Av(13452, 13524, 13542, 15324, 15342, 31452, 31524, 31542, 34152)
Counting Sequence
1, 1, 2, 6, 24, 111, 546, 2762, 14200, 73887, 388409, 2060542, 11021931, 59396792, 322232488, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(x -1\right) \left(3 x -1\right) \left(4 x -3\right) x^{3} F \left(x
\right)^{4}-x^{2} \left(29 x^{3}-58 x^{2}+37 x -7\right) F \left(x
\right)^{3}+x \left(x -1\right) \left(12 x^{3}+3 x^{2}-17 x +5\right) F \left(x
\right)^{2}-\left(x -1\right) \left(13 x^{3}-13 x^{2}+1\right) F \! \left(x \right)+\left(3 x -1\right) \left(x -1\right)^{2} = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 546\)
\(\displaystyle a(7) = 2762\)
\(\displaystyle a(8) = 14200\)
\(\displaystyle a(9) = 73887\)
\(\displaystyle a(10) = 388409\)
\(\displaystyle a(11) = 2060542\)
\(\displaystyle a(12) = 11021931\)
\(\displaystyle a(13) = 59396792\)
\(\displaystyle a(14) = 322232488\)
\(\displaystyle a(15) = 1758648248\)
\(\displaystyle a(16) = 9649982956\)
\(\displaystyle a(17) = 53208146080\)
\(\displaystyle a(18) = 294665208539\)
\(\displaystyle a(19) = 1638323429341\)
\(\displaystyle a(20) = 9141843254029\)
\(\displaystyle a(21) = 51179241261866\)
\(\displaystyle a(22) = 287381629847972\)
\(\displaystyle a(23) = 1618164162470222\)
\(\displaystyle a(24) = 9134611240679163\)
\(\displaystyle a(25) = 51686538753126316\)
\(\displaystyle a(26) = 293095897148274730\)
\(\displaystyle a(27) = 1665404690926479898\)
\(\displaystyle a(28) = 9480849175417407226\)
\(\displaystyle a(29) = 54067674790414204596\)
\(\displaystyle a(30) = 308845969910109281325\)
\(\displaystyle a(31) = 1766913673513726062513\)
\(\displaystyle a(32) = 10123186899738121045544\)
\(\displaystyle a(33) = 58077866600993125046950\)
\(\displaystyle a(34) = 333627344304467436317079\)
\(\displaystyle a(35) = 1918841615589515955694506\)
\(\displaystyle a(36) = 11048786029959494104163769\)
\(\displaystyle a(37) = 63688589503218276925160635\)
\(\displaystyle a(38) = 367498900366679725671633598\)
\(\displaystyle a(39) = 2122635076336808757678340034\)
\(\displaystyle a(40) = 12271529278119029717084003381\)
\(\displaystyle a(41) = 71007915806467013997945493536\)
\(\displaystyle a(42) = 411226968858539672814864481340\)
\(\displaystyle a(43) = 2383451965524746439761372834922\)
\(\displaystyle a(44) = 13825013940619452748683412885877\)
\(\displaystyle a(45) = 80249899864682740759624152263221\)
\(\displaystyle a(46) = 466154081721326119984274741474893\)
\(\displaystyle a(47) = 2709615919968577233838734154048576\)
\(\displaystyle a(48) = 15760398673731736391909417535138071\)
\(\displaystyle a(49) = 91726870222208391203727776250857352\)
\(\displaystyle a(50) = 534177047827978978978079720269933365\)
\(\displaystyle a(51) = 3112598613150193471003566781086983736\)
\(\displaystyle a(52) = 18146831578185277967275838498054495689\)
\(\displaystyle a(53) = 105854509156890355776870352936691394034\)
\(\displaystyle a(54) = 617789244576710023800225662848354847896\)
\(\displaystyle a(55) = 3607329096885131680321859004968183802017\)
\(\displaystyle a(56) = 21073567588787241250900696306575838392226\)
\(\displaystyle a(57) = 123165782819481924262485632555923460747382\)
\(\displaystyle a(58) = 720169925934205667373163504580397542467826\)
\(\displaystyle a{\left(n + 59 \right)} = - \frac{4284230123520000 \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) a{\left(n \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{746496000 \left(n + 2\right) \left(337450622 n^{2} + 1396386503 n + 1333004265\right) a{\left(n + 1 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(518807 n^{2} + 60484214 n + 1762842240\right) a{\left(n + 58 \right)}}{2352 \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(112012993 n^{3} + 19340291585 n^{2} + 1113087160238 n + 21353393413360\right) a{\left(n + 57 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(3944253252 n^{3} + 669474792523 n^{2} + 37877087413683 n + 714318466188470\right) a{\left(n + 56 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{5 \left(61143497057 n^{3} + 10198917104082 n^{2} + 567063976669015 n + 10509554796923034\right) a{\left(n + 55 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(2060117801996 n^{3} + 337586759486297 n^{2} + 18439715070809575 n + 335736467990544280\right) a{\left(n + 54 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{41472 \left(84119733747562 n^{3} + 731502854545683 n^{2} + 2110415921139971 n + 2018231631461940\right) a{\left(n + 2 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(101809170160157 n^{3} + 16384009425611973 n^{2} + 878881100361252268 n + 15715086199187502762\right) a{\left(n + 53 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(1405300183274720 n^{3} + 222017584739003973 n^{2} + 11691855542007241321 n + 205237806865672902726\right) a{\left(n + 52 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(16588559348203123 n^{3} + 2571882420342650169 n^{2} + 132914529882887129684 n + 2289669391262207398206\right) a{\left(n + 51 