01243_02143
Counting sequence:
1, 1, 2, 6, 24, 118, 672, 4258, 29241, 213865, 1645677, 13204357, 109723588, 939262476, 8247972113, 74046481335, 677723017097, 6309462532773, 59633410974352, 571266127477676, 5539077943518018, 54296295286835008, 537514293368807533, 5369183957725678389, 54073546482277396154, 548681689581766621100, 5605967152865629994885, 57642145388748915304763, 596183145214130228291490, 6199856422465315861962002, 64800357714174279256379413, 680479513799018765985505011, 7177234945273730123404401024, 76011459598092977571541111820, 808104256225281308417511413837, 8622212418198070620863203850353, 92307820495423891657171718663791, 991379845129549903912963579675277, 10679327438513099365991099262987656, 115365698865710163272427703365570560, 1249599747671314359844132124673642160, 13569510001415426197241670509646847766, 147706167394582697021191569206867027126, 1611464489460829871424834101977202422804, 17618978618801079183205283774923491150217, 193033327243837384019936858402003406004925, 2119006584411508285214327602155352541979357, 23304538536711356689014502390279700453154209, 256755226754373019745377725395127106639294230, 2833566941489464749977202873574989968985788170, 31322044126176875227373612359346657344468380861, 346767379449327561973539766347108256556442288227, 3844756701567239956241629325985027551625923278124, 42688872167535233561749488290556262542949916454038, 474624336546257467927415963915208321938683594290335, 5283851777574030259870884607326758240754032337862221, 58897074697403689077487458534387333032198834947604507, 657291096907790395034558842601943452977237334960513015, 7343825331505097047213791198717840279219389729381785401, 82142559904024903900593553374121334151063292572888712415, 919765681159149069115609436239758667894873572641795516283, 10309366237745608857056015553868141592530274339161322693597, 115668779895147527111077444717089664676429030257909495645042, 1299015146370484971937857114706423341192224040317983491725656, 14601967744490471114260559913593782918000680481596350788022991, 164283380376482578698152626735319396829003251624534127585048493, 1849897236843896080995720335004342255052107426630632223200229529, 20847817572129484224940219831909625873314025043351224181361823239, 235136749766106493673475721720312634472874998150549687989389297233, 2654090975730729961860489240656294211719008734169469049868299112515, 29980265768165784085279631406314310454140564129451196604506638758819, 338898017565965098080072097758965106568358426454807425649950619809393, 3833596729838858415315783785036208521542029481453748115745493771075389, 43394839591154232667397199469617653483420989431740775570693953733452311, 491535454800427892297139385010334748657561020975365194940754628253351385, 5571189682465655336685771552003212018298901964588947838934433633293238077, 63184271629242047961419801830903066061380630838160238150666762919071338395, 717017783394972376768619590969921486684150996094171104774921860363140612753, 8141474646307829196532295188829773058817761342974610839532451283103692651766, 92495593317873864685801355476026252121906118567964236149763002845298631010956, 1051421243921198275456307657497440356349985724756362374759938030336853890973277, 11958133367525839642821699108250615045002596196559988149929311551473319847541157, 136073780575426656451677641393458999013098544890960390764974822566373634420982068, 1549186318954822997062531062519613265352385738633164621731916644682867166497914282, 17645947104569329887123791647569166434823516429166883133359082812729232091430906150, 201090992518494836007487178393406568242040646892709141198281977559419795625943000934, 2292667179759341737860919502744122258364567255957602325135439583665343796581742591568, 26150789149381047678767987106764588817330436735886516071511867171845209596129908806248, 298413736020140149960934122236311929940491644555411013152247604179594196230783554610600, 3406732814632021102305842933447304652442491563967482585032730527047092477701106820933914, 38907900763293226936036512733081191650293705547353455549640036039753489600859716163403471, 444542583222125837761545017067673285074788422232546256987325279756242766904756784437907099, 5081130259458381654415301167526366539963365707837930593735140519645750943955984670718386943, 58099765980326461464284532735224933528274489319377295230907694274316327649394658918490459207, 664586304281318223293421721183789877275511364033671063228393897819625077809912429039560766911, 7604791984526366470719212861218342326606027609155061950817788559330212440905605110924598817425, 87051924180472453505345381315749058652423072544221668657312097546667067908020542220779473318065, 996829224978040641051293324902591870823603859074358815421406259216266442294427320972452498187293, 11418548293681502866337695465620881786385539082511590012046303162239852370234805938959234063465190, 130841429705576951680338471467198168246218906210227902963259318489257295357367098407193779599949072, 1499755814430652478316167697947496895008309439332382155955110454492463147122394188721082622216869619
