0231_1302

Counting sequence:
1, 1, 2, 6, 22, 89, 379, 1664, 7460, 33977, 156727, 730619, 3436710, 16291842, 77758962, 373369867, 1802399037, 8742691627, 42590945206, 208300979739, 1022385319050, 5034470059883, 24865173540949, 123147075005750, 611447895295479, 3043093928368030, 15178127146082582, 75858065515710393, 379844994678126287, 1905364793769760032, 9573439076720851051, 48176072356668013251, 242788301361438124753, 1225236563073269933702, 6191187386852741058618, 31322651823594072167784, 158651772743689064994401, 804464097863912917673770, 4083374892869000251757240, 20747225701843888412033277, 105513490154367753462777380, 537085727023300797589817967, 2736205698038335994360804334, 13951036193573797765389613773, 71187048777569190826904533333, 363510997365543264165162149123, 1857557850822864803622563892641, 9498661749977767976664659443665, 48603285278004402514248169246636, 248851657830669510729398570045426, 1274900864498964013890155978182964, 6535264004757397163986824238446301, 33519007888515998952391582506420838, 172009115105745348589195295705909061, 883152163409490596168323256249199968, 4536650513621207477348521025033771724, 23315417225598238263010001942493865818, 119881427372900730966502563425459781155, 616672528294777063131979268417494694362, 3173545745624630294791686209004516729172, 16338650886779606254866765632448298512218, 84151720350779875699137457727697168020942, 433590311021732130774758946947142769860677, 2234912666852101217323060160527456368455111, 11523936727793691842918693599040136629385141, 59442303215003830911699074927652471155365050, 306718662987718221784808176520293995388807002, 1583179461511729731795869262696367040104585046, 8174500377004029558621532552844306485119268130, 42221081523099064103560516484406575837762659856, 218137667650396405943749880399624502561647360956, 1127356898425198218103694520323121067991521849223, 5827980182104747945477290476457425898093613753662, 30136801542510072234659555404196101817463891452176, 155881800819333348210963601683942599889746005152826, 806509852596996432499411556124165164946994691833916, 4173850730424813798378247232785640900056883868726063, 21605991768757142241519021145734139944719772963794620, 111871317145829663297311435946401186724339088225068548, 579385803469363776510070689631783205302236062415209632, 3001365613398115164751752630184550737456256641487750895, 15551396967953760703036796468032673220310027099384879072, 80596642895735775472870623076163022044526639296566783660, 417791127303126945215997821120678735314845095760141145829, 2166177024386193092064346107660588639974256984938971644303, 11233600793874696506194276059601864600637857798723234551009, 58268286557356163743405102024622788097227254559494581721984, 302295519945052890074858513272955266766579116061552307915461, 1568611621300609797945509388276456581644185710939993710728075, 8141070501763715075260496856920049541687048668838972870900383, 42259869584141080850775346580687453643718280001791895805135665, 219408564997916105995788578714669407972443162157102289227950770, 1139347189039314452254822340342326092293179442982021108422662544, 5917442239822951566046529306171188821485082866053801104497280020, 30738721963882572438963227956785656784046653248350026831204637869, 159701823835216377829121360796557272285670122131488128312301836813, 829859817598396180294273439270935473713640092028651536119134778498, 4312895494897085829431258001163071901718157506914027034644440365334, 22418216735683529641233916447100658736770450001591761862219862342525, 116546639603266036881894335008467317713180969469033650147594567370673, 605987529645739556367159419860119751402569033222135894207614109794633

Implicit equation for the generating function in Maple syntax:
x^3*F(x)^6+x*(x^2-7*x+2)*F(x)^5+(x^4-6*x^3+14*x^2-1)*F(x)^4+(2*x^3-5*x^2-9*x+2)*F(x)^3-x*(x-9)*F(x)^2+(-2*x-2)*F(x)+1 = 0

