###### Av(1342, 2413)
Counting Sequence
1, 1, 2, 6, 22, 89, 379, 1664, 7460, 33977, 156727, 730619, 3436710, 16291842, 77758962, ...
Implicit Equation for the Generating Function
$$\displaystyle x^{3} F \left(x \right)^{6}+x \left(x^{2}-7 x +2\right) F \left(x \right)^{5}+\left(x^{4}-6 x^{3}+14 x^{2}-1\right) F \left(x \right)^{4}+\left(2 x^{3}-5 x^{2}-9 x +2\right) F \left(x \right)^{3}-x \left(x -9\right) F \left(x \right)^{2}+\left(-2 x -2\right) F \! \left(x \right)+1 = 0$$
Recurrence
$$\displaystyle a \! \left(0\right) = 1$$
$$\displaystyle a \! \left(1\right) = 1$$
$$\displaystyle a \! \left(2\right) = 2$$
$$\displaystyle a \! \left(3\right) = 6$$
$$\displaystyle a \! \left(4\right) = 22$$
$$\displaystyle a \! \left(5\right) = 89$$
$$\displaystyle a \! \left(6\right) = 379$$
$$\displaystyle a \! \left(7\right) = 1664$$
$$\displaystyle a \! \left(8\right) = 7460$$
$$\displaystyle a \! \left(9\right) = 33977$$
$$\displaystyle a \! \left(10\right) = 156727$$
$$\displaystyle a \! \left(11\right) = 730619$$
$$\displaystyle a \! \left(12\right) = 3436710$$
$$\displaystyle a \! \left(13\right) = 16291842$$
$$\displaystyle a \! \left(14\right) = 77758962$$
$$\displaystyle a \! \left(15\right) = 373369867$$
$$\displaystyle a \! \left(16\right) = 1802399037$$
$$\displaystyle a \! \left(17\right) = 8742691627$$
$$\displaystyle a \! \left(18\right) = 42590945206$$
$$\displaystyle a \! \left(19\right) = 208300979739$$
$$\displaystyle a \! \left(20\right) = 1022385319050$$
$$\displaystyle a \! \left(21\right) = 5034470059883$$
$$\displaystyle a \! \left(22\right) = 24865173540949$$
$$\displaystyle a \! \left(23\right) = 123147075005750$$
$$\displaystyle a \! \left(24\right) = 611447895295479$$
$$\displaystyle a \! \left(25\right) = 3043093928368030$$
$$\displaystyle a \! \left(26\right) = 15178127146082582$$
$$\displaystyle a \! \left(27\right) = 75858065515710393$$
$$\displaystyle a \! \left(28\right) = 379844994678126287$$
$$\displaystyle a \! \left(29\right) = 1905364793769760032$$
$$\displaystyle a \! \left(30\right) = 9573439076720851051$$
$$\displaystyle a \! \left(31\right) = 48176072356668013251$$
$$\displaystyle a \! \left(32\right) = 242788301361438124753$$
$$\displaystyle a \! \left(33\right) = 1225236563073269933702$$
$$\displaystyle a \! \left(34\right) = 6191187386852741058618$$
$$\displaystyle a \! \left(35\right) = 31322651823594072167784$$
$$\displaystyle a \! \left(36\right) = 158651772743689064994401$$
$$\displaystyle a \! \left(37\right) = 804464097863912917673770$$
$$\displaystyle a \! \left(38\right) = 4083374892869000251757240$$
$$\displaystyle a \! \left(39\right) = 20747225701843888412033277$$
$$\displaystyle a \! \left(40\right) = 105513490154367753462777380$$
$$\displaystyle a \! \left(41\right) = 537085727023300797589817967$$
$$\displaystyle a \! \left(42\right) = 2736205698038335994360804334$$
$$\displaystyle a \! \left(43\right) = 13951036193573797765389613773$$
$$\displaystyle a \! \left(44\right) = 71187048777569190826904533333$$
$$\displaystyle a \! \left(n +45\right) = \frac{3 \left(711 n^{2}+61694 n +1338315\right) a \! \left(n +44\right)}{16 \left(n +47\right) \left(2 n +89\right)}+\frac{51328125 n \left(2 n +5\right) \left(2 n +3\right) \left(2 n -1\right) \left(n +1\right) a \! \left(n \right)}{1835008 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(389824168479054289 n^{5}+69192103268297329303 n^{4}+4911848935338080179853 n^{3}+174319181064794219642021 n^{2}+3092844165504107494487094 n +21946968290433107127186864\right) a \! \left(n +35\right)}{3670016 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(580066103893024748 n^{5}+105803325383053964325 n^{4}+7718326690258847004230 n^{3}+281488067559117843084915 n^{2}+5132285119774014133055702 n +37425399660000145594659120\right) a \! \left(n +36\right)}{9175040 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(6569605397241391 n^{5}+1230563335696736944 n^{4}+92187465695568156945 n^{3}+3452661084674873981028 n^{2}+64647408711953474505500 n +484121418374146373606000\right) a \! \left(n +37\right)}{1835008 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(236611954321372 n^{5}+45486212975080727 n^{4}+3497255113608442478 n^{3}+134428140134170315489 n^{2}+2583267003290610814626 n +19854342093915338489460\right) a \! \left(n +38\right)}{458752 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(428553895214981 n^{5}+84504814094363775 n^{4}+6664431761078814785 n^{3}+262761252171002047785 n^{2}+5179369280786018418794 n +40831995261103829762760\right) a \! \left(n +39\right)}{2293760 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(333746684554 n^{5}+67466077079085 n^{4}+5454572800338565 n^{3}+220472078805694770 n^{2}+4455175222357969786 n +36006845154822265890\right) a \! \left(n +40\right)}{17920 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(53763112147 n^{5}+11135006662590 n^{4}+922367653989145 n^{3}+38197580696839530 n^{2}+790836218641354228 n +6548575253332576320\right) a \! \left(n +41\right)}{35840 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(85041798837847459960 n^{5}+13844291741719089349411 n^{4}+901371018051883846754294 n^{3}+29338778043698076778283877 n^{2}+477405083211440979170562354 n +3106916644447274600508834512\right) a \! \left(n +32\right)}{14680064 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(385194232851261511453 n^{5}+64595970032217988604520 n^{4}+4332396439856265467297875 n^{3}+145264371311627715572419980 n^{2}+2435001198607484727708142372 n +16324480274986294670624575440\right) a \! \left(n +33\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(8482025431841735694 n^{5}+1463969610875954449765 n^{4}+101056365761300116498670 n^{3}+3487429501579398783703735 n^{2}+60166997287980733007168476 n +415157929952107086681801820\right) a \! \left(n +34\right)}{18350080 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(9566009083465162288826 n^{5}+1463351520699773948730915 n^{4}+89526971008852373613762320 n^{3}+2738151791039210065235296875 n^{2}+41865911161058237942916784844 n +256008226689819414099638027820\right) a \! \left(n +30\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(1238766631119755932731 n^{5}+195583983277863575991385 n^{4}+12350040349304100523323265 n^{3}+389857427513724141367309505 n^{2}+6152428801737213280284460994 n +38831277872867448590302834200\right) a \! \left(n +31\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(128537249678439121877386 n^{5}+17139559986691699264707075 n^{4}+913979150702541069973414330 n^{3}+24364070489224149780032729565 n^{2}+324669318769269770273895282904 n +1730219978969790964960016295420\right) a \! \left(n +26\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(10658124507203535767727 n^{5}+1473385563425306715244609 n^{4}+81456152283963332878790987 n^{3}+2251200906223163872381820075 n^{2}+31102009857354325938948816658 n +171845188002670185447643970616\right) a \! \left(n +27\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(17710783739941317276025 n^{5}+2535258746345346922189242 n^{4}+145139061619703051307282451 n^{3}+4153697671458007789492784070 n^{2}+59425793001660674581688011180 n +340013011248465976607658092832\right) a \! \left(n +28\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(3638411855807994698497 n^{5}+538704079587347090765985 n^{4}+31898583413960283569859210 n^{3}+944248495421754727248179525 n^{2}+13973203063896799898047728893 n +82697301723829616411398775830\right) a \! \left(n +29\right)}{36700160 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(368088399151912288864492 n^{5}+47284619689058761732667685 n^{4}+2429112532338124722311005750 n^{3}+62380124911916375465740405995 n^{2}+800786114129044943802527646958 n +4111016678817776702270488909200\right) a \! \left(n +25\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(15521506624277723543591 n^{5}+1694903262728854209149692 n^{4}+74009446319963876074903985 n^{3}+1615362930771584238937369556 n^{2}+17623536720538627584851122700 n +76885607973691131709780110912\right) a \! \left(n +21\right)}{14680064 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(35296722389010391967988 