0123_0132_0213_0321
Counting sequence:
1, 1, 2, 6, 20, 69, 241, 845, 2966, 10415, 36580, 128494, 451385, 1585697, 5570519, 19569140, 68746109, 241504212, 848401468, 2980424741, 10470198661, 36781690609, 129213667314, 453926167295, 1594637547704, 5601943869150, 19679566158537, 69134095815605, 242867305394827, 853190127592440, 2997247376053253, 10529296510532784, 36989300880737468, 129943000301818877, 456488306764188521, 1603638316249639461, 5633563469726411486, 19790645462786293215, 69524316170121514412, 244238145138420853950, 858005872286339199705, 3014165033314589255209, 10588728051297498453967, 37198083218767273263180, 130676450320280249872189, 459064908476071041922316, 1612689889246538012185740, 5665361544430872652581845, 19902351743590224992140813, 69916739085251159748043049, 245616722450372484640658778, 862848798965072586125626639, 3031178180573181813800397440, 10648495047340118286861760398, 37408044007424669928226149033, 131414040222610289067382647677, 461656053553673939631247213731, 1621792552924519720503186466352, 5697339100126480771283797968229, 20014688539108572397210426664488, 70311376991520656152851365625644, 247003081001425649991734461085037, 867719061049743474119981695383153, 3048287356807110642745283220704637, 10708599392099095693688190680557990, 37619189898349686064161964338773199, 132155793375952166097185665966427892, 464261824085519188194653899489876558, 1630946595659682199301878118135538553, 5729497149875336193658855689916003505, 20127659408217313227551837060178635271, 70708242391221659366435382429198781156, 248397264711991179475930811640595933117, 872616812832263895735822834317113443908, 3065493104042137230423592147095485419292, 10769042989704869360932974767490390752901, 37831527580731258179200722502827902149269, 132901733279351804112860227611209758717089, 466882302623492301023051590104375557383682, 1640152307455875988034795919073105706634847, 5761836712457722430868267395932283205789640, 20241267929880189315713153773829004607381758, 71107347857213766953269673555415656215292041, 249799317750384223181223511674396190229021125, 877542209475430990199049672618527960034760955, 3082795967363432570003702638730762751393534376, 10829827755035548698077610646939574941408841861, 38045063781514768432003924330969025266386086048, 133651883564493095777865044579703978184472195548, 469517572185434493821654491467295148346632291549, 1649409979953848797264726565020630764825793656185, 5794358812404324449526171027856017983123665052693, 20355517703262038491185926206192355317412221670574, 71508706033322800772770248399361435888802929684479, 251209284534223483430720882575965931912814387393212, 882495407017842487482417689756738759689630722872478, 3100196494932845334899962164313782116835903999281945, 10890955613777577395439118032610589016529530820460985, 38259805265615156428273054621774572974025764573623935, 134406267996446564411545676987958527494784301766986684, 472167716257772723979613058340410981279976871459615485
Generating function in Maple syntax:
-(x^5+7*x^4-15*x^3+13*x^2-6*x+1)/(4*x^5-18*x^4+25*x^3-18*x^2+7*x-1)
Generating function in latex syntax:
-\frac{x^{5}+7 x^{4}-15 x^{3}+13 x^{2}-6 x +1}{4 x^{5}-18 x^{4}+25 x^{3}-18 x^{2}+7 x -1}
Generating function in sympy syntax:
(-x**5 - 7*x**4 + 15*x**3 - 13*x**2 + 6*x - 1)/(4*x**5 - 18*x**4 + 25*x**3 - 18*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(4*x^5-18*x^4+25*x^3-18*x^2+7*x-1)*F(x)+x^5+7*x^4-15*x^3+13*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{5}-18 x^{4}+25 x^{3}-18 x^{2}+7 x -1\right) F \! \left(x \right)+x^{5}+7 x^{4}-15 x^{3}+13 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
4333/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 1)^(-n)+4333/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 2)^(-n)+4333/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 3)^(-n)+4333/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 4)^(-n)+4333/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 5)^(-n)+950/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 1)^(-n-1)+950/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 2)^(-n-1)+950/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 3)^(-n-1)+950/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 4)^(-n-1)+950/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 5)^(-n-1)-9509/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 1)^(-n+1)-9509/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 2)^(-n+1)-9509/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 3)^(-n+1)-9509/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 4)^(-n+1)-9509/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 5)^(-n+1)+16089/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 1)^(-n+2)+16089/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 2)^(-n+2)+16089/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 3)^(-n+2)+16089/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 4)^(-n+2)+16089/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 5)^(-n+2)-2442/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 1)^(-n+3)-2442/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 2)^(-n+3)-2442/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 3)^(-n+3)-2442/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 4)^(-n+3)-2442/48611*RootOf(4*_Z^5-18*_Z^4+25*_Z^3-18*_Z^2+7*_Z-1,index = 5)^(-n+3)-piecewise(n = 0,1/4,0)
Explicit closed form in latex syntax:
