0123_0132_0321
Counting sequence:
1, 1, 2, 6, 21, 76, 278, 1021, 3756, 13827, 50916, 187512, 690593, 2543444, 9367525, 34500756, 127067006, 467990629, 1723620240, 6348133335, 23380322908, 86110274536, 317146150489, 1168056674504, 4301979997337, 15844292751908, 58354900065926, 214922459155549, 791564434141796, 2915350288952555, 10737303169170660, 39545738220088616, 145647877007190497, 536424530973311244, 1975664069691487725, 7276416887922312676, 26799213256487134302, 98702128015613201669, 363522241551336976808, 1338860901576557140287, 4931055954432560490748, 18161194189114531210232, 66888102147419735779769, 246350441622682321320032, 907314427219575724299873, 3341660215497621274282196, 12307412580288662851881670, 45328487833372137805070813, 166945878823538623140175132, 614865568836476014067468371, 2264564243243233024469891108, 8340442971103589552323795992, 30718046159116903920483123809, 113135281075938087631148309508, 416679881195265550078651129973, 1534641729279506145019912682484, 5652121313105415932194801049982, 20816894737417922280312803701093, 76669109260616438184536006319488, 282374119145181074317423640755111, 1039990472459753044142929667292636, 3830309187262916089699885064906568, 14107118150160235586296945091477337, 51956845458940768416424657232897592, 191358274688696184406398882044912297, 704776992682746771999996201766950980, 2595710116131591175393649703436604998, 9560060951111153458049062363116512541, 35209927649843537576200975668381208724, 129678985463280253262652260418975914683, 477610730644610664926062092454655654820, 1759051470151042825513716197782362964296, 6478627627282060111794140722583166138145, 23860936786220560495011036203219836851772, 87880387185467422762851398610982084180861, 323665517454771357870622943610122444460740, 1192067656326720392718822192153761820170462, 4390413005484442377039489485338183406361989, 16169993587548413103412484837029576814663960, 59554463849923406754518943173977290408445711, 219340480578976292051846196569661419770139900, 807836110184008494591687804682548253912980440, 2975279251666693553515043773836408608097937209, 10958022937823305138033462573626784133657364560, 40358654280466678959738975089444412053914281329, 148641865834036972149831632057286330413952987252, 547451461713315671425449368476103559390485561094, 2016276513016011851898121385327714575307048187421, 7425993464730072748000134955387730667770524577484, 27350107280536389573638984608575308170100489367587, 100731083566074709405099968584242968308804113372004, 370994932206954348060015196534754800932890835167928, 1366382995701215635559620074941849547322273472438305, 5032420469560341510442874993770514005005891177401780, 18534522064549867634727881187233998578479044253786885, 68263077427490539006348317372534765982510930051443284, 251414507676151300407209585712771645635232699299801214, 925965500708385151707193074819091484921570975192250725, 3410352554541397677930526525993251550774554676385017456, 12560408068518136203229732346527926209479378839561496439, 46260276122364295256359202075490166425248209626627914332
Generating function in Maple syntax:
-(x^6+5*x^4-12*x^3+12*x^2-6*x+1)/(2*x^5-13*x^4+21*x^3-17*x^2+7*x-1)
Generating function in latex syntax:
-\frac{x^{6}+5 x^{4}-12 x^{3}+12 x^{2}-6 x +1}{2 x^{5}-13 x^{4}+21 x^{3}-17 x^{2}+7 x -1}
Generating function in sympy syntax:
(-x**6 - 5*x**4 + 12*x**3 - 12*x**2 + 6*x - 1)/(2*x**5 - 13*x**4 + 21*x**3 - 17*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^5-13*x^4+21*x^3-17*x^2+7*x-1)*F(x)+x^6+5*x^4-12*x^3+12*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{5}-13 x^{4}+21 x^{3}-17 x^{2}+7 x -1\right) F \! \left(x \right)+x^{6}+5 x^{4}-12 x^{3}+12 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
37364/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n)+37364/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n)+37364/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n)+37364/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n)+37364/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n)-60644/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(1-n)-60644/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(1-n)-60644/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(1-n)-60644/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(1-n)-60644/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(1-n)-3041/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n-1)-3041/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n-1)-3041/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n-1)-3041/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n-1)-3041/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n-1)+60239/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n+2)+60239/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n+2)+60239/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n+2)+60239/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n+2)+60239/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n+2)-5384/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 