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(56691438031946553 n^{3} + 8622176674496399578 n^{2} + 437115646608193335347 n + 7386791344108842538748\right) a{\left(n + 50 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{288 \left(103032789525144818 n^{3} + 1141766970006991377 n^{2} + 4216458416360326933 n + 5188653128344307844\right) a{\left(n + 3 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(1533017504169565003 n^{3} + 228628069540817306373 n^{2} + 11365617117961203680354 n + 188337836420308548980370\right) a{\left(n + 49 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(4089482773184893625 n^{3} + 597795239938591587642 n^{2} + 29128530034213496153361 n + 473115055600187605363430\right) a{\left(n + 48 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{24 \left(6919493882884897520 n^{3} + 90155597543139753951 n^{2} + 388939182284944629955 n + 555228987721174744074\right) a{\left(n + 4 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(14645602391413584502 n^{3} + 2097508628723312950276 n^{2} + 100134397291409148233161 n + 1593477228938458769057349\right) a{\left(n + 47 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{3 \left(374939713290084622130 n^{3} + 4990046349937987895793 n^{2} + 20376322562809136821479 n + 23526162677353561428686\right) a{\left(n + 5 \right)}}{98 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(567105510242017996132 n^{3} + 79538123336197593006369 n^{2} + 3718525355146374474511439 n + 57949554603432281130160548\right) a{\left(n + 46 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3139058437854009321775 n^{3} - 126204528883817655507453 n^{2} - 2106234521538434230456015 n - 7492585646314077202103475\right) a{\left(n + 6 \right)}}{588 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3316354698865518651485 n^{3} + 455282695399968128684061 n^{2} + 20834645000862724134587032 n + 317816072856113744896268142\right) a{\left(n + 45 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(17657987067926901023306 n^{3} + 2371671764465311911565305 n^{2} + 106182645295723788489794971 n + 1584667134265362953809512786\right) a{\left(n + 44 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(85960502750141815303873 n^{3} + 11289648464083841928789789 n^{2} + 494251657077282183857497202 n + 7212769615450873120373309022\right) a{\left(n + 43 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(127985361825051366058514 n^{3} + 16427619400208840592168347 n^{2} + 702871200181736376736796045 n + 10024520376615733499477739284\right) a{\left(n + 42 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(1578435956252052916266016 n^{3} + 197892081249520199129877813 n^{2} + 8270219273839989706824233987 n + 115210677346139780681771221128\right) a{\left(n + 41 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(1996049652036931476695096 n^{3} + 244288607613409443755762079 n^{2} + 9966035008528735204188824573 n + 135527943789292075182284082610\right) a{\left(n + 40 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3123014247163584002403670 n^{3} + 97262717922916632284550561 n^{2} + 940976056067809777763817761 n + 2903258741546345354187769464\right) a{\left(n + 7 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(21012494710200484937788907 n^{3} + 2508833284876224509962847181 n^{2} + 99851182280521711914862966036 n + 1324712877914076957115297424964\right) a{\left(n + 39 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(34167274190570578425290405 n^{3} + 3977285781823539133337201763 n^{2} + 154329899228949796410740420707 n + 1996181676060056917781111074089\right) a{\left(n + 38 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(49909145417762677744405829 n^{3} + 1525758875216944086231184398 n^{2} + 15199844755418980550853780169 n + 49607593999185477802958646216\right) a{\left(n + 8 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(51576494068059824234098460 n^{3} + 5849490425311806005749583655 n^{2} + 221141511222866246489413568206 n + 2786816899805731812423732479763\right) a{\left(n + 37 \right)}}{7056 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(83663360580635324984619723 n^{3} + 2710291780124965926995646485 n^{2} + 28940709143791311330255486506 n + 102056382777191813094236965904\right) a{\left(n + 9 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(504209472938448445113993523 n^{3} + 54165866956945434704122564036 n^{2} + 1939650362639766425943973662237 n + 23152834382623437994437818369270\right) a{\left(n + 35 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(579037604223591564187417403 n^{3} + 63937705784727168661153737144 n^{2} + 2353380343373918601028363574215 n + 28874328184601076548999710001004\right) a{\left(n + 36 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(978816538869389348316373279 n^{3} + 34041382032562287012530744442 n^{2} + 392028066617977430122154406701 n + 1496258387459543504590797125370\right) a{\left(n + 10 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(1227081613274887045706050743 n^{3} + 128149823497155495782234720756 