\frac{4333 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{48611}+\frac{4333 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{48611}+\frac{4333 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{48611}+\frac{4333 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{48611}+\frac{4333 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{48611}+\frac{950 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{48611}+\frac{950 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{48611}+\frac{950 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{48611}+\frac{950 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{48611}+\frac{950 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{48611}-\frac{9509 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{48611}-\frac{9509 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{48611}-\frac{9509 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{48611}-\frac{9509 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{48611}-\frac{9509 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{48611}+\frac{16089 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{48611}+\frac{16089 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{48611}+\frac{16089 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{48611}+\frac{16089 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{48611}+\frac{16089 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{48611}-\frac{2442 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{48611}-\frac{2442 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{48611}-\frac{2442 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{48611}-\frac{2442 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{48611}-\frac{2442 \mathit{RootOf}\! \left(4 \textit{\_Z}^{5}-18 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-18 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{48611}-\left(\left\{\begin{array}{cc}\frac{1}{4} & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 69
a(n+5) = 4*a(n)-18*a(n+1)+25*a(n+2)-18*a(n+3)+7*a(n+4), n >= 6
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) = 20
a \! \left(5\right) = 69
a \! \left(n +5\right) = 4 a \! \left(n \right)-18 a \! \left(n +1\right)+25 a \! \left(n +2\right)-18 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14784/
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[16,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[15,x] = F[12,x]*F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[174,x]+F[18,x]+F[19,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[34,x]
F[21,x] = F[22,x]+F[7,x]
F[22,x] = F[18,x]+F[23,x]+F[27,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[4,x]
F[26,x] = F[14,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[11,x]+F[29,x]
F[29,x] = F[30,x]+F[32,x]
F[30,x] = F[31,x]
F[31,x] = F[25,x]*F[4,x]
F[32,x] = F[33,x]
F[33,x] = F[30,x]*F[4,x]
F[34,x] = F[17,x]+F[35,x]
F[35,x] = F[136,x]+F[172,x]+F[18,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[22,x]+F[39,x]
F[39,x] = F[18,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[26,x]+F[43,x]
F[43,x] = F[32,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[29,x]
F[46,x] = F[35,x]+F[47,x]
F[47,x] = F[132,x]+F[170,x]+F[18,x]+F[48,x]+F[91,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[169,x]+F[18,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] = 3*F[18,x]+F[66,x]+F[70,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] = F[4,x]*F[71,x]
F[71,x] = 2*F[18,x]+F[168,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[77,x]
F[74,x] = F[30,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[26,x]*F[4,x]
F[77,x] = F[71,x]+F[78,x]
F[78,x] = 2*F[18,x]+F[79,x]+F[91,x]+F[92,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[75,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[43,x]
F[84,x] = F[78,x]+F[85,x]
F[85,x] = 2*F[18,x]+F[60,x]+F[61,x]+F[86,x]+F[90,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[82,x]
F[89,x] = F[85,x]
F[90,x] = F[4,x]*F[64,x]
F[91,x] = 0
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = 2*F[18,x]+F[105,x]+F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[14,x]+F[98,x]
F[98,x] = F[33,x]
F[99,x] = F[100,x]+F[94,x]
F[100,x] = 2*F[18,x]+F[101,x]+F[70,x]+F[91,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[98,x]
F[104,x] = F[100,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[166,x]+F[18,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[112,x]
F[109,x] = F[110,x]+F[12,x]
F[110,x] = F[111,x]+F[18,x]+F[23,x]
F[111,x] = F[11,x]*F[4,x]
F[112,x] = F[106,x]+F[113,x]
F[113,x] = F[114,x]+F[136,x]+F[164,x]+F[18,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[119,x]
F[116,x] = F[110,x]+F[117,x]
F[117,x] = F[118,x]+F[18,x]+F[40,x]+F[41,x]
F[118,x] = F[29,x]*F[4,x]
F[119,x] = F[113,x]+F[120,x]
F[120,x] = F[121,x]+F[132,x]+F[134,x]+F[18,x]+F[91,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[117,x]+F[124,x]
F[124,x] = F[52,x]
F[125,x] = F[120,x]+F[126,x]
F[126,x] = F[127,x]+F[131,x]+F[18,x]+F[60,x]+F[61,x]+F[62,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[124,x]
F[130,x] = F[126,x]
F[131,x] = 0
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[64,x]+F[93,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[65,x]+F[71,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[93,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]+F[163,x]+F[18,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[144,x]
F[142,x] = F[143,x]+F[4,x]
F[143,x] = F[15,x]+F[18,x]+F[23,x]
F[144,x] = F[139,x]+F[145,x]
F[145,x] = F[105,x]+F[136,x]+F[146,x]+F[18,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[150,x]
F[148,x] = F[143,x]+F[149,x]
F[149,x] = F[18,x]+F[33,x]+F[40,x]+F[41,x]
F[150,x] = F[145,x]+F[151,x]
F[151,x] = F[132,x]+F[152,x]+F[18,x]+F[70,x]+F[91,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[156,x]