1)^(-n+3)-5384/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 2)^(-n+3)-5384/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 3)^(-n+3)-5384/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 4)^(-n+3)-5384/126571*RootOf(2*_Z^5-13*_Z^4+21*_Z^3-17*_Z^2+7*_Z-1,index = 5)^(-n+3)-1/2*piecewise(n = 0,13/2,n = 1,1,0)
Explicit closed form in latex syntax:
\frac{37364 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{126571}+\frac{37364 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{126571}+\frac{37364 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{126571}+\frac{37364 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{126571}+\frac{37364 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{126571}-\frac{60644 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{1-n}}{126571}-\frac{60644 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{1-n}}{126571}-\frac{60644 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{1-n}}{126571}-\frac{60644 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{1-n}}{126571}-\frac{60644 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{1-n}}{126571}-\frac{3041 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{126571}-\frac{3041 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{126571}-\frac{3041 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{126571}-\frac{3041 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{126571}-\frac{3041 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{126571}+\frac{60239 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{126571}+\frac{60239 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{126571}+\frac{60239 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{126571}+\frac{60239 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{126571}+\frac{60239 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{126571}-\frac{5384 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{126571}-\frac{5384 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{126571}-\frac{5384 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{126571}-\frac{5384 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{126571}-\frac{5384 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-13 \textit{\_Z}^{4}+21 \textit{\_Z}^{3}-17 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{126571}-\frac{\left(\left\{\begin{array}{cc}\frac{13}{2} & n =0 \\ 1 & n =1 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 76
a(6) = 278
a(n+5) = 2*a(n)-13*a(n+1)+21*a(n+2)-17*a(n+3)+7*a(n+4), n >= 7
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) = 21
a \! \left(5\right) = 76
a \! \left(6\right) = 278
a \! \left(n +5\right) = 2 a \! \left(n \right)-13 a \! \left(n +1\right)+21 a \! \left(n +2\right)-17 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14621/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[15,x]+F[181,x]+F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[34,x]
F[23,x] = F[24,x]+F[7,x]
F[24,x] = F[15,x]+F[25,x]+F[28,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[14,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[16,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[4,x]
F[34,x] = F[20,x]+F[35,x]
F[35,x] = F[140,x]+F[15,x]+F[179,x]+F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[46,x]
F[38,x] = F[24,x]+F[39,x]
F[39,x] = F[15,x]+F[40,x]+F[41,x]+F[44,x]
F[40,x] = 0
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[27,x]+F[43,x]
F[43,x] = F[32,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[30,x]
F[46,x] = F[35,x]+F[47,x]
F[47,x] = F[138,x]+F[15,x]+F[177,x]+F[48,x]+F[92,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[54,x]
F[50,x] = F[39,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[43,x]
F[54,x] = F[47,x]+F[55,x]
F[55,x] = F[15,x]+F[176,x]+F[56,x]+F[60,x]+F[61,x]+F[62,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[51,x]
F[59,x] = F[55,x]
F[60,x] = 0
F[61,x] = 0
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = 2*F[15,x]+F[66,x]+F[70,x]+F[71,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[32,x]
F[69,x] = F[65,x]
F[70,x] = 0
F[71,x] = F[4,x]*F[72,x]
F[72,x] = 2*F[15,x]+F[113,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[31,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[27,x]*F[4,x]
F[78,x] = F[72,x]+F[79,x]