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/23971/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[21,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[51,x,k[0],k[1]]+F[52,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[1,x]+F[15,x,k[0],k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[22,x,k[0],k[1],k[2]]+F[49,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1],k[2]]*F[7,x]
F[16,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[14,x,k[0],k[1],k[2]]*k[0]-F[14,x,1,k[1],k[2]])
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]*F[21,x,k[0]]
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1]]*k[1]-F[19,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[19,x,k[0],k[1]] = (F[20,x,k[0],1]*k[0]-F[20,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[11,x,k[0],k[0]*k[1]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[23,x,k[0],k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = (-F[24,x,1,k[1],k[2]]*k[1]+F[24,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0]*k[1],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[1,x]+F[26,x,k[0],k[1],k[2]]+F[42,x,k[0],k[1],k[2]]+F[45,x,k[0],k[1],k[2]]+F[48,x,k[0],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]*F[7,x]
F[27,x,k[0],k[1],k[2]] = F[28,x,1,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2],k[3]] = F[1,x]+F[29,x,k[0],k[1],k[2],k[3]]+F[31,x,k[0],k[1],k[2],k[3]]+F[35,x,k[0],k[1],k[2],k[3]]+F[38,x,k[0],k[1],k[2],k[3]]+F[41,x,k[0],k[1],k[2],k[3]]
F[29,x,k[0],k[1],k[2],k[3]] = F[30,x,k[0],k[1],k[2],k[3]]*F[7,x]
F[30,x,k[0],k[1],k[2],k[3]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2],k[3]]*k[0]-F[28,x,1,k[1],k[2],k[3]])
F[31,x,k[0],k[1],k[2],k[3]] = F[21,x,k[0]]*F[32,x,k[0],k[1],k[2],k[3]]
F[32,x,k[0],k[1],k[2],k[3]] = (F[33,x,k[0],k[1],k[3]]*k[1]-F[33,x,k[0],k[2],k[3]]*k[2])/(-k[2]+k[1])
F[33,x,k[0],k[1],k[2]] = (F[34,x,k[0],1,k[2]]*k[0]-F[34,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[34,x,k[0],k[1],k[2]] = F[25,x,k[0],k[0]*k[1],k[2]]
F[35,x,k[0],k[1],k[2],k[3]] = F[21,x,k[1]]*F[36,x,k[0],k[1],k[2],k[3]]
F[36,x,k[0],k[1],k[2],k[3]] = (-F[37,x,1,k[1],k[2],k[3]]*k[1]+F[37,x,k[0]/k[1],k[1],k[2],k[3]]*k[0])/(-k[1]+k[0])
F[37,x,k[0],k[1],k[2],k[3]] = (F[24,x,k[0],k[1],k[2]]*k[2]-F[24,x,k[0],k[1],k[3]]*k[3])/(-k[3]+k[2])
F[38,x,k[0],k[1],k[2],k[3]] = F[21,x,k[2]]*F[39,x,k[0],k[1],k[2],k[3]]
F[39,x,k[0],k[1],k[2],k[3]] = (F[40,x,k[0],k[1],k[2],1]*k[2]-F[40,x,k[0],k[1],k[2],k[3]/k[2]]*k[3])/(-k[3]+k[2])
F[40,x,k[0],k[1],k[2],k[3]] = F[28,x,k[0],k[1],k[2],k[2]*k[3]]
F[41,x,k[0],k[1],k[2],k[3]] = F[21,x,k[3]]*F[28,x,k[0],k[1],k[2],k[3]]
F[42,x,k[0],k[1],k[2]] = F[21,x,k[0]]*F[43,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = (F[44,x,k[0],k[1]]*k[1]-F[44,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[44,x,k[0],k[1]] = F[24,x,1,k[0],k[1]]
F[45,x,k[0],k[1],k[2]] = F[21,x,k[1]]*F[46,x,k[0],k[1],k[2]]
F[46,x,k[0],k[1],k[2]] = (F[47,x,k[0],k[1],1]*k[1]-F[47,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[47,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[1]*k[2]]
F[48,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[25,x,k[0],k[1],k[2]]
F[49,x,k[0],k[1],k[2]] = F[21,x,k[2]]*F[50,x,k[0],k[1],k[2]]
F[50,x,k[0],k[1],k[2]] = F[40,x,k[0],k[1],k[2],1]
F[51,x,k[0],k[1]] = F[21,x,k[0]]*F[44,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[21,x,k[1]]*F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[47,x,k[0],k[1],1]
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = \frac{F_{4}\! \left(x , y_{0}\right) y_{0}-F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}-F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{21}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{19}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{20}\! \left(x , y_{0}, 1\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{21}\! \left(x , y_{0}\right) = y_{0} x
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{-F_{24}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}+F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{7}\! \left(x \right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0}-F_{28}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{33}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{1}-F_{33}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{2}}{-y_{2}+y_{1}}
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{34}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{34}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{1}\right) F_{36}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{-F_{37}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right) y_{1}+F_{37}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}, y_{3}\right) y_{0}}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}-F_{24}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{3}}{-y_{3}+y_{2}}