n^{5}+4022197971292239262008319 n^{4}+183287692393952320061253618 n^{3}+4174977104370293955189964561 n^{2}+47536344675132314042803878306 n +216440301024030498934329444088\right) a \! \left(n +22\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(105945948512292763386809 n^{5}+12581924307514811860659339 n^{4}+597527059536133215725814137 n^{3}+14184904365178819732340184549 n^{2}+168327070295645053559476502750 n +798786072151881069050772021264\right) a \! \left(n +23\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(93748733270563835330302 n^{5}+11586983716611504119467347 n^{4}+572702854566571669228032556 n^{3}+14149888933958627434303662345 n^{2}+174760028110309958888103597058 n +863151675643941175444392530208\right) a \! \left(n +24\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(22182720719763079307114 n^{5}+2119924321325295996541485 n^{4}+80987898757675041166863530 n^{3}+1546045784768200005456948865 n^{2}+14747706741322116684776327666 n +56235853722309499772137158020\right) a \! \left(n +18\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(39526123429818781403396 n^{5}+3950079282320638901719875 n^{4}+157836410890144085798569340 n^{3}+3152071596573463986396002705 n^{2}+31460794489265039248346799824 n +125549448972141795437641777900\right) a \! \left(n +19\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(357668300317901653492901 n^{5}+37379979248926948308878730 n^{4}+1562112381436115579975666315 n^{3}+32629374475769556049824717030 n^{2}+340664432369778040592244359384 n +1422179418592647443005904998920\right) a \! \left(n +20\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(848143111237275661703 n^{5}+49279033702173488736990 n^{4}+1060276262138416670797535 n^{3}+9818016714047674278510960 n^{2}+29440192257620786011912952 n -39711561344988804786890040\right) a \! \left(n +14\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(542542746268161146687 n^{5}+52442162894799707755120 n^{4}+1958753032501526457362395 n^{3}+35685120402242797299428310 n^{2}+319030114243271321494880568 n +1124191609330225274341704020\right) a \! \left(n +15\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(685627384575046458194 n^{5}+61071753864319007628877 n^{4}+2168029452847856461423860 n^{3}+38353428039283860281601193 n^{2}+338194608056610664254007336 n +1189415383887270716862759748\right) a \! \left(n +16\right)}{14680064 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(12168716472779311749329 n^{5}+1115189239296672445026897 n^{4}+40831283206574611034927357 n^{3}+746617969328102593886870955 n^{2}+6818248878548659157474570726 n +24877814439119670117224414784\right) a \! \left(n +17\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3125 \left(2 n +5\right) \left(n +1\right) \left(5844766 n^{3}+31111579 n^{2}+47346871 n +16420824\right) a \! \left(n +1\right)}{3670016 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(676580621 n^{4}+113704460501 n^{3}+7165428810169 n^{2}+200678249108179 n +2107492879506450\right) a \! \left(n +42\right)}{7168 \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(141047581533413686043 n^{5}+7973738651189699376960 n^{4}+179997828264990978902405 n^{3}+2027877950107068600944280 n^{2}+11400837972427284457555112 n +25585575852516232323397560\right) a \! \left(n +11\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(207997587192645254791 n^{5}+12581191771137250086879 n^{4}+303411698818576936848487 n^{3}+3645545274511462799505225 n^{2}+21815209506036280453925434 n +51992675967067398217285920\right) a \! \left(n +12\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(1870597767554620840633 n^{5}+118299698915061146121270 n^{4}+2968130475031003916281915 n^{3}+36874306466337405498616950 n^{2}+226377761095322758833291712 n +547925252771274191831616960\right) a \! \left(n +13\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(7389042576619067467 n^{5}+320003988676387338180 n^{4}+5536087681374026889865 n^{3}+47819755923528255578040 n^{2}+206220699680008019645848 n +355163221998739510452840\right) a \! \left(n +8\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(35390684051706424469 n^{5}+1688987986847937479220 n^{4}+32215373809687372381655 n^{3}+306958551804425844403500 n^{2}+1460988641485460759666876 n +2778593391888555874849200\right) a \! \left(n +9\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(68076189554293444343 n^{5}+3552918361911561938145 n^{4}+74094106646205032083535 n^{3}+771741149695130689752555 n^{2}+4014413201781101634223502 n +8342581162948835092203720\right) a \! \left(n +10\right)}{73400320 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(32453565325557 n^{5}+434693092848108 n^{4}+1305448122321525 n^{3}-5327030359668160 n^{2}-35376982384693602 n -50768941067137028\right) a \! \left(n +4\right)}{14680064 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{3 \left(2160860644971833 n^{5}+85881372455945685 n^{4}+1224363570261052125 n^{3}+8185375984167540715 n^{2}+26198902021240464322 n +32480636818561437560\right) a \! \left(n +5\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{\left(134552705478331609 n^{5}+4844905328027314035 n^{4}+68848723065778936345 n^{3}+483474218874132221985 n^{2}+1679815451161160878786 n +2312356032894643101600\right) a \! \left(n +6\right)}{146800640 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{\left(238967950544078687 n^{5}+9363144453722723697 n^{4}+146206876529445486251 n^{3}+1137385932930999033819 n^{2}+4408093158384567436970 n +6809005899295117412856\right) a \! \left(n +7\right)}{29360128 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}+\frac{125 \left(10657166542 n^{5}+133775077869 n^{4}+658685742160 n^{3}+1587059314515 n^{2}+1866945466438 n +855614943036\right) a \! \left(n +2\right)}{7340032 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{75 \left(336282990947 n^{5}+5187740002407 n^{4}+31180364041709 n^{3}+90995141129037 n^{2}+128474250866672 n +69850544725980\right) a \! \left(n +3\right)}{14680064 \left(n +44\right) \left(2 n +89\right) \left(n +47\right) \left(n +46\right) \left(n +45\right)}-\frac{3 \left(653496 n^{3}+83616601 n^{2}+3566307525 n +50701628750\right) a \! \left(n +43\right)}{448 \left(n +46\right) \left(n +47\right) \left(2 n +89\right)}, \quad n \geq 45$$
Heatmap

To create this heatmap, we sampled 1,000,000 permutations of length 300 uniformly at random. The color of the point $$(i, j)$$ represents how many permutations have value $$j$$ at index $$i$$ (darker = more).

### This specification was found using the strategy pack "Point And Row Placements" and has 16 rules.

Found on April 26, 2021.

Finding the specification took 5 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_{15}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{3}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14} \left(x \right)^{2} F_{15}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{15}\! \left(x \right) &= x\\ \end{align*}

### This specification was found using the strategy pack "Point And Row And Col Placements Req Corrob" and has 22 rules.

Found on April 26, 2021.

Finding the specification took 16 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_{13}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{13}\! \left(x \right) F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= x\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{16} \left(x \right)^{2} F_{13}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{13}\! \left(x \right) F_{19}\! \left(x \right)\\ \end{align*}

### This specification was found using the strategy pack "Point And Col Placements" and has 22 rules.

Found on April 26, 2021.

Finding the specification took 16 seconds.

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\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{13}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{13}\! \left(x \right) F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{13}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)\\ F_{13}\! \left(x \right) &= x\\ F_{14}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{13}\! \left(x \right)\\ \end{align*}