02341_02431_03241_03421_04231_04321_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3032, 16768, 95200, 551616, 3248704, 19389824, 117021824, 712934784, 4378663296, 27081760768, 168530142720, 1054464293888, 6629484729344, 41860283723776, 265346078982144, 1687918305128448, 10771600724946944, 68941213290561536, 442427575548461056, 2846278279028277248, 18352802795930714112, 118588983399050477568, 767782177646313963520, 4979949953583054159872, 32355831231314785304576, 210558709598477868859392, 1372283371473310644043776, 8956227437720371727171584, 58530384475270519722344448, 382983331944009873075732480, 2508941882400991929769656320, 16454549025616564077550632960, 108029063908515559257203015680, 709955335647042588246947135488, 4670200441621999823030967074816, 30749210383371183418869593145344, 202631835191481477341835580932096, 1336408589142930743577593910394880, 8820891887800248207842645616099328, 58265606039163432331609113918177280, 385145134336372438153517545014951936, 2547626122504518352345059373749370880, 16862954879453957806433295950799699968, 111688049002357150695437617236627423232, 740191010374927339591042095346440208384, 4908340231496856276155167387891053625344, 32566383524953585451743428317786442563584, 216191815025584682630056511117746832932864, 1435936154519986687271388927327684383473664, 9542210244935909701914535112333926642745344, 63441440797270789570274207083212497542447104, 421987847864035609812611921038977453621510144, 2808165677749896476430412181660982199948673024, 18695400057152198602207487588448805555099664384, 124517318934667876794981726485209358256018817024, 829663030380469516181045468969536049927205945344, 5530253014033277151822501447252768859542807117824, 36876876211546599304952640241147534160671889424384, 245993675479930831097444153196071492613044745273344, 1641532619888105819578474921872098778213883171569664, 10957870017566776973105407282369370881605292622086144, 73172741259813866085843525165796055741778731533860864, 488781499590815166836805313147069246378053989830754304, 3266016193584304781795368579264512180429852251116273664, 21830119367222551518533931442637549583622332430852030464, 145956794906772063908303688832159280080899640502259810304, 976156255610674843557272264494043237596719247573399896064, 6530368897526884156516901341340588540795663316718016528384, 43699464151943991822416314642734234924153890236505455067136, 292503682425016754060674563942105692653276520602464103170048, 1958395155753861178134642484752434547321354421959929815367680, 13115357344387311565189942714961388193723791568257286571819008, 87855288245258220807434419257706594739689863298371489558953984, 588655136964617290378727748345647523048224760353278335983288320, 3945087074043245943220480883373516924524093473530185640451244032, 26445534184872537656159891065987775800859037331423199995782758400, 177315113420178270897337884230405370625266596595435545595983429632, 1189144072556897353149632380542090761485313566766072150285002735616, 7976571139909459540659278969016771924893549063198932776385393983488, 53516644031346094053926692320853113400857456125935108098831390081024, 359128814933435016089195982265693019466937665060517425108183095967744, 2410451231956942090854929022749562369399574571652226108644638813323264, 16181962673932422697324006066082806072538705480272489528566942504321024, 108654292659157748756692409960562400231087476550442681279273807325954048, 729698734574219233499039079740131475511427827391906327937304723961413632, 4901393049759263611751090007430767774012294012253411802436338374951305216, 32928578431873330449020032769024918701977767073681026659850428402339151872, 221259681850061598025738379239459902333741804125566760798692238214534529024, 1486982386224470765974742392790534351529288241405564703964975432734162812928, 9994982631681983889853581814359374515798045147833434066823431563531721375744, 67193835351681822367645151916299435337512265309445122107677199827970631401472, 451800305895479427783024480062272990740768619553108820595092326774304243974144, 3038308670897522420440114885270044773604035642037350319633558033754618737983488, 20435448375693751784554643691894531632637310470282343031794326419655948117213184
Generating function in Maple syntax:
(4*x-5+(8*x^2-8*x+1)^(1/2))/(4*x-4)
Generating function in latex syntax:
\frac{4 x -5+\sqrt{8 x^{2}-8 x +1}}{4 x -4}
Generating function in sympy syntax:
(4*x + sqrt(8*x**2 - 8*x + 1) - 5)/(4*x - 4)
Implicit equation for the generating function in Maple syntax:
(2*x-2)*F(x)^2+(-4*x+5)*F(x)+x-3 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -2\right) F \! \left(x \right)^{2}+\left(-4 x +5\right) F \! \left(x \right)+x -3 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+3) = 8*n/(n+3)*a(n)-4*(3+4*n)/(n+3)*a(n+1)+3*(5+3*n)/(n+3)*a(n+2), n >= 3
