F_{92}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= -F_{99}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= -F_{28}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= \frac{F_{98}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{98}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= -F_{102}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{112}\! \left(x \right) &= \frac{F_{113}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= -F_{107}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{117}\! \left(x \right) &= \frac{F_{118}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{139}\! \left(x \right)\\
F_{121}\! \left(x \right) &= -F_{136}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{0}\! \left(x \right) F_{15}\! \left(x \right)}\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{15}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{127}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{139}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{121}\! \left(x \right) F_{144}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{144}\! \left(x \right) &= \frac{F_{145}\! \left(x \right)}{F_{15}\! \left(x \right) F_{154}\! \left(x \right)}\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{213}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= \frac{F_{150}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= -F_{154}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{15}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{15}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{156}\! \left(x \right) &= \frac{F_{157}\! \left(x \right)}{F_{139}\! \left(x \right)}\\
F_{157}\! \left(x \right) &= -F_{171}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{163}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{139}\! \left(x \right) F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= \frac{F_{161}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right) F_{166}\! \left(x \right)\\
F_{164}\! \left(x \right) &= \frac{F_{165}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{165}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{169}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{168}\! \left(x \right) &= 0\\
F_{169}\! \left(x \right) &= F_{15}\! \left(x \right) F_{166}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{140}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{164}\! \left(x \right) F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= -F_{212}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= -F_{189}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= \frac{F_{180}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{188}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{183}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{15}\! \left(x \right) F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{139}\! \left(x \right) F_{151}\! \left(x \right)\\
F_{189}\! \left(x \right) &= -F_{209}\! \left(x \right)+F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= \frac{F_{191}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= -F_{200}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= \frac{F_{194}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{15}\! \left(x \right) F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{140}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{184}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{140}\! \left(x \right) F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{203}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{0}\! \left(x \right) F_{139}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= \frac{F_{206}\! \left(x \right)}{F_{15}\! \left(x \right) F_{23}\! \left(x \right)}\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= -F_{208}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{139}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{173}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= \frac{F_{211}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{211}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{183}\! \left(x \right) F_{210}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{139}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{15}\! \left(x \right) F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{232}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{231}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{15}\! \left(x \right) F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{223}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{2}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{15}\! \left(x \right) F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{227}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{134}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{122}\! \left(x \right) F_{228}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{122}\! \left(x \right) F_{229}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{122}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{236}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{132}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{15}\! \left(x \right) F_{19}\! \left(x \right) F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{243}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{15}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)+F_{265}\! \left(x \right)\\
F_{249}\! \left(x \right) &= -F_{250}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{15}\! \left(x \right) F_{252}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{15}\! \left(x \right) F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)+F_{261}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{258}\! \left(x \right)+F_{259}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{12}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{152}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{152}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{15}\! \left(x \right) F_{243}\! \left(x \right) F_{249}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{15}\! \left(x \right) F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{271}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{23}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{15}\! \left(x \right) F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)+F_{278}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)+F_{276}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{11}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{277}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{122}\! \left(x \right) F_{248}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{122}\! \left(x \right) F_{18}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 307 rules.
Finding the specification took 56812 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_{24}\! \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 , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{294}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{273}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{268}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{24}\! \left(x \right) &= x\\
F_{25}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{24}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{24}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{258}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{26}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{24}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{24}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{26}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{24}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{38}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{26}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{24}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{24}\! \left(x \right) F_{26}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{24}\! \left(x \right) F_{35}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{250}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{24}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{2}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{0}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{24}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{0}\! \left(x \right) F_{24}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= \frac{F_{74}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= \frac{F_{77}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{85}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{84}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= -F_{220}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= -F_{234}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{96}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{24}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{224}\! \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_{26} \left(x \right)^{2}\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{222}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{108}\! \left(x \right) &= \frac{F_{109}\! \left(x \right)}{F_{0}\! \left(x \right) F_{24}\! \left(x \right)}\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{219}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{87}\! \left(x \right) F_{94}\! \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_{87}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{0}\! \left(x \right) F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= \frac{F_{133}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{133}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{139}\! \left(x \right) &= \frac{F_{140}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= -F_{142}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{151}\! \left(x \right) &= \frac{F_{152}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{155}\! \left(x \right) &= -F_{159}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= -F_{157}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{157}\! \left(x \right) &= \frac{F_{158}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{158}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{155}\! \left(x \right) F_{164}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{164}\! \left(x \right) &= \frac{F_{165}\! \left(x \right)}{F_{183}\! \left(x \right) F_{24}\! \left(x \right)}\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= -F_{218}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{2}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{0}\! \left(x \right) F_{164}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{176}\! \left(x \right) &= -F_{216}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{177}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= \frac{F_{179}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= -F_{183}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{24}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{188}\! \left(x , y\right) &= F_{187}\! \left(x \right)+F_{213}\! \left(x , y\right)\\
F_{189}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{188}\! \left(x , y\right) F_{201}\! \left(x , y\right)\\
F_{189}\! \left(x , y\right) &= F_{190}\! \left(x , y\right)\\
F_{191}\! \left(x , y\right) &= F_{190}\! \left(x , y\right)+F_{208}\! \left(x , y\right)\\
F_{192}\! \left(x , y\right) &= F_{191}\! \left(x , y\right) F_{24}\! \left(x \right)\\
F_{192}\! \left(x , y\right) &= F_{193}\! \left(x , y\right)\\
F_{193}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{194}\! \left(x , y\right)\\
F_{194}\! \left(x , y\right) &= F_{195}\! \left(x , y\right)+F_{207}\! \left(x , y\right)\\
F_{195}\! \left(x , y\right) &= F_{196}\! \left(x , y\right) F_{27}\! \left(x \right)\\
F_{196}\! \left(x , y\right) &= F_{197}\! \left(x , y\right)+F_{198}\! \left(x , y\right)\\
F_{197}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)\\
F_{198}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{202}\! \left(x , y\right)\\
F_{199}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)\\
F_{200}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{201}\! \left(x , y\right)\\
F_{201}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{199}\! \left(x , y\right)\\
F_{202}\! \left(x , y\right) &= F_{203}\! \left(x \right)+F_{204}\! \left(x , y\right)+F_{206}\! \left(x , y\right)\\
F_{203}\! \left(x \right) &= 0\\
F_{204}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{205}\! \left(x , y\right)\\
F_{205}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{202}\! \left(x , y\right)\\
F_{206}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{199}\! \left(x , y\right)\\
F_{207}\! \left(x , y\right) &= F_{181}\! \left(x \right) F_{201}\! \left(x , y\right)\\
F_{208}\! \left(x , y\right) &= F_{199}\! \left(x , y\right) F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{211}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{0}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{0}\! \left(x \right) F_{24}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{213}\! \left(x , y\right) &= F_{201}\! \left(x , y\right) F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= \frac{F_{215}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{215}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{184}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{117}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{156}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)+F_{229}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{156}\! \left(x \right) F_{231}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{220}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{2}\! \left(x \right) F_{239}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{0}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{24}\! \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_{50}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{156}\! \left(x \right) F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{0}\! \left(x \right) F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{35}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{156}\! \left(x \right) F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)+F_{255}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{24}\! \left(x \right) F_{26}\! \left(x \right) F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{261}\! \left(x \right)\\
F_{261}\! \left(x \right) &= \frac{F_{262}\! \left(x \right)}{F_{24}\! \left(x \right)}\\
F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= -F_{266}\! \left(x \right)+F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{26}\! \left(x \right) F_{54}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{122}\! \left(x \right) F_{24}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{268}\! \left(x , y\right) &= F_{269}\! \left(x , y\right)\\
F_{269}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{270}\! \left(x , y\right)\\
F_{270}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{271}\! \left(x , y\right)\\
F_{271}\! \left(x , y\right) &= F_{272}\! \left(x , y\right)\\
F_{272}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{17}\! \left(x , y\right) F_{270}\! \left(x , y\right)\\
F_{273}\! \left(x , y\right) &= F_{274}\! \left(x , y\right)\\
F_{274}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{275}\! \left(x , y\right)\\
F_{275}\! \left(x , y\right) &= F_{276}\! \left(x , y\right)+F_{292}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{276}\! \left(x , y\right)+F_{277}\! \left(x , y\right)\\
F_{277}\! \left(x , y\right) &= F_{278}\! \left(x , y\right)\\
F_{278}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{279}\! \left(x , y\right)\\
F_{279}\! \left(x , y\right) &= F_{280}\! \left(x , y\right)+F_{290}\! \left(x , y\right)\\
F_{280}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{281}\! \left(x , y\right)\\
F_{281}\! \left(x , y\right) &= F_{282}\! \left(x , y\right)\\
F_{282}\! \left(x , y\right) &= F_{24}\! \left(x \right) F_{283}\! \left(x , y\right)\\
F_{283}\! \left(x , y\right) &= F_{284}\! \left(x , y\right)+F_{288}\! \left(x , y\right)\\
F_{284}\! \left(x , y\right) &= F_{285}\! \left(x , y\right)+F_{286}\! \left(x , y\right)\\
F_{285}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{26}\! \left(x \right)\\
F_{286}\! \left(x , y\right) &= F_{287}\! \left(x , y\right)\\
F_{287}\! \left(x , y\right) &= F_{181}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{288}\! \left(x , y\right) &= F_{289}\! \left(x , y\right)\\
F_{289}\! \left(x , y\right) &= F_{181}\! \left(x \right) F_{275}\! \left(x , y\right)\\
F_{290}\! \left(x , y\right) &= F_{291}\! \left(x , y\right)\\
F_{291}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{17}\! \left(x , y\right) F_{275}\! \left(x , y\right)\\
F_{292}\! \left(x , y\right) &= F_{293}\! \left(x , y\right)\\
F_{293}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{270}\! \left(x , y\right) F_{276}\! \left(x , y\right)\\
F_{294}\! \left(x , y\right) &= F_{295}\! \left(x , y\right)\\
F_{295}\! \left(x , y\right) &= F_{24}\! \left(x \right) F_{296}\! \left(x , y\right)\\
F_{296}\! \left(x , y\right) &= F_{297}\! \left(x , y\right)+F_{298}\! \left(x , y\right)\\
F_{297}\! \left(x , y\right) &= F_{26}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{298}\! \left(x , y\right) &= F_{299}\! \left(x , y\right)\\
F_{299}\! \left(x , y\right) &= F_{24}\! \left(x \right) F_{300}\! \left(x , y\right)\\
F_{300}\! \left(x , y\right) &= F_{301}\! \left(x , y\right)+F_{305}\! \left(x , y\right)\\
F_{301}\! \left(x , y\right) &= F_{302}\! \left(x , y\right)+F_{303}\! \left(x , y\right)\\
F_{302}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{51}\! \left(x \right)\\
F_{303}\! \left(x , y\right) &= F_{304}\! \left(x , y\right)\\
F_{304}\! \left(x , y\right) &= F_{156}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{305}\! \left(x , y\right) &= F_{306}\! \left(x , y\right)\\
F_{306}\! \left(x , y\right) &= F_{156}\! \left(x \right) F_{275}\! \left(x , y\right)\\
\end{align*}\)