n^{2} + 4461113928211921173367855640959 n + 51766555496931969240662852369662\right) a{\left(n + 34 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(2784097437516612931019723951 n^{3} + 282428331938414658130731592732 n^{2} + 9550142662193353961798658185363 n + 107643833093974860912586746729848\right) a{\left(n + 33 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3168671470266593224383406753 n^{3} + 118445287810134420691814292543 n^{2} + 1469491925724921475182847201052 n + 6053693447363413664157839269440\right) a{\left(n + 11 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(4401756625507241958224292115 n^{3} + 176473358941681777565995276440 n^{2} + 2351354049304676952591400503599 n + 10414847334464082648608192737446\right) a{\left(n + 12 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(7703629676735889425528818203 n^{3} + 351911835389152072195574836220 n^{2} + 5350031408537932999682036008081 n + 27070999537989711261607878210544\right) a{\left(n + 14 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(8838053010561432694057057532 n^{3} + 870145127225474664704617792374 n^{2} + 28556228517202189772803907191996 n + 312380577298226792802139102738737\right) a{\left(n + 32 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(10719224175582652041934677180 n^{3} + 991377322560975361039606379754 n^{2} + 30561785854834516318012798671060 n + 314038309348388777299261901843579\right) a{\left(n + 30 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(14900061694063867561471703639 n^{3} + 723012418813886081015545034223 n^{2} + 11680248663454533193727223749768 n + 62825218110775288156952744950020\right) a{\left(n + 15 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(21414109129973837830426549813 n^{3} + 917942831710667318154329973597 n^{2} + 13088112919500873205087084107692 n + 62079811370129451780669175270692\right) a{\left(n + 13 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(34903776547270252213825012541 n^{3} + 3332205253325508010308513867312 n^{2} + 106037777912033151075726394512319 n + 1124757832997994118262633935935510\right) a{\left(n + 31 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(55290828609157128488047607075 n^{3} + 4948960534833038292918956142309 n^{2} + 147649695632888255939731782890185 n + 1468280032530443431032944160365793\right) a{\left(n + 29 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(108210464587814510607450009089 n^{3} + 7764777317209849652750623247141 n^{2} + 185684241544295496444591152566383 n + 1479819878023400487977319940204265\right) a{\left(n + 23 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(108403202572562367233900599971 n^{3} + 7142940788266416319478101897666 n^{2} + 156838192076115057395615842535374 n + 1147544098983125599410092788673189\right) a{\left(n + 21 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(156107512969087606607842501319 n^{3} + 8021941979232376080010705250868 n^{2} + 137278232496467970267654702331105 n + 782362894385809021922409810757920\right) a{\left(n + 16 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(177364785759158751696505213424 n^{3} + 15348180127021226723902928210709 n^{2} + 442686670324890161039892711025177 n + 4255849472047613260594226305566420\right) a{\left(n + 28 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(247555477275220231280719608223 n^{3} + 13433889144164572584896852198106 n^{2} + 242819824168307659621142017282715 n + 1461947884550496369261969060621540\right) a{\left(n + 17 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(265262959132210663381876844476 n^{3} + 22167131777907281690080023692703 n^{2} + 617424034158970915713255162522617 n + 5731905253376126961167170055482212\right) a{\left(n + 27 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(289445255940341145171855000212 n^{3} + 18226945759106369889543863267601 n^{2} + 382445635906873251784269427153018 n + 2673856007667748450671874941762696\right) a{\left(n + 20 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(358242089524366140424768643800 n^{3} + 20476328759039856088477218100677 n^{2} + 389893602649454717768779881562211 n + 2473244738932011188797368101160486\right) a{\left(n + 18 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(369690429017856067383394973912 n^{3} + 29798712606590928642000230878059 n^{2} + 800548120276074583515912669444055 n + 7168173447758281499865482570982918\right) a{\left(n + 26 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(474971115469716842194716439717 n^{3} + 28526850708465703604829681758199 n^{2} + 570833326942214022199850762230730 n + 3805744002617401801823424334445970\right) a{\left(n + 19 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(479728399912553310864070036978 n^{3} + 37250198853572416345171276968933 n^{2} + 964006725432534611548074106445837 n + 8314775774619374168171058521935302\right) a{\left(n + 25 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(579032516240980055050910673838 n^{3} + 43253150224063110147062860790505 n^{2} + 1076802948231772965863232694845521 n + 8934277878053956277582384731943412\right) a{\left(n + 24 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(675311268758873244666843322135 n^{3} + 46475312594275848953163762306129 n^{2} + 1065874309696840270185821334144608 n + 8146238150665278541989125895614148\right) a{\left(n + 22 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)}, \quad n \geq 59\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 111\)