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(n +3\right) = \frac{8 n a \! \left(n \right)}{n +3}-\frac{4 \left(3+4 n \right) a \! \left(n +1\right)}{n +3}+\frac{3 \left(5+3 n \right) a \! \left(n +2\right)}{n +3}, \quad n \geq 3
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24172/
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[100,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[40,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[24,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[9,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[17,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[21,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[9,x,k[0]]
F[20,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]*F[9,x,k[0]]
F[23,x,k[0]] = F[13,x,k[0]]+F[21,x,k[0]]
F[24,x,k[0]] = F[25,x]+F[26,x,k[0]]+F[36,x,k[0]]
F[25,x] = 0
F[26,x,k[0]] = F[27,x,k[0]]*F[9,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[29,x,k[0]]
F[28,x,k[0]] = F[24,x,k[0]]+F[7,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[33,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[9,x,k[0]]
F[32,x,k[0]] = F[30,x,k[0]]+F[7,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]*F[9,x,k[0]]
F[35,x,k[0]] = F[24,x,k[0]]+F[33,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[9,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[39,x,k[0]]
F[38,x,k[0]] = F[18,x,k[0]]+F[30,x,k[0]]
F[39,x,k[0]] = F[21,x,k[0]]+F[33,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[100,x]*F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[44,x,k[0]]
F[43,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]*F[49,x,k[0]]*F[9,x,k[0]]
F[47,x,k[0]] = F[46,x,k[0]]*F[9,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[49,x,k[0]] = F[16,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[7,x,k[0]]
F[51,x,k[0]] = F[25,x]+F[52,x,k[0]]+F[62,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]*F[9,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[55,x,k[0]]
F[54,x,k[0]] = F[13,x,k[0]]+F[51,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[66,x,k[0]]
F[56,x,k[0]] = F[25,x]+F[57,x,k[0]]+F[62,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]*F[9,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[65,x,k[0]]
F[59,x,k[0]] = F[13,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[25,x]+F[61,x,k[0]]+F[62,x,k[0]]
F[61,x,k[0]] = F[13,x,k[0]]*F[9,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]*F[9,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]
F[64,x,k[0]] = F[60,x,k[0]]+F[9,x,k[0]]
F[65,x,k[0]] = F[60,x,k[0]]
F[66,x,k[0]] = F[25,x]+F[67,x,k[0]]+F[80,x,k[0]]+F[89,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]*F[9,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[85,x,k[0]]
F[69,x,k[0]] = F[51,x,k[0]]+F[70,x,k[0]]
F[70,x,k[0]] = F[25,x]+F[71,x,k[0]]+F[72,x,k[0]]+F[80,x,k[0]]
F[71,x,k[0]] = F[51,x,k[0]]*F[9,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]*F[9,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]+F[75,x,k[0]]
F[74,x,k[0]] = F[60,x,k[0]]+F[70,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[81,x,k[0]]
F[76,x,k[0]] = F[25,x]+F[77,x,k[0]]+F[78,x,k[0]]+F[80,x,k[0]]
F[77,x,k[0]] = F[60,x,k[0]]*F[9,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]*F[9,x,k[0]]
F[79,x,k[0]] = F[65,x,k[0]]
F[80,x,k[0]] = 0
F[81,x,k[0]] = F[25,x]+F[82,x,k[0]]+F[83,x,k[0]]+F[86,x,k[0]]+F[88,x,k[0]]
F[82,x,k[0]] = F[70,x,k[0]]*F[9,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]*F[9,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[70,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]*F[9,x,k[0]]
F[87,x,k[0]] = F[75,x,k[0]]
F[88,x,k[0]] = 0
F[89,x,k[0]] = F[9,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[55,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[95,x,k[0]]
F[92,x,k[0]] = F[25,x]+F[78,x,k[0]]+F[80,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[9,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[60,x,k[0]]
F[95,x,k[0]] = F[25,x]+F[83,x,k[0]]+F[88,x,k[0]]+F[96,x,k[0]]+F[98,x,k[0]]
F[96,x,k[0]] = F[9,x,k[0]]*F[97,x,k[0]]
F[97,x,k[0]] = F[70,x,k[0]]
F[98,x,k[0]] = F[9,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[91,x,k[0]]
F[100,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{26}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{100}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{49}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{49}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{57}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{60}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = 0
F_{81}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{83}\! \left(x , y\right)+F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 0