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

Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 89
a \! \left(6\right) = 379
a \! \left(7\right) = 1664
a \! \left(8\right) = 7460
a \! \left(9\right) = 33977
a \! \left(10\right) = 156727
a \! \left(11\right) = 730619
a \! \left(12\right) = 3436710
a \! \left(13\right) = 16291842
a \! \left(14\right) = 77758962
a \! \left(15\right) = 373369867
a \! \left(16\right) = 1802399037
a \! \left(17\right) = 8742691627
a \! \left(18\right) = 42590945206
a \! \left(19\right) = 208300979739
a \! \left(20\right) = 1022385319050
a \! \left(21\right) = 5034470059883
a \! \left(22\right) = 24865173540949
a \! \left(23\right) = 123147075005750
a \! \left(24\right) = 611447895295479
a \! \left(25\right) = 3043093928368030
a \! \left(26\right) = 15178127146082582
a \! \left(27\right) = 75858065515710393
a \! \left(28\right) = 379844994678126287
a \! \left(29\right) = 1905364793769760032
a \! \left(30\right) = 9573439076720851051
a \! \left(31\right) = 48176072356668013251
a \! \left(32\right) = 242788301361438124753
a \! \left(33\right) = 1225236563073269933702
a \! \left(34\right) = 6191187386852741058618
a \! \left(35\right) = 31322651823594072167784
a \! \left(36\right) = 158651772743689064994401
a \! \left(37\right) = 804464097863912917673770
a \! \left(38\right) = 4083374892869000251757240
a \! \left(39\right) = 20747225701843888412033277
a \! \left(40\right) = 105513490154367753462777380
a \! \left(41\right) = 537085727023300797589817967
a \! \left(42\right) = 2736205698038335994360804334
a \! \left(43\right) = 13951036193573797765389613773
a \! \left(44\right) = 71187048777569190826904533333
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

Specification 1
Strategy pack name: point_and_row_placements
Tree: http://permpal.com/tree/158/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[15,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[0,x]*F[15,x]*F[6,x]
F[6,x] = F[3,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[0,x]*F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[14,x]*F[3,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[15,x]
F[14,x] = F[1,x]+F[12,x]
F[15,x] = x
System of equations in latex syntax:
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
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_15(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_0(x)*F_15(x)*F_6(x))
Eq(F_6(x), F_3(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_0(x)*F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_14(x)*F_3(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_15(x))
Eq(F_14(x), F_1(x) + F_12(x))
Eq(F_15(x), x)
Pack JSON:
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Specification JSON:
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0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "gps": [{"patt": [1, 0], "pos": [[0, 0], [3, 0]]}], "strategy_class": "ObstructionInferralStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 2]], [[2, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}]}

Specification 2
Strategy pack name: point_and_row_and_col_placements_req_corrob
Tree: http://permpal.com/tree/159/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[13,x]*F[3,x]*F[6,x]
F[6,x] = F[0,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[0,x]*F[13,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]*F[19,x]*F[9,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]^2*F[13,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[13,x]*F[19,x]
System of equations in latex syntax:
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)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_13(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_13(x)*F_3(x)*F_6(x))
Eq(F_6(x), F_0(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_0(x)*F_13(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x)*F_19(x)*F_9(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_16(x)**2)
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_13(x)*F_19(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]], [[2, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}

Specification 3
Strategy pack name: row_and_col_placements_req_corrob
Tree: http://permpal.com/tree/160/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[13,x]*F[3,x]*F[6,x]
F[6,x] = F[0,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[0,x]*F[13,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]*F[19,x]*F[9,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]^2*F[13,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[13,x]*F[19,x]
System of equations in latex syntax:
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)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_13(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_13(x)*F_3(x)*F_6(x))
Eq(F_6(x), F_0(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_0(x)*F_13(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x)*F_19(x)*F_9(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_16(x)**2)
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_13(x)*F_19(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "row_and_col_placements_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 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"comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]], [[2, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}

Specification 4
Strategy pack name: row_and_col_placements
Tree: http://permpal.com/tree/161/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[5,x]
F[5,x] = F[13,x]*F[3,x]*F[6,x]
F[6,x] = F[0,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[0,x]*F[13,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]*F[19,x]*F[9,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]^2*F[13,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[13,x]*F[19,x]
System of equations in latex syntax:
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)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_13(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_13(x)*F_3(x)*F_6(x))
Eq(F_6(x), F_0(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_0(x)*F_13(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x)*F_19(x)*F_9(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_16(x)**2)
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_13(x)*F_19(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_and_col_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], 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true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}

Specification 5
Strategy pack name: point_and_col_placements
Tree: http://permpal.com/tree/162/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[13,x]*F[4,x]*F[7,x]
F[7,x] = F[0,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[0,x]*F[10,x]*F[13,x]
F[10,x] = F[0,x]+F[11,x]+F[20,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[13,x]*F[14,x]*F[16,x]
F[13,x] = x
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[1,x]+F[17,x]+F[19,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[14,x]*F[16,x]
F[19,x] = F[13,x]*F[16,x]
F[20,x] = F[21,x]
F[21,x] = F[0,x]*F[10,x]*F[13,x]
System of equations in latex syntax:
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)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_13(x)*F_4(x)*F_7(x))
Eq(F_7(x), F_0(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_0(x)*F_10(x)*F_13(x))
Eq(F_10(x), F_0(x) + F_11(x) + F_20(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_13(x)*F_14(x)*F_16(x))
Eq(F_13(x), x)
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_17(x) + F_19(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_14(x)*F_16(x))
Eq(F_19(x), F_13(x)*F_16(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_0(x)*F_10(x)*F_13(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_and_col_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 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