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{2}\right) F_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right) y_{2}-F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, \frac{y_{3}}{y_{2}}\right) y_{3}}{-y_{3}+y_{2}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{2} y_{3}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{21}\! \left(x , y_{3}\right) F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{44}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{44}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , 1, y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{47}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{47}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{2}\right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{52}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{1}\right) F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{47}\! \left(x , y_{0}, y_{1}, 1\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)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_21(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_51(x, k_0, k_1) + F_52(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_1(x) + F_15(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_22(x, k_0, k_1, k_2) + F_49(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1, k_2)*F_7(x))
Eq(F_16(x, k_0, k_1, k_2), (k_0*F_14(x, k_0, k_1, k_2) - F_14(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2)*F_21(x, k_0))
Eq(F_18(x, k_0, k_1, k_2), (-k_1*F_19(x, k_0, k_1) + k_2*F_19(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, 1) + k_1*F_20(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_11(x, k_0, k_0*k_1))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0, k_1, k_2), F_21(x, k_1)*F_23(x, k_0, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*F_24(x, k_0/k_1, k_1, k_2) + k_1*F_24(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0*k_1, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_1(x) + F_26(x, k_0, k_1, k_2) + F_42(x, k_0, k_1, k_2) + F_45(x, k_0, k_1, k_2) + F_48(x, k_0, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2)*F_7(x))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, 1, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_1(x) + F_29(x, k_0, k_1, k_2, k_3) + F_31(x, k_0, k_1, k_2, k_3) + F_35(x, k_0, k_1, k_2, k_3) + F_38(x, k_0, k_1, k_2, k_3) + F_41(x, k_0, k_1, k_2, k_3))
Eq(F_29(x, k_0, k_1, k_2, k_3), F_30(x, k_0, k_1, k_2, k_3)*F_7(x))
Eq(F_30(x, k_0, k_1, k_2, k_3), (k_0*F_28(x, k_0, k_1, k_2, k_3) - F_28(x, 1, k_1, k_2, k_3))/(k_0 - 1))
Eq(F_31(x, k_0, k_1, k_2, k_3), F_21(x, k_0)*F_32(x, k_0, k_1, k_2, k_3))
Eq(F_32(x, k_0, k_1, k_2, k_3), (-k_1*F_33(x, k_0, k_1, k_3) + k_2*F_33(x, k_0, k_2, k_3))/(-k_1 + k_2))
Eq(F_33(x, k_0, k_1, k_2), (-k_0*F_34(x, k_0, 1, k_2) + k_1*F_34(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_34(x, k_0, k_1, k_2), F_25(x, k_0, k_0*k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2, k_3), F_21(x, k_1)*F_36(x, k_0, k_1, k_2, k_3))
Eq(F_36(x, k_0, k_1, k_2, k_3), (-k_0*F_37(x, k_0/k_1, k_1, k_2, k_3) + k_1*F_37(x, 1, k_1, k_2, k_3))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1, k_2, k_3), (-k_2*F_24(x, k_0, k_1, k_2) + k_3*F_24(x, k_0, k_1, k_3))/(-k_2 + k_3))
Eq(F_38(x, k_0, k_1, k_2, k_3), F_21(x, k_2)*F_39(x, k_0, k_1, k_2, k_3))
Eq(F_39(x, k_0, k_1, k_2, k_3), (-k_2*F_40(x, k_0, k_1, k_2, 1) + k_3*F_40(x, k_0, k_1, k_2, k_3/k_2))/(-k_2 + k_3))
Eq(F_40(x, k_0, k_1, k_2, k_3), F_28(x, k_0, k_1, k_2, k_2*k_3))
Eq(F_41(x, k_0, k_1, k_2, k_3), F_21(x, k_3)*F_28(x, k_0, k_1, k_2, k_3))
Eq(F_42(x, k_0, k_1, k_2), F_21(x, k_0)*F_43(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), (-k_1*F_44(x, k_0, k_1) + k_2*F_44(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_44(x, k_0, k_1), F_24(x, 1, k_0, k_1))
Eq(F_45(x, k_0, k_1, k_2), F_21(x, k_1)*F_46(x, k_0, k_1, k_2))
Eq(F_46(x, k_0, k_1, k_2), (-k_1*F_47(x, k_0, k_1, 1) + k_2*F_47(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_47(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_1*k_2))
Eq(F_48(x, k_0, k_1, k_2), F_21(x, k_2)*F_25(x, k_0, k_1, k_2))
Eq(F_49(x, k_0, k_1, k_2), F_21(x, k_2)*F_50(x, k_0, k_1, k_2))
Eq(F_50(x, k_0, k_1, k_2), F_40(x, k_0, k_1, k_2, 1))
Eq(F_51(x, k_0, k_1), F_21(x, k_0)*F_44(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_21(x, k_1)*F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_47(x, k_0, k_1, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [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, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [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, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [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, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": 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