Av(12453, 14253, 21453, 24153, 24513, 41253, 42153, 42513)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3030, 16724, 94608, 545272, 3189000, 18872340, 112779866, 679514008, ...
Implicit Equation for the Generating Function
\(\displaystyle -F \left(x
\right)^{6}+\left(2 x^{2}-3 x +7\right) F \left(x
\right)^{5}+\left(-4 x^{3}-7 x^{2}+15 x -20\right) F \left(x
\right)^{4}+\left(2 x^{4}+7 x^{3}+12 x^{2}-31 x +30\right) F \left(x
\right)^{3}+\left(-4 x^{4}-x^{3}-13 x^{2}+33 x -25\right) F \left(x
\right)^{2}+\left(x -1\right) \left(x^{3}-x^{2}+7 x -11\right) F \! \left(x \right)-2 \left(x -1\right)^{2} = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3030\)
\(\displaystyle a(8) = 16724\)
\(\displaystyle a(9) = 94608\)
\(\displaystyle a(10) = 545272\)
\(\displaystyle a(11) = 3189000\)
\(\displaystyle a(12) = 18872340\)
\(\displaystyle a(13) = 112779866\)
\(\displaystyle a(14) = 679514008\)
\(\displaystyle a(15) = 4122937606\)
\(\displaystyle a(16) = 25167922580\)
\(\displaystyle a(17) = 154451420008\)
\(\displaystyle a(18) = 952297701396\)
\(\displaystyle a(19) = 5896151321776\)
\(\displaystyle a(20) = 36643283656576\)
\(\displaystyle a(21) = 228503737216904\)
\(\displaystyle a(22) = 1429326441677912\)
\(\displaystyle a(23) = 8965885886777164\)
\(\displaystyle a(24) = 56386895687059192\)
\(\displaystyle a(25) = 355466251344673822\)
\(\displaystyle a(26) = 2245826442501313628\)
\(\displaystyle a(27) = 14218140955315353518\)
\(\displaystyle a(28) = 90185530031538881032\)
\(\displaystyle a(29) = 573064229028994820510\)
\(\displaystyle a(30) = 3647477066430960618660\)
\(\displaystyle a(31) = 23251975008904605853710\)
\(\displaystyle a(32) = 148444611542465006149492\)
\(\displaystyle a(33) = 949006660390786335574592\)
\(\displaystyle a(34) = 6074918000763760916118260\)
\(\displaystyle a(35) = 38935596953997423138785708\)
\(\displaystyle a(36) = 249838829358447256889842160\)
\(\displaystyle a(37) = 1604919941016812290104099300\)
\(\displaystyle a(38) = 10320549125280147070675347688\)
\(\displaystyle a(39) = 66433278929879354530943470000\)
\(\displaystyle a(40) = 428036790472685270939759215384\)
\(\displaystyle a(41) = 2760384508652111998450674316552\)
\(\displaystyle a(42) = 17816935646171125082472749372832\)
\(\displaystyle a(43) = 115094474740830546914993598206008\)
\(\displaystyle a(44) = 744077487077645731877047066900080\)
\(\displaystyle a(45) = 4814035417458883230541541050733572\)
\(\displaystyle a(46) = 31168360030688263198846657327244296\)
\(\displaystyle a{\left(n + 47 \right)} = \frac{25165824 n \left(n - 2\right) \left(n - 1\right) \left(n + 1\right) \left(2 n - 1\right) a{\left(n \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{3145728 n \left(n - 1\right) \left(n + 1\right) \left(406 n^{2} + 665 n + 291\right) a{\left(n + 1 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{262144 n \left(n + 1\right) \left(4118 n^{3} - 3751 n^{2} - 43216 n - 40401\right) a{\left(n + 2 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{49152 \left(n + 1\right) \left(909270 n^{4} + 13595079 n^{3} + 66932558 n^{2} + 136096063 n + 98640894\right) a{\left(n + 3 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{\left(n + 43\right) \left(17563298 n^{4} + 2945172341 n^{3} + 185198191157 n^{2} + 5175715813614 n + 54240738737400\right) a{\left(n + 43 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2 \left(448 n^{2} + 39875 n + 886833\right) a{\left(n + 46 \right)}}{5 \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(1886 n^{3} + 246138 n^{2} + 10706323 n + 155213118\right) a{\left(n + 45 \right)}}{\left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(32769 n^{4} + 5605114 n^{3} + 359516663 n^{2} + 10248336358 n + 109547262168\right) a{\left(n + 44 \right)}}{\left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(37305381 n^{5} + 7704812035 n^{4} + 636499396035 n^{3} + 26289915863765 n^{2} + 542919579443544 n + 4484631419578800\right) a{\left(n + 42 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(101011969 n^{5} + 20491564676 n^{4} + 1662663540635 n^{3} + 67448191122478 n^{2} + 