F[154,x] = F[149,x]+F[155,x]
F[155,x] = F[52,x]
F[156,x] = F[151,x]+F[157,x]
F[157,x] = F[158,x]+F[162,x]+F[18,x]+F[60,x]+F[61,x]+F[62,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[155,x]
F[161,x] = F[157,x]
F[162,x] = 0
F[163,x] = F[2,x]*F[4,x]
F[164,x] = F[165,x]*F[4,x]
F[165,x] = F[106,x]+F[94,x]
F[166,x] = F[167,x]*F[4,x]
F[167,x] = F[139,x]+F[2,x]
F[168,x] = F[138,x]*F[4,x]
F[169,x] = 0
F[170,x] = F[171,x]*F[4,x]
F[171,x] = F[135,x]
F[172,x] = F[173,x]*F[4,x]
F[173,x] = F[135,x]+F[165,x]
F[174,x] = F[175,x]*F[4,x]
F[175,x] = F[165,x]+F[167,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_{16}\! \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_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{174}\! \left(x \right)+F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{17}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{136}\! \left(x \right)+F_{172}\! \left(x \right)+F_{18}\! \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_{22}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \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_{26}\! \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_{29}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{132}\! \left(x \right)+F_{170}\! \left(x \right)+F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{91}\! \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_{169}\! \left(x \right)+F_{18}\! \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) = 3 F_{18}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \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) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{168}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{74}\! \left(x \right) = F_{30}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{79}\! \left(x \right)+F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{75}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{84}\! \left(x \right) = F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{82}\! \left(x \right)
F_{89}\! \left(x \right) = F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{91}\! \left(x \right) = 0
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{105}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{14}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{33}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{94}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{101}\! \left(x \right)+F_{70}\! \left(x \right)+F_{91}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{98}\! \left(x \right)
F_{104}\! \left(x \right) = F_{100}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{166}\! \left(x \right)+F_{18}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{112}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{111}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{106}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{136}\! \left(x \right)+F_{164}\! \left(x \right)+F_{18}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{116}\! \left(x \right) = F_{110}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{18}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{118}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{113}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{132}\! \left(x \right)+F_{134}\! \left(x \right)+F_{18}\! \left(x \right)+F_{91}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{117}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{52}\! \left(x \right)
F_{125}\! \left(x \right) = F_{120}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{131}\! \left(x \right)+F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{124}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)
F_{131}\! \left(x \right) = 0
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{64}\! \left(x \right)+F_{93}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{65}\! \left(x \right)+F_{71}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{93}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{163}\! \left(x \right)+F_{18}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{144}\! \left(x \right) = F_{139}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{105}\! \left(x \right)+F_{136}\! \left(x \right)+F_{146}\! \left(x \right)+F_{18}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{150}\! \left(x \right)
F_{148}\! \left(x \right) = F_{143}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{150}\! \left(x \right) = F_{145}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{132}\! \left(x \right)+F_{152}\! \left(x \right)+F_{18}\! \left(x \right)+F_{70}\! \left(x \right)+F_{91}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{156}\! \left(x \right)
F_{154}\! \left(x \right) = F_{149}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{52}\! \left(x \right)
F_{156}\! \left(x \right) = F_{151}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{162}\! \left(x \right)+F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{62}\! \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_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{155}\! \left(x \right)
F_{161}\! \left(x \right) = F_{157}\! \left(x \right)
F_{162}\! \left(x \right) = 0
F_{163}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{4}\! \left(x \right)
F_{165}\! \left(x \right) = F_{106}\! \left(x \right)+F_{94}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{4}\! \left(x \right)
F_{167}\! \left(x \right) = F_{139}\! \left(x \right)+F_{2}\! \left(x \right)
F_{168}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{169}\! \left(x \right) = 0