F[79,x] = 2*F[15,x]+F[80,x]+F[92,x]+F[93,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[76,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[43,x]
F[85,x] = F[79,x]+F[86,x]
F[86,x] = 2*F[15,x]+F[60,x]+F[61,x]+F[87,x]+F[91,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[83,x]
F[90,x] = F[86,x]
F[91,x] = F[4,x]*F[64,x]
F[92,x] = 0
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[113,x]+F[142,x]+F[15,x]+F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[100,x]+F[98,x]
F[98,x] = F[14,x]+F[99,x]
F[99,x] = F[15,x]+F[33,x]+F[40,x]+F[77,x]
F[100,x] = F[101,x]+F[95,x]
F[101,x] = F[102,x]+F[15,x]+F[71,x]+F[92,x]+F[93,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[106,x]
F[104,x] = F[105,x]+F[99,x]
F[105,x] = F[84,x]
F[106,x] = F[101,x]+F[107,x]
F[107,x] = F[108,x]+F[112,x]+F[15,x]+F[60,x]+F[61,x]+F[91,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[105,x]
F[111,x] = F[107,x]
F[112,x] = 0
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]+F[15,x]+F[175,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[120,x]
F[118,x] = F[119,x]+F[4,x]
F[119,x] = F[15,x]+F[18,x]+F[25,x]
F[120,x] = F[115,x]+F[121,x]
F[121,x] = F[122,x]+F[140,x]+F[142,x]+F[15,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[119,x]+F[125,x]
F[125,x] = F[15,x]+F[33,x]+F[40,x]+F[41,x]
F[126,x] = F[121,x]+F[127,x]
F[127,x] = F[128,x]+F[138,x]+F[15,x]+F[71,x]+F[92,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[125,x]+F[131,x]
F[131,x] = F[52,x]
F[132,x] = F[127,x]+F[133,x]
F[133,x] = F[112,x]+F[134,x]+F[15,x]+F[60,x]+F[61,x]+F[62,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[131,x]
F[137,x] = F[133,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[64,x]+F[94,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[114,x]+F[94,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[15,x]+F[173,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[146,x]+F[149,x]
F[146,x] = F[12,x]+F[147,x]
F[147,x] = F[148,x]+F[15,x]+F[25,x]
F[148,x] = F[11,x]*F[4,x]
F[149,x] = F[143,x]+F[150,x]
F[150,x] = F[140,x]+F[15,x]+F[151,x]+F[171,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[156,x]
F[153,x] = F[147,x]+F[154,x]
F[154,x] = F[15,x]+F[155,x]+F[40,x]+F[41,x]
F[155,x] = F[30,x]*F[4,x]
F[156,x] = F[150,x]+F[157,x]
F[157,x] = F[138,x]+F[15,x]+F[158,x]+F[169,x]+F[92,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[162,x]
F[160,x] = F[154,x]+F[161,x]
F[161,x] = F[52,x]
F[162,x] = F[157,x]+F[163,x]
F[163,x] = F[15,x]+F[164,x]+F[168,x]+F[60,x]+F[61,x]+F[62,x]
F[164,x] = F[165,x]*F[4,x]
F[165,x] = F[166,x]+F[167,x]
F[166,x] = F[161,x]
F[167,x] = F[163,x]
F[168,x] = 0
F[169,x] = F[170,x]*F[4,x]
F[170,x] = F[65,x]+F[72,x]
F[171,x] = F[172,x]*F[4,x]
F[172,x] = F[143,x]+F[95,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[115,x]+F[2,x]
F[175,x] = F[2,x]*F[4,x]
F[176,x] = 0
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[170,x]
F[179,x] = F[180,x]*F[4,x]
F[180,x] = F[170,x]+F[172,x]
F[181,x] = F[182,x]*F[4,x]
F[182,x] = F[172,x]+F[174,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)+F_{181}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{140}\! \left(x \right)+F_{15}\! \left(x \right)+F_{179}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{27}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{32}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{30}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{138}\! \left(x \right)+F_{15}\! \left(x \right)+F_{177}\! \left(x \right)+F_{48}\! \left(x \right)+F_{92}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{43}\! \left(x \right)
F_{54}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{176}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{51}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = 0
F_{61}\! \left(x \right) = 0
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{32}\! \left(x \right)
F_{69}\! \left(x \right) = F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = 0
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{113}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{31}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{78}\! \left(x \right) = F_{72}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{80}\! \left(x \right)+F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{76}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{85}\! \left(x \right) = F_{79}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{83}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{92}\! \left(x \right) = 0