1367957532200034 n + 11096882123154516\right) a{\left(n + 41 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4096 \left(1030242116 n^{5} + 19761394180 n^{4} + 144126993595 n^{3} + 504852806510 n^{2} + 853083766269 n + 556554827610\right) a{\left(n + 4 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(1939002588 n^{5} + 389504500145 n^{4} + 31282750160380 n^{3} + 1255659217192195 n^{2} + 25189453566480212 n + 202041750251615880\right) a{\left(n + 40 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(8193839008 n^{5} + 1856934501905 n^{4} + 164371806966410 n^{3} + 7146049196850955 n^{2} + 153189390547889682 n + 1298990779307215200\right) a{\left(n + 39 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2048 \left(16817905192 n^{5} + 386160057830 n^{4} + 3455353182425 n^{3} + 15129611276740 n^{2} + 32507197625853 n + 27457659484200\right) a{\left(n + 5 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(123318885487 n^{5} + 21819270529115 n^{4} + 1539101280253385 n^{3} + 54081134371933015 n^{2} + 946164485217658338 n + 6589703951040057300\right) a{\left(n + 38 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{512 \left(303682184156 n^{5} + 7789692344080 n^{4} + 78594808790845 n^{3} + 390418988274080 n^{2} + 955958280413259 n + 924022444956300\right) a{\left(n + 6 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{256 \left(320873322310 n^{5} + 7758304578491 n^{4} + 68748580331036 n^{3} + 256932531742861 n^{2} + 283646491053522 n - 257698257758028\right) a{\left(n + 7 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{12 \left(560387574512 n^{5} + 99229911611280 n^{4} + 7022138550774605 n^{3} + 248232406857229560 n^{2} + 4383163390905550043 n + 30925925916246532740\right) a{\left(n + 37 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{128 \left(4517476131284 n^{5} + 19608472844110 n^{4} - 1649168539495805 n^{3} - 24816441889892800 n^{2} - 132301053074854059 n - 246920088668642730\right) a{\left(n + 8 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{128 \left(6725073736426 n^{5} + 761659747262855 n^{4} + 19612521826542080 n^{3} + 212624862807791035 n^{2} + 1058548673477277654 n + 2002601600535656430\right) a{\left(n + 9 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(13508677780592 n^{5} + 2347209728753275 n^{4} + 163056949253401090 n^{3} + 5660809223367192215 n^{2} + 98211551525594932188 n + 681199197914341577520\right) a{\left(n + 36 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2 \left(162210625293118 n^{5} + 27525684785774015 n^{4} + 1867699139809815080 n^{3} + 63342172883737618525 n^{2} + 1073725959592995918042 n + 7277722878315739988700\right) a{\left(n + 35 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{64 \left(193195583364608 n^{5} + 10388640754686475 n^{4} + 213544833714540460 n^{3} + 2127280219448160365 n^{2} + 10355433018033202452 n + 19811217941829631080\right) a{\left(n + 10 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{24 \left(256945930245669 n^{5} + 41335109834601630 n^{4} + 2659122595485235205 n^{3} + 85508495256377680885 n^{2} + 1374458387938102397346 n + 8834769273879031152195\right) a{\left(n + 33 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{32 \left(364306364455796 n^{5} + 17764746073851376 n^{4} + 343248631847261941 n^{3} + 3284912768179820858 n^{2} + 15567570481470252999 n + 29215834139383337286\right) a{\left(n + 11 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(389678724426908 n^{5} + 64431035625163630 n^{4} + 4260084767373069835 n^{3} + 140794285526019721100 n^{2} + 2325918139238942162607 n + 15365099986017957973080\right) a{\left(n + 34 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{48 \left(617616454064874 n^{5} - 79384729348888610 n^{4} - 4990982186689823175 n^{3} - 100676686325950138530 n^{2} - 872989249574926102489 n - 2803048421737554949170\right) a{\left(n + 14 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(1017473949503387 n^{5} + 159069529231348300 n^{4} + 9944705710706242027 n^{3} + 310776394407849197156 n^{2} + 4854620483103866081532 n + 30325213285892546895702\right) a{\left(n + 32 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{96 \left(1657375652636702 n^{5} + 80844447955339070 n^{4} + 1551602678241364765 n^{3} + 14577253574181253660 n^{2} + 66556404691724993253 n + 116733736758007769670\right) a{\left(n + 12 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{96 \left(2556877209096213 n^{5} + 121525771566718395 n^{4} + 2177653145971761720 n^{3} + 17575008418637832445 n^{2} + 55946198097562152167 n + 19814085580846510020\right) a{\left(n + 13 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(13183020942014822 n^{5} + 1938845147883676993 n^{4} + 114033627807689924716 n^{3} + 3352680290560702539311 n^{2} + 49274111830859147121642 n + 289601852395628111883084\right) a{\left(n + 30 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{6 \left(15618135818809313 n^{5} + 2137735266040948552 n^{4} + 117057607360034590763 n^{3} + 3205295260255050866240 n^{2} + 43888549430042697317432 n + 240398496503120752744644\right) a{\left(n + 28 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{16 \left(45181220545851251 n^{5} + 3434008447132168384 n^{4} + 103916924619670165495 n^{3} + 1565544500788769106290 n^{2} + 11745052574053106133990 n + 35110657113642681271506\right) a{\left(n + 16 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{\left(56359727465027998 n^{5} + 8552847683407311755 n^{4} + 519033700832189909900 n^{3} + 15744639025737181033825 n^{2} + 238738112633071203604602 n + 1447612987609944433159920\right) a{\left(n + 31 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(66043576423588492 n^{5} + 9389373102903869420 n^{4} + 533898693394796531195 n^{3} + 15177567301730307914065 n^{2} + 215705788189258712430948 n + 1226093221305392097915270\right) a{\left(n + 29 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{8 \left(131421848193909448 n^{5} + 10067626327861173650 n^{4} + 303678827200360538465 n^{3} + 4522739140154747797720 n^{2} + 33332350588112295161067 n + 97414392190319576449650\right) a{\left(n + 15 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{\left(155910453691014310 n^{5} + 20431309674371487905 n^{4} + 1071455379316840630148 n^{3} + 28106822460268497230551 n^{2} + 368809369219073615837190 n + 1936543968969020238778560\right) a{\left(n + 27 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{6 \left(217590402462500689 n^{5} + 27144744909935490545 n^{4} + 1355419769263526853235 n^{3} + 33862347804992852888535 n^{2} + 423270484350090551551856 n + 2117718917069046214982700\right) a{\left(n + 26 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(411932820125763254 n^{5} + 46346999497893677215 n^{4} + 2086005228940855790566 n^{3} + 46950265158095553163517 n^{2} + 528458512359986869484868 n + 2379831047184684882830796\right) a{\left(n + 24 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(572886235259146069 n^{5} + 67833392455949589080 n^{4} + 3214400210469102470375 n^{3} + 76201646417186378812240 n^{2} + 903760481636841792497766 n + 4290157565989638928885350\right) a{\left(n + 25 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{24 \left(624247070216599027 n^{5} + 54818303141565806795 n^{4} + 1922310312277667223705 n^{3} + 33647856321160606568815 n^{2} + 293983180116366951167528 n + 1025655822318377506760670\right) a{\left(n + 19 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{8 \left(953311396848095269 n^{5} + 75460711633158531680 n^{4} + 2382190639064845099685 n^{3} + 37491273599126987829760 n^{2} + 294165718392391512919896 n + 920563505531629535625210\right) a{\left(n + 17 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{8 \left(1350966080939435101 n^{5} + 138194871689534139350 n^{4} + 5650989693476935926140 n^{3} + 115468083725263415218735 n^{2} + 1179002633617430319309429 n + 4812649498721108891674305\right) a{\left(n + 22 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(1767879836108839171 n^{5} + 189542851173632926685 n^{4} + 8126000038137534908285 n^{3} + 174134978630711500013245 n^{2} + 1865310752710538825036484 n + 7990605458014804708417830\right) a{\left(n + 23 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{8 \left(1970930740755408008 n^{5} + 182551050986910083995 n^{4} + 6755126773924562705590 n^{3} + 124833743674791046290590 n^{2} + 1152079720117342524268092 n + 4247929379878857571230405\right) a{\left(n + 20 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(2986075196508907282 n^{5} + 248590311063100669565 n^{4} + 8259330564302876097485 n^{3} + 136895054390346868625665 n^{2} + 1131887851149054440325573 n + 3734798545683822623978790\right) a{\left(n + 18 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(3538179155811609146 n^{5} + 344869744246956736060 n^{4} + 13434092814903458091055 n^{3} + 261430500046886394616940 n^{2} + 2541591913576640608714149 n + 9875390765570027431020270\right) a{\left(n + 21 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)}, \quad n \geq 47\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3030\)
\(\displaystyle a(8) = 16724\)
\(\displaystyle a(9) = 94608\)
\(\displaystyle a(10) = 545272\)
\(\displaystyle a(11) = 3189000\)
\(\displaystyle a(12) = 18872340\)
\(\displaystyle a(13) = 112779866\)
\(\displaystyle a(14) = 679514008\)
\(\displaystyle a(15) = 4122937606\)
\(\displaystyle a(16) = 25167922580\)
\(\displaystyle a(17) = 154451420008\)
\(\displaystyle a(18) = 952297701396\)
\(\displaystyle a(19) = 5896151321776\)
\(\displaystyle a(20) = 36643283656576\)
\(\displaystyle a(21) = 228503737216904\)
\(\displaystyle a(22) = 1429326441677912\)
\(\displaystyle a(23) = 8965885886777164\)
\(\displaystyle a(24) = 56386895687059192\)
\(\displaystyle a(25) = 355466251344673822\)
\(\displaystyle a(26) = 2245826442501313628\)
\(\displaystyle a(27) = 14218140955315353518\)
\(\displaystyle a(28) = 90185530031538881032\)
\(\displaystyle a(29) = 573064229028994820510\)
\(\displaystyle a(30) = 3647477066430960618660\)
\(\displaystyle a(31) = 23251975008904605853710\)
\(\displaystyle a(32) = 148444611542465006149492\)
\(\displaystyle a(33) = 949006660390786335574592\)
\(\displaystyle a(34) = 6074918000763760916118260\)
\(\displaystyle a(35) = 38935596953997423138785708\)
\(\displaystyle a(36) = 249838829358447256889842160\)
\(\displaystyle a(37) = 1604919941016812290104099300\)
\(\displaystyle a(38) = 10320549125280147070675347688\)
\(\displaystyle a(39) = 66433278929879354530943470000\)
\(\displaystyle a(40) = 428036790472685270939759215384\)
\(\displaystyle a(41) = 2760384508652111998450674316552\)
\(\displaystyle a(42) = 17816935646171125082472749372832\)
\(\displaystyle a(43) = 115094474740830546914993598206008\)
\(\displaystyle a(44) = 744077487077645731877047066900080\)
\(\displaystyle a(45) = 4814035417458883230541541050733572\)
\(\displaystyle a(46) = 31168360030688263198846657327244296\)
\(\displaystyle a{\left(n + 47 \right)} = \frac{25165824 n \left(n - 2\right) \left(n - 1\right) \left(n + 1\right) \left(2 n - 1\right) a{\left(n \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{3145728 n \left(n - 1\right) \left(n + 1\right) \left(406 n^{2} + 665 n + 291\right) a{\left(n + 1 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{262144 n \left(n + 1\right) \left(4118 n^{3} - 3751 n^{2} - 43216 n - 40401\right) a{\left(n + 2 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{49152 \left(n + 1\right) \left(909270 n^{4} + 13595079 n^{3} + 66932558 n^{2} + 136096063 n + 98640894\right) a{\left(n + 3 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{\left(n + 43\right) \left(17563298 n^{4} + 2945172341 n^{3} + 185198191157 n^{2} + 5175715813614 n + 54240738737400\right) a{\left(n + 43 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2 \left(448 n^{2} + 39875 n + 886833\right) a{\left(n + 46 \right)}}{5 \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(1886 n^{3} + 246138 n^{2} + 10706323 n + 155213118\right) a{\left(n + 45 \right)}}{\left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(32769 n^{4} + 5605114 n^{3} + 359516663 n^{2} + 10248336358 n + 109547262168\right) a{\left(n + 44 \right)}}{\left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(37305381 n^{5} + 7704812035 n^{4} + 636499396035 n^{3} + 26289915863765 n^{2} + 