\(\displaystyle a(6) = 546\)
\(\displaystyle a(7) = 2762\)
\(\displaystyle a(8) = 14200\)
\(\displaystyle a(9) = 73887\)
\(\displaystyle a(10) = 388409\)
\(\displaystyle a(11) = 2060542\)
\(\displaystyle a(12) = 11021931\)
\(\displaystyle a(13) = 59396792\)
\(\displaystyle a(14) = 322232488\)
\(\displaystyle a(15) = 1758648248\)
\(\displaystyle a(16) = 9649982956\)
\(\displaystyle a(17) = 53208146080\)
\(\displaystyle a(18) = 294665208539\)
\(\displaystyle a(19) = 1638323429341\)
\(\displaystyle a(20) = 9141843254029\)
\(\displaystyle a(21) = 51179241261866\)
\(\displaystyle a(22) = 287381629847972\)
\(\displaystyle a(23) = 1618164162470222\)
\(\displaystyle a(24) = 9134611240679163\)
\(\displaystyle a(25) = 51686538753126316\)
\(\displaystyle a(26) = 293095897148274730\)
\(\displaystyle a(27) = 1665404690926479898\)
\(\displaystyle a(28) = 9480849175417407226\)
\(\displaystyle a(29) = 54067674790414204596\)
\(\displaystyle a(30) = 308845969910109281325\)
\(\displaystyle a(31) = 1766913673513726062513\)
\(\displaystyle a(32) = 10123186899738121045544\)
\(\displaystyle a(33) = 58077866600993125046950\)
\(\displaystyle a(34) = 333627344304467436317079\)
\(\displaystyle a(35) = 1918841615589515955694506\)
\(\displaystyle a(36) = 11048786029959494104163769\)
\(\displaystyle a(37) = 63688589503218276925160635\)
\(\displaystyle a(38) = 367498900366679725671633598\)
\(\displaystyle a(39) = 2122635076336808757678340034\)
\(\displaystyle a(40) = 12271529278119029717084003381\)
\(\displaystyle a(41) = 71007915806467013997945493536\)
\(\displaystyle a(42) = 411226968858539672814864481340\)
\(\displaystyle a(43) = 2383451965524746439761372834922\)
\(\displaystyle a(44) = 13825013940619452748683412885877\)
\(\displaystyle a(45) = 80249899864682740759624152263221\)
\(\displaystyle a(46) = 466154081721326119984274741474893\)
\(\displaystyle a(47) = 2709615919968577233838734154048576\)
\(\displaystyle a(48) = 15760398673731736391909417535138071\)
\(\displaystyle a(49) = 91726870222208391203727776250857352\)
\(\displaystyle a(50) = 534177047827978978978079720269933365\)
\(\displaystyle a(51) = 3112598613150193471003566781086983736\)
\(\displaystyle a(52) = 18146831578185277967275838498054495689\)
\(\displaystyle a(53) = 105854509156890355776870352936691394034\)
\(\displaystyle a(54) = 617789244576710023800225662848354847896\)
\(\displaystyle a(55) = 3607329096885131680321859004968183802017\)
\(\displaystyle a(56) = 21073567588787241250900696306575838392226\)
\(\displaystyle a(57) = 123165782819481924262485632555923460747382\)
\(\displaystyle a(58) = 720169925934205667373163504580397542467826\)
\(\displaystyle a{\left(n + 59 \right)} = - \frac{4284230123520000 \left(n + 1\right) \left(n + 2\right) \left(2 n + 1\right) a{\left(n \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{746496000 \left(n + 2\right) \left(337450622 n^{2} + 1396386503 n + 1333004265\right) a{\left(n + 1 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(518807 n^{2} + 60484214 n + 1762842240\right) a{\left(n + 58 \right)}}{2352 \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(112012993 n^{3} + 19340291585 n^{2} + 1113087160238 n + 21353393413360\right) a{\left(n + 57 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(3944253252 n^{3} + 669474792523 n^{2} + 37877087413683 n + 714318466188470\right) a{\left(n + 56 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{5 \left(61143497057 n^{3} + 10198917104082 n^{2} + 567063976669015 n + 10509554796923034\right) a{\left(n + 55 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(2060117801996 n^{3} + 337586759486297 n^{2} + 18439715070809575 n + 335736467990544280\right) a{\left(n + 54 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{41472 \left(84119733747562 n^{3} + 731502854545683 n^{2} + 2110415921139971 n + 2018231631461940\right) a{\left(n + 2 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(101809170160157 n^{3} + 16384009425611973 n^{2} + 878881100361252268 n + 15715086199187502762\right) a{\left(n + 53 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(1405300183274720 n^{3} + 222017584739003973 n^{2} + 11691855542007241321 n + 205237806865672902726\right) a{\left(n + 52 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(16588559348203123 n^{3} + 2571882420342650169 n^{2} + 132914529882887129684 n + 2289669391262207398206\right) a{\left(n + 51 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(56691438031946553 n^{3} + 8622176674496399578 n^{2} + 437115646608193335347 n + 7386791344108842538748\right) a{\left(n + 50 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{288 \left(103032789525144818 n^{3} + 1141766970006991377 n^{2} + 4216458416360326933 n + 5188653128344307844\right) a{\left(n + 3 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(1533017504169565003 n^{3} + 228628069540817306373 n^{2} + 11365617117961203680354 n + 188337836420308548980370\right) a{\left(n + 49 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(4089482773184893625 n^{3} + 597795239938591587642 n^{2} + 29128530034213496153361 n + 473115055600187605363430\right) a{\left(n + 48 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{24 \left(6919493882884897520 n^{3} + 90155597543139753951 n^{2} + 388939182284944629955 n + 555228987721174744074\right) a{\left(n + 4 \right)}}{49 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(14645602391413584502 n^{3} + 2097508628723312950276 n^{2} + 100134397291409148233161 n + 1593477228938458769057349\right) a{\left(n + 47 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{3 \left(374939713290084622130 n^{3} + 4990046349937987895793 n^{2} + 20376322562809136821479 n + 23526162677353561428686\right) a{\left(n + 5 \right)}}{98 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(567105510242017996132 n^{3} + 79538123336197593006369 n^{2} + 3718525355146374474511439 n + 57949554603432281130160548\right) a{\left(n + 46 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3139058437854009321775 n^{3} - 126204528883817655507453 n^{2} - 2106234521538434230456015 n - 7492585646314077202103475\right) a{\left(n + 6 \right)}}{588 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3316354698865518651485 n^{3} + 455282695399968128684061 n^{2} + 20834645000862724134587032 n + 317816072856113744896268142\right) a{\left(n + 45 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(17657987067926901023306 n^{3} + 2371671764465311911565305 n^{2} + 106182645295723788489794971 n + 1584667134265362953809512786\right) a{\left(n + 44 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(85960502750141815303873 n^{3} + 11289648464083841928789789 n^{2} + 494251657077282183857497202 n + 7212769615450873120373309022\right) a{\left(n + 43 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(127985361825051366058514 n^{3} + 16427619400208840592168347 n^{2} + 702871200181736376736796045 n + 10024520376615733499477739284\right) a{\left(n + 42 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(1578435956252052916266016 n^{3} + 197892081249520199129877813 n^{2} + 8270219273839989706824233987 n + 115210677346139780681771221128\right) a{\left(n + 41 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(1996049652036931476695096 n^{3} + 244288607613409443755762079 n^{2} + 9966035008528735204188824573 n + 135527943789292075182284082610\right) a{\left(n + 40 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3123014247163584002403670 n^{3} + 97262717922916632284550561 n^{2} + 940976056067809777763817761 n + 2903258741546345354187769464\right) a{\left(n + 7 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(21012494710200484937788907 n^{3} + 2508833284876224509962847181 n^{2} + 99851182280521711914862966036 n + 1324712877914076957115297424964\right) a{\left(n + 39 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(34167274190570578425290405 n^{3} + 3977285781823539133337201763 n^{2} + 154329899228949796410740420707 n + 1996181676060056917781111074089\right) a{\left(n + 38 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(49909145417762677744405829 n^{3} + 1525758875216944086231184398 n^{2} + 15199844755418980550853780169 n + 49607593999185477802958646216\right) a{\left(n + 8 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(51576494068059824234098460 n^{3} + 5849490425311806005749583655 n^{2} + 221141511222866246489413568206 n + 2786816899805731812423732479763\right) a{\left(n + 37 \right)}}{7056 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(83663360580635324984619723 n^{3} + 2710291780124965926995646485 n^{2} + 28940709143791311330255486506 n + 102056382777191813094236965904\right) a{\left(n + 9 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(504209472938448445113993523 n^{3} + 54165866956945434704122564036 n^{2} + 1939650362639766425943973662237 n + 23152834382623437994437818369270\right) a{\left(n + 35 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(579037604223591564187417403 n^{3} + 63937705784727168661153737144 n^{2} + 2353380343373918601028363574215 n + 28874328184601076548999710001004\right) a{\left(n + 36 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(978816538869389348316373279 n^{3} + 34041382032562287012530744442 n^{2} + 392028066617977430122154406701 n + 1496258387459543504590797125370\right) a{\left(n + 10 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(1227081613274887045706050743 n^{3} + 128149823497155495782234720756 n^{2} + 4461113928211921173367855640959 n + 51766555496931969240662852369662\right) a{\left(n + 34 