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{113}\! \left(x \right)+F_{142}\! \left(x \right)+F_{15}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{40}\! \left(x \right)+F_{77}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{95}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{15}\! \left(x \right)+F_{71}\! \left(x \right)+F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{99}\! \left(x \right)
F_{105}\! \left(x \right) = F_{84}\! \left(x \right)
F_{106}\! \left(x \right) = F_{101}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)+F_{15}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{91}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right)
F_{111}\! \left(x \right) = F_{107}\! \left(x \right)
F_{112}\! \left(x \right) = 0
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{15}\! \left(x \right)+F_{175}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{120}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{120}\! \left(x \right) = F_{115}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{140}\! \left(x \right)+F_{142}\! \left(x \right)+F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{119}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{126}\! \left(x \right) = F_{121}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{138}\! \left(x \right)+F_{15}\! \left(x \right)+F_{71}\! \left(x \right)+F_{92}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{125}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{52}\! \left(x \right)
F_{132}\! \left(x \right) = F_{127}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{112}\! \left(x \right)+F_{134}\! \left(x \right)+F_{15}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{131}\! \left(x \right)
F_{137}\! \left(x \right) = F_{133}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{64}\! \left(x \right)+F_{94}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{114}\! \left(x \right)+F_{94}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{15}\! \left(x \right)+F_{173}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{149}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{148}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{143}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{140}\! \left(x \right)+F_{15}\! \left(x \right)+F_{151}\! \left(x \right)+F_{171}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{156}\! \left(x \right)
F_{153}\! \left(x \right) = F_{147}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{15}\! \left(x \right)+F_{155}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{155}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{156}\! \left(x \right) = F_{150}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{138}\! \left(x \right)+F_{15}\! \left(x \right)+F_{158}\! \left(x \right)+F_{169}\! \left(x \right)+F_{92}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{4}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{162}\! \left(x \right)
F_{160}\! \left(x \right) = F_{154}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{52}\! \left(x \right)
F_{162}\! \left(x \right) = F_{157}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{15}\! \left(x \right)+F_{164}\! \left(x \right)+F_{168}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{4}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{167}\! \left(x \right)
F_{166}\! \left(x \right) = F_{161}\! \left(x \right)
F_{167}\! \left(x \right) = F_{163}\! \left(x \right)
F_{168}\! \left(x \right) = 0
F_{169}\! \left(x \right) = F_{170}\! \left(x \right) F_{4}\! \left(x \right)
F_{170}\! \left(x \right) = F_{65}\! \left(x \right)+F_{72}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{4}\! \left(x \right)
F_{172}\! \left(x \right) = F_{143}\! \left(x \right)+F_{95}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{115}\! \left(x \right)+F_{2}\! \left(x \right)
F_{175}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = 0
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{170}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right) F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{170}\! \left(x \right)+F_{172}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right) F_{4}\! \left(x \right)
F_{182}\! \left(x \right) = F_{172}\! \left(x \right)+F_{174}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_15(x) + F_181(x) + F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_34(x))
Eq(F_23(x), F_24(x) + F_7(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_28(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_14(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_4(x))
Eq(F_34(x), F_20(x) + F_35(x))
Eq(F_35(x), F_140(x) + F_15(x) + F_179(x) + F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_46(x))
Eq(F_38(x), F_24(x) + F_39(x))