542919579443544 n + 4484631419578800\right) a{\left(n + 42 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(101011969 n^{5} + 20491564676 n^{4} + 1662663540635 n^{3} + 67448191122478 n^{2} + 1367957532200034 n + 11096882123154516\right) a{\left(n + 41 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4096 \left(1030242116 n^{5} + 19761394180 n^{4} + 144126993595 n^{3} + 504852806510 n^{2} + 853083766269 n + 556554827610\right) a{\left(n + 4 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{6 \left(1939002588 n^{5} + 389504500145 n^{4} + 31282750160380 n^{3} + 1255659217192195 n^{2} + 25189453566480212 n + 202041750251615880\right) a{\left(n + 40 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(8193839008 n^{5} + 1856934501905 n^{4} + 164371806966410 n^{3} + 7146049196850955 n^{2} + 153189390547889682 n + 1298990779307215200\right) a{\left(n + 39 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2048 \left(16817905192 n^{5} + 386160057830 n^{4} + 3455353182425 n^{3} + 15129611276740 n^{2} + 32507197625853 n + 27457659484200\right) a{\left(n + 5 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(123318885487 n^{5} + 21819270529115 n^{4} + 1539101280253385 n^{3} + 54081134371933015 n^{2} + 946164485217658338 n + 6589703951040057300\right) a{\left(n + 38 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{512 \left(303682184156 n^{5} + 7789692344080 n^{4} + 78594808790845 n^{3} + 390418988274080 n^{2} + 955958280413259 n + 924022444956300\right) a{\left(n + 6 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{256 \left(320873322310 n^{5} + 7758304578491 n^{4} + 68748580331036 n^{3} + 256932531742861 n^{2} + 283646491053522 n - 257698257758028\right) a{\left(n + 7 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{12 \left(560387574512 n^{5} + 99229911611280 n^{4} + 7022138550774605 n^{3} + 248232406857229560 n^{2} + 4383163390905550043 n + 30925925916246532740\right) a{\left(n + 37 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{128 \left(4517476131284 n^{5} + 19608472844110 n^{4} - 1649168539495805 n^{3} - 24816441889892800 n^{2} - 132301053074854059 n - 246920088668642730\right) a{\left(n + 8 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{128 \left(6725073736426 n^{5} + 761659747262855 n^{4} + 19612521826542080 n^{3} + 212624862807791035 n^{2} + 1058548673477277654 n + 2002601600535656430\right) a{\left(n + 9 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(13508677780592 n^{5} + 2347209728753275 n^{4} + 163056949253401090 n^{3} + 5660809223367192215 n^{2} + 98211551525594932188 n + 681199197914341577520\right) a{\left(n + 36 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{2 \left(162210625293118 n^{5} + 27525684785774015 n^{4} + 1867699139809815080 n^{3} + 63342172883737618525 n^{2} + 1073725959592995918042 n + 7277722878315739988700\right) a{\left(n + 35 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{64 \left(193195583364608 n^{5} + 10388640754686475 n^{4} + 213544833714540460 n^{3} + 2127280219448160365 n^{2} + 10355433018033202452 n + 19811217941829631080\right) a{\left(n + 10 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{24 \left(256945930245669 n^{5} + 41335109834601630 n^{4} + 2659122595485235205 n^{3} + 85508495256377680885 n^{2} + 1374458387938102397346 n + 8834769273879031152195\right) a{\left(n + 33 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{32 \left(364306364455796 n^{5} + 17764746073851376 n^{4} + 343248631847261941 n^{3} + 3284912768179820858 n^{2} + 15567570481470252999 n + 29215834139383337286\right) a{\left(n + 11 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(389678724426908 n^{5} + 64431035625163630 n^{4} + 4260084767373069835 n^{3} + 140794285526019721100 n^{2} + 2325918139238942162607 n + 15365099986017957973080\right) a{\left(n + 34 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{48 \left(617616454064874 n^{5} - 79384729348888610 n^{4} - 4990982186689823175 n^{3} - 100676686325950138530 n^{2} - 872989249574926102489 n - 2803048421737554949170\right) a{\left(n + 14 