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(2784097437516612931019723951 n^{3} + 282428331938414658130731592732 n^{2} + 9550142662193353961798658185363 n + 107643833093974860912586746729848\right) a{\left(n + 33 \right)}}{9408 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(3168671470266593224383406753 n^{3} + 118445287810134420691814292543 n^{2} + 1469491925724921475182847201052 n + 6053693447363413664157839269440\right) a{\left(n + 11 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(4401756625507241958224292115 n^{3} + 176473358941681777565995276440 n^{2} + 2351354049304676952591400503599 n + 10414847334464082648608192737446\right) a{\left(n + 12 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(7703629676735889425528818203 n^{3} + 351911835389152072195574836220 n^{2} + 5350031408537932999682036008081 n + 27070999537989711261607878210544\right) a{\left(n + 14 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(8838053010561432694057057532 n^{3} + 870145127225474664704617792374 n^{2} + 28556228517202189772803907191996 n + 312380577298226792802139102738737\right) a{\left(n + 32 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(10719224175582652041934677180 n^{3} + 991377322560975361039606379754 n^{2} + 30561785854834516318012798671060 n + 314038309348388777299261901843579\right) a{\left(n + 30 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(14900061694063867561471703639 n^{3} + 723012418813886081015545034223 n^{2} + 11680248663454533193727223749768 n + 62825218110775288156952744950020\right) a{\left(n + 15 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(21414109129973837830426549813 n^{3} + 917942831710667318154329973597 n^{2} + 13088112919500873205087084107692 n + 62079811370129451780669175270692\right) a{\left(n + 13 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(34903776547270252213825012541 n^{3} + 3332205253325508010308513867312 n^{2} + 106037777912033151075726394512319 n + 1124757832997994118262633935935510\right) a{\left(n + 31 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(55290828609157128488047607075 n^{3} + 4948960534833038292918956142309 n^{2} + 147649695632888255939731782890185 n + 1468280032530443431032944160365793\right) a{\left(n + 29 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(108210464587814510607450009089 n^{3} + 7764777317209849652750623247141 n^{2} + 185684241544295496444591152566383 n + 1479819878023400487977319940204265\right) a{\left(n + 23 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(108403202572562367233900599971 n^{3} + 7142940788266416319478101897666 n^{2} + 156838192076115057395615842535374 n + 1147544098983125599410092788673189\right) a{\left(n + 21 \right)}}{4704 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(156107512969087606607842501319 n^{3} + 8021941979232376080010705250868 n^{2} + 137278232496467970267654702331105 n + 782362894385809021922409810757920\right) a{\left(n + 16 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(177364785759158751696505213424 n^{3} + 15348180127021226723902928210709 n^{2} + 442686670324890161039892711025177 n + 4255849472047613260594226305566420\right) a{\left(n + 28 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(247555477275220231280719608223 n^{3} + 13433889144164572584896852198106 n^{2} + 242819824168307659621142017282715 n + 1461947884550496369261969060621540\right) a{\left(n + 17 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(265262959132210663381876844476 n^{3} + 22167131777907281690080023692703 n^{2} + 617424034158970915713255162522617 n + 5731905253376126961167170055482212\right) a{\left(n + 27 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(289445255940341145171855000212 n^{3} + 18226945759106369889543863267601 n^{2} + 382445635906873251784269427153018 n + 2673856007667748450671874941762696\right) a{\left(n + 20 \right)}}{14112 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(358242089524366140424768643800 n^{3} + 20476328759039856088477218100677 n^{2} + 389893602649454717768779881562211 n + 2473244738932011188797368101160486\right) a{\left(n + 18 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(369690429017856067383394973912 n^{3} + 29798712606590928642000230878059 n^{2} + 800548120276074583515912669444055 n + 7168173447758281499865482570982918\right) a{\left(n + 26 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(474971115469716842194716439717 n^{3} + 28526850708465703604829681758199 n^{2} + 570833326942214022199850762230730 n + 3805744002617401801823424334445970\right) a{\left(n + 19 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} - \frac{\left(479728399912553310864070036978 n^{3} + 37250198853572416345171276968933 n^{2} + 964006725432534611548074106445837 n + 8314775774619374168171058521935302\right) a{\left(n + 25 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(579032516240980055050910673838 n^{3} + 43253150224063110147062860790505 n^{2} + 1076802948231772965863232694845521 n + 8934277878053956277582384731943412\right) a{\left(n + 24 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)} + \frac{\left(675311268758873244666843322135 n^{3} + 46475312594275848953163762306129 n^{2} + 1065874309696840270185821334144608 n + 8146238150665278541989125895614148\right) a{\left(n + 22 \right)}}{28224 \left(n + 59\right) \left(n + 60\right) \left(2 n + 119\right)}, \quad n \geq 59\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 147 rules.