Eq(F_39(x), F_15(x) + F_40(x) + F_41(x) + F_44(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_27(x) + F_43(x))
Eq(F_43(x), F_32(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_30(x))
Eq(F_46(x), F_35(x) + F_47(x))
Eq(F_47(x), F_138(x) + F_15(x) + F_177(x) + F_48(x) + F_92(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_54(x))
Eq(F_50(x), F_39(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_43(x))
Eq(F_54(x), F_47(x) + F_55(x))
Eq(F_55(x), F_15(x) + F_176(x) + F_56(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_51(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), 0)
Eq(F_61(x), 0)
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), 2*F_15(x) + F_66(x) + F_70(x) + F_71(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_32(x))
Eq(F_69(x), F_65(x))
Eq(F_70(x), 0)
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_113(x) + 2*F_15(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_31(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_27(x)*F_4(x))
Eq(F_78(x), F_72(x) + F_79(x))
Eq(F_79(x), 2*F_15(x) + F_80(x) + F_92(x) + F_93(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_76(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_43(x))
Eq(F_85(x), F_79(x) + F_86(x))
Eq(F_86(x), 2*F_15(x) + F_60(x) + F_61(x) + F_87(x) + F_91(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_83(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_4(x)*F_64(x))
Eq(F_92(x), 0)
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_113(x) + F_142(x) + F_15(x) + F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_100(x) + F_98(x))
Eq(F_98(x), F_14(x) + F_99(x))
Eq(F_99(x), F_15(x) + F_33(x) + F_40(x) + F_77(x))
Eq(F_100(x), F_101(x) + F_95(x))
Eq(F_101(x), F_102(x) + F_15(x) + F_71(x) + F_92(x) + F_93(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_106(x))
Eq(F_104(x), F_105(x) + F_99(x))
Eq(F_105(x), F_84(x))
Eq(F_106(x), F_101(x) + F_107(x))
Eq(F_107(x), F_108(x) + F_112(x) + F_15(x) + F_60(x) + F_61(x) + F_91(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_105(x))
Eq(F_111(x), F_107(x))
Eq(F_112(x), 0)
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x) + F_15(x) + F_175(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_120(x))
Eq(F_118(x), F_119(x) + F_4(x))
Eq(F_119(x), F_15(x) + F_18(x) + F_25(x))
Eq(F_120(x), F_115(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_140(x) + F_142(x) + F_15(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_119(x) + F_125(x))
Eq(F_125(x), F_15(x) + F_33(x) + F_40(x) + F_41(x))
Eq(F_126(x), F_121(x) + F_127(x))
Eq(F_127(x), F_128(x) + F_138(x) + F_15(x) + F_71(x) + F_92(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_125(x) + F_131(x))
Eq(F_131(x), F_52(x))
Eq(F_132(x), F_127(x) + F_133(x))
Eq(F_133(x), F_112(x) + F_134(x) + F_15(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_131(x))
Eq(F_137(x), F_133(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_64(x) + F_94(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_114(x) + F_94(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_15(x) + F_173(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_146(x) + F_149(x))
Eq(F_146(x), F_12(x) + F_147(x))
Eq(F_147(x), F_148(x) + F_15(x) + F_25(x))
Eq(F_148(x), F_11(x)*F_4(x))
Eq(F_149(x), F_143(x) + F_150(x))
Eq(F_150(x), F_140(x) + F_15(x) + F_151(x) + F_171(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_156(x))
Eq(F_153(x), F_147(x) + F_154(x))
Eq(F_154(x), F_15(x) + F_155(x) + F_40(x) + F_41(x))
Eq(F_155(x), F_30(x)*F_4(x))
Eq(F_156(x), F_150(x) + F_157(x))
Eq(F_157(x), F_138(x) + F_15(x) + F_158(x) + F_169(x) + F_92(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_162(x))
Eq(F_160(x), F_154(x) + F_161(x))
Eq(F_161(x), F_52(x))
Eq(F_162(x), F_157(x) + F_163(x))
Eq(F_163(x), F_15(x) + F_164(x) + F_168(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_164(x), F_165(x)*F_4(x))
Eq(F_165(x), F_166(x) + F_167(x))
Eq(F_166(x), F_161(x))
Eq(F_167(x), F_163(x))
Eq(F_168(x), 0)
Eq(F_169(x), F_170(x)*F_4(x))
Eq(F_170(x), F_65(x) + F_72(x))
Eq(F_171(x), F_172(x)*F_4(x))
Eq(F_172(x), F_143(x) + F_95(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_115(x) + F_2(x))
Eq(F_175(x), F_2(x)*F_4(x))
Eq(F_176(x), 0)
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_170(x))
Eq(F_179(x), F_180(x)*F_4(x))
Eq(F_180(x), F_170(x) + F_172(x))
Eq(F_181(x), F_182(x)*F_4(x))
Eq(F_182(x), F_172(x) + F_174(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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [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": 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, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], 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