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(1017473949503387 n^{5} + 159069529231348300 n^{4} + 9944705710706242027 n^{3} + 310776394407849197156 n^{2} + 4854620483103866081532 n + 30325213285892546895702\right) a{\left(n + 32 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{96 \left(1657375652636702 n^{5} + 80844447955339070 n^{4} + 1551602678241364765 n^{3} + 14577253574181253660 n^{2} + 66556404691724993253 n + 116733736758007769670\right) a{\left(n + 12 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{96 \left(2556877209096213 n^{5} + 121525771566718395 n^{4} + 2177653145971761720 n^{3} + 17575008418637832445 n^{2} + 55946198097562152167 n + 19814085580846510020\right) a{\left(n + 13 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(13183020942014822 n^{5} + 1938845147883676993 n^{4} + 114033627807689924716 n^{3} + 3352680290560702539311 n^{2} + 49274111830859147121642 n + 289601852395628111883084\right) a{\left(n + 30 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{6 \left(15618135818809313 n^{5} + 2137735266040948552 n^{4} + 117057607360034590763 n^{3} + 3205295260255050866240 n^{2} + 43888549430042697317432 n + 240398496503120752744644\right) a{\left(n + 28 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{16 \left(45181220545851251 n^{5} + 3434008447132168384 n^{4} + 103916924619670165495 n^{3} + 1565544500788769106290 n^{2} + 11745052574053106133990 n + 35110657113642681271506\right) a{\left(n + 16 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{\left(56359727465027998 n^{5} + 8552847683407311755 n^{4} + 519033700832189909900 n^{3} + 15744639025737181033825 n^{2} + 238738112633071203604602 n + 1447612987609944433159920\right) a{\left(n + 31 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(66043576423588492 n^{5} + 9389373102903869420 n^{4} + 533898693394796531195 n^{3} + 15177567301730307914065 n^{2} + 215705788189258712430948 n + 1226093221305392097915270\right) a{\left(n + 29 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{8 \left(131421848193909448 n^{5} + 10067626327861173650 n^{4} + 303678827200360538465 n^{3} + 4522739140154747797720 n^{2} + 33332350588112295161067 n + 97414392190319576449650\right) a{\left(n + 15 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{\left(155910453691014310 n^{5} + 20431309674371487905 n^{4} + 1071455379316840630148 n^{3} + 28106822460268497230551 n^{2} + 368809369219073615837190 n + 1936543968969020238778560\right) a{\left(n + 27 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{6 \left(217590402462500689 n^{5} + 27144744909935490545 n^{4} + 1355419769263526853235 n^{3} + 33862347804992852888535 n^{2} + 423270484350090551551856 n + 2117718917069046214982700\right) a{\left(n + 26 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{2 \left(411932820125763254 n^{5} + 46346999497893677215 n^{4} + 2086005228940855790566 n^{3} + 46950265158095553163517 n^{2} + 528458512359986869484868 n + 2379831047184684882830796\right) a{\left(n + 24 \right)}}{\left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(572886235259146069 n^{5} + 67833392455949589080 n^{4} + 3214400210469102470375 n^{3} + 76201646417186378812240 n^{2} + 903760481636841792497766 n + 4290157565989638928885350\right) a{\left(n + 25 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{24 \left(624247070216599027 n^{5} + 54818303141565806795 n^{4} + 1922310312277667223705 n^{3} + 33647856321160606568815 n^{2} + 293983180116366951167528 n + 1025655822318377506760670\right) a{\left(n + 19 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{8 \left(953311396848095269 n^{5} + 75460711633158531680 n^{4} + 2382190639064845099685 n^{3} + 37491273599126987829760 n^{2} + 294165718392391512919896 n + 920563505531629535625210\right) a{\left(n + 17 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{8 \left(1350966080939435101 n^{5} + 138194871689534139350 n^{4} + 5650989693476935926140 n^{3} + 115468083725263415218735 n^{2} + 1179002633617430319309429 n + 4812649498721108891674305\right) a{\left(n + 22 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(1767879836108839171 n^{5} + 