Finding the specification took 29273 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{0}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{95}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{36}\! \left(x \right) &= -F_{47}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{38}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{0} \left(x \right)^{2}\\
F_{41}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{4}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{47}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= \frac{F_{54}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{54}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= \frac{F_{58}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{61}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{68}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{22} \left(x \right)^{2} F_{4}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{22} \left(x \right)^{2} F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{4}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{35}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{4}\! \left(x \right) F_{78}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{95}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{97}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{4}\! \left(x \right) F_{76}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{0}\! \left(x \right) F_{102}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{107}\! \left(x \right) &= \frac{F_{108}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= -F_{110}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{47}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{126}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{125}\! \left(x \right) &= 0\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{23}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{131}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{137}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{142}\! \left(x \right)+F_{144}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{136}\! \left(x \right) F_{4}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 149 rules.
Finding the specification took 18759 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{0}\! \left(x \right) F_{4}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{99}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{36}\! \left(x \right) &= -F_{47}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{38}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{0} \left(x \right)^{2}\\
F_{41}\! \left(x \right) &= -F_{65}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{4}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{47}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= \frac{F_{54}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{54}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= \frac{F_{58}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{61}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{67}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{22} \left(x \right)^{2} F_{4}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{22} \left(x \right)^{2} F_{4}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{4}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{4}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{4}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{94}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{4}\! \left(x \right) F_{77}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{99}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{4}\! \left(x \right) F_{75}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{2}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{0}\! \left(x \right) F_{104}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{109}\! \left(x \right) &= \frac{F_{110}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= -F_{112}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{47}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{4}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{128}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{127}\! \left(x \right) &= 0\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{23}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{133}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{139}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{144}\! \left(x \right)+F_{146}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{138}\! \left(x \right) F_{4}\! \left(x \right)\\
\end{align*}\)