F_{89}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{9}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{100}\! \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_3(x))
Eq(F_3(x), F_100(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_40(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_24(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_9(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_17(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_21(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_9(x, k_0))
Eq(F_20(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0)*F_9(x, k_0))
Eq(F_23(x, k_0), F_13(x, k_0) + F_21(x, k_0))
Eq(F_24(x, k_0), F_25(x) + F_26(x, k_0) + F_36(x, k_0))
Eq(F_25(x), 0)
Eq(F_26(x, k_0), F_27(x, k_0)*F_9(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_29(x, k_0))
Eq(F_28(x, k_0), F_24(x, k_0) + F_7(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_33(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_9(x, k_0))
Eq(F_32(x, k_0), F_30(x, k_0) + F_7(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0)*F_9(x, k_0))
Eq(F_35(x, k_0), F_24(x, k_0) + F_33(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_9(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_39(x, k_0))
Eq(F_38(x, k_0), F_18(x, k_0) + F_30(x, k_0))
Eq(F_39(x, k_0), F_21(x, k_0) + F_33(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_100(x)*F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_44(x, k_0))
Eq(F_43(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0)*F_49(x, k_0)*F_9(x, k_0))
Eq(F_47(x, k_0), F_46(x, k_0)*F_9(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_49(x, k_0), F_16(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_7(x, k_0))
Eq(F_51(x, k_0), F_25(x) + F_52(x, k_0) + F_62(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0)*F_9(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_55(x, k_0))
Eq(F_54(x, k_0), F_13(x, k_0) + F_51(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_66(x, k_0))
Eq(F_56(x, k_0), F_25(x) + F_57(x, k_0) + F_62(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0)*F_9(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_65(x, k_0))
Eq(F_59(x, k_0), F_13(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_25(x) + F_61(x, k_0) + F_62(x, k_0))
Eq(F_61(x, k_0), F_13(x, k_0)*F_9(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0)*F_9(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0))
Eq(F_64(x, k_0), F_60(x, k_0) + F_9(x, k_0))
Eq(F_65(x, k_0), F_60(x, k_0))
Eq(F_66(x, k_0), F_25(x) + F_67(x, k_0) + F_80(x, k_0) + F_89(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0)*F_9(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_85(x, k_0))
Eq(F_69(x, k_0), F_51(x, k_0) + F_70(x, k_0))
Eq(F_70(x, k_0), F_25(x) + F_71(x, k_0) + F_72(x, k_0) + F_80(x, k_0))
Eq(F_71(x, k_0), F_51(x, k_0)*F_9(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0)*F_9(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0) + F_75(x, k_0))
Eq(F_74(x, k_0), F_60(x, k_0) + F_70(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_81(x, k_0))
Eq(F_76(x, k_0), F_25(x) + F_77(x, k_0) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_77(x, k_0), F_60(x, k_0)*F_9(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0)*F_9(x, k_0))
Eq(F_79(x, k_0), F_65(x, k_0))
Eq(F_80(x, k_0), 0)
Eq(F_81(x, k_0), F_25(x) + F_82(x, k_0) + F_83(x, k_0) + F_86(x, k_0) + F_88(x, k_0))
Eq(F_82(x, k_0), F_70(x, k_0)*F_9(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0)*F_9(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_70(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0)*F_9(x, k_0))
Eq(F_87(x, k_0), F_75(x, k_0))
Eq(F_88(x, k_0), 0)
Eq(F_89(x, k_0), F_9(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_55(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_95(x, k_0))
Eq(F_92(x, k_0), F_25(x) + F_78(x, k_0) + F_80(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_9(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_60(x, k_0))
Eq(F_95(x, k_0), F_25(x) + F_83(x, k_0) + F_88(x, k_0) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_96(x, k_0), F_9(x, k_0)*F_97(x, k_0))
Eq(F_97(x, k_0), F_70(x, k_0))
Eq(F_98(x, k_0), F_9(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_91(x, k_0))
Eq(F_100(x), 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"}]], "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": "point_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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [2, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [1, 1], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 1], [2, 1], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": 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