189542851173632926685 n^{4} + 8126000038137534908285 n^{3} + 174134978630711500013245 n^{2} + 1865310752710538825036484 n + 7990605458014804708417830\right) a{\left(n + 23 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{8 \left(1970930740755408008 n^{5} + 182551050986910083995 n^{4} + 6755126773924562705590 n^{3} + 124833743674791046290590 n^{2} + 1152079720117342524268092 n + 4247929379878857571230405\right) a{\left(n + 20 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} - \frac{4 \left(2986075196508907282 n^{5} + 248590311063100669565 n^{4} + 8259330564302876097485 n^{3} + 136895054390346868625665 n^{2} + 1131887851149054440325573 n + 3734798545683822623978790\right) a{\left(n + 18 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)} + \frac{4 \left(3538179155811609146 n^{5} + 344869744246956736060 n^{4} + 13434092814903458091055 n^{3} + 261430500046886394616940 n^{2} + 2541591913576640608714149 n + 9875390765570027431020270\right) a{\left(n + 21 \right)}}{5 \left(n + 44\right) \left(n + 45\right) \left(n + 46\right) \left(n + 47\right) \left(2 n + 93\right)}, \quad n \geq 47\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 55 rules.
Finding the specification took 2389 seconds.
Copy 55 equations to clipboard:
\(\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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{0}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{19}\! \left(x \right) x +F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+2\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{47}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x\\
F_{30}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{19}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{11}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{16}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{37} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{25}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{11}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{50}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 28 rules.
Finding the specification took 60 seconds.
Copy 28 equations to clipboard:
\(\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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{10}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= y F_{12}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= -\frac{-F_{14}\! \left(x , y\right) y +F_{14}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , 1, y\right)\\
F_{20}\! \left(x , y , z\right) &= -\frac{-y F_{21}\! \left(x , y , z\right)+F_{21}\! \left(x , 1, z\right)}{-1+y}\\
F_{21}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , z\right)+F_{15}\! \left(x , z\right)+F_{22}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\
F_{23}\! \left(x , y , z\right) &= -\frac{-y F_{21}\! \left(x , y , z\right)+F_{21}\! \left(x , 1, z\right)}{-1+y}\\
F_{24}\! \left(x , y , z\right) &= y F_{25}\! \left(x , y , z\right)\\
F_{25}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 54 rules.
Finding the specification took 5480 seconds.
Copy 54 equations to clipboard:
\(\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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{10}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{0}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{19}\! \left(x \right) x +F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+2\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{11}\! \left(x \right) F_{46}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{11}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{16}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{11}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= -F_{25}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{45}\! \left(x \right) x +F_{45} \left(x \right)^{2}+x\\
F_{46}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{11}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{11}\! \left(x \right)}\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{49}\! \left(x \right)\\
\end{align*}\)