F_{170}\! \left(x \right) = F_{171}\! \left(x \right) F_{4}\! \left(x \right)
F_{171}\! \left(x \right) = F_{135}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{4}\! \left(x \right)
F_{173}\! \left(x \right) = F_{135}\! \left(x \right)+F_{165}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{165}\! \left(x \right)+F_{167}\! \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_16(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))
Eq(F_15(x), F_12(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_174(x) + F_18(x) + F_19(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_34(x))
Eq(F_21(x), F_22(x) + F_7(x))
Eq(F_22(x), F_18(x) + F_23(x) + F_27(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_4(x))
Eq(F_26(x), F_14(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_11(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_32(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_25(x)*F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_30(x)*F_4(x))
Eq(F_34(x), F_17(x) + F_35(x))
Eq(F_35(x), F_136(x) + F_172(x) + F_18(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_22(x) + F_39(x))
Eq(F_39(x), F_18(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_26(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_29(x))
Eq(F_46(x), F_35(x) + F_47(x))
Eq(F_47(x), F_132(x) + F_170(x) + F_18(x) + F_48(x) + F_91(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_169(x) + F_18(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), 3*F_18(x) + F_66(x) + F_70(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), F_4(x)*F_71(x))
Eq(F_71(x), F_168(x) + 2*F_18(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_77(x))
Eq(F_74(x), F_30(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_26(x)*F_4(x))
Eq(F_77(x), F_71(x) + F_78(x))
Eq(F_78(x), 2*F_18(x) + F_79(x) + F_91(x) + F_92(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_75(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_43(x))
Eq(F_84(x), F_78(x) + F_85(x))
Eq(F_85(x), 2*F_18(x) + F_60(x) + F_61(x) + F_86(x) + F_90(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_82(x))
Eq(F_89(x), F_85(x))
Eq(F_90(x), F_4(x)*F_64(x))
Eq(F_91(x), 0)
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_105(x) + 2*F_18(x) + F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_14(x) + F_98(x))
Eq(F_98(x), F_33(x))
Eq(F_99(x), F_100(x) + F_94(x))
Eq(F_100(x), F_101(x) + 2*F_18(x) + F_70(x) + F_91(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_98(x))
Eq(F_104(x), F_100(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_166(x) + F_18(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_112(x))
Eq(F_109(x), F_110(x) + F_12(x))
Eq(F_110(x), F_111(x) + F_18(x) + F_23(x))
Eq(F_111(x), F_11(x)*F_4(x))
Eq(F_112(x), F_106(x) + F_113(x))
Eq(F_113(x), F_114(x) + F_136(x) + F_164(x) + F_18(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_119(x))
Eq(F_116(x), F_110(x) + F_117(x))
Eq(F_117(x), F_118(x) + F_18(x) + F_40(x) + F_41(x))
Eq(F_118(x), F_29(x)*F_4(x))
Eq(F_119(x), F_113(x) + F_120(x))
Eq(F_120(x), F_121(x) + F_132(x) + F_134(x) + F_18(x) + F_91(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_117(x) + F_124(x))
Eq(F_124(x), F_52(x))
Eq(F_125(x), F_120(x) + F_126(x))
Eq(F_126(x), F_127(x) + F_131(x) + F_18(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_124(x))
Eq(F_130(x), F_126(x))
Eq(F_131(x), 0)
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_64(x) + F_93(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_65(x) + F_71(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_93(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x) + F_163(x) + F_18(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_144(x))
Eq(F_142(x), F_143(x) + F_4(x))
Eq(F_143(x), F_15(x) + F_18(x) + F_23(x))
Eq(F_144(x), F_139(x) + F_145(x))
Eq(F_145(x), F_105(x) + F_136(x) + F_146(x) + F_18(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_150(x))
Eq(F_148(x), F_143(x) + F_149(x))
Eq(F_149(x), F_18(x) + F_33(x) + F_40(x) + F_41(x))
Eq(F_150(x), F_145(x) + F_151(x))
Eq(F_151(x), F_132(x) + F_152(x) + F_18(x) + F_70(x) + F_91(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_156(x))
Eq(F_154(x), F_149(x) + F_155(x))
Eq(F_155(x), F_52(x))
Eq(F_156(x), F_151(x) + F_157(x))
Eq(F_157(x), F_158(x) + F_162(x) + F_18(x) + F_60(x) + F_61(x) + F_62(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_155(x))
Eq(F_161(x), F_157(x))
Eq(F_162(x), 0)
Eq(F_163(x), F_2(x)*F_4(x))
Eq(F_164(x), F_165(x)*F_4(x))
Eq(F_165(x), F_106(x) + F_94(x))
Eq(F_166(x), F_167(x)*F_4(x))
Eq(F_167(x), F_139(x) + F_2(x))
Eq(F_168(x), F_138(x)*F_4(x))
Eq(F_169(x), 0)
Eq(F_170(x), F_171(x)*F_4(x))
Eq(F_171(x), F_135(x))
Eq(F_172(x), F_173(x)*F_4(x))
Eq(F_173(x), F_135(x) + F_165(x))
Eq(F_174(x), F_175(x)*F_4(x))
Eq(F_175(x), F_165(x) + F_167(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, 2, 1, 3], "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, 2, 1, 3], "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, 2, 1, 3], "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": [1, 0, 2], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [1, 0, 2], "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, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [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": [1, 0, 2], "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": [1, 0, 2], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [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": [[{"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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], 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