0132_0213_0231_1023_2103
Counting sequence:
1, 1, 2, 6, 19, 58, 173, 513, 1521, 4512, 13388, 39727, 117884, 349801, 1037973, 3080001, 9139358, 27119430, 80472119, 238786802, 708557665, 2102519737, 6238856005, 18512703384, 54933177864, 163004503863, 483687077880, 1435255982281, 4258868654713, 12637440597369, 37499373143450, 111272767244062, 330182285522123, 979757620599938, 2907257709497365, 8626773818055465, 25598427777754153, 75958813632209032, 225394364783088484, 668817971828222167, 1984599215117463140, 5888947681651774465, 17474412230471032349, 51852232233584287273, 153862341814119102118, 456559326547018045102, 1354759171083529375871, 4020008583585289374506, 11928665520067559315001, 35396208274446768946609, 105031996923736195319181, 311663901744858623436656, 924807587171347749369232, 2744203189722785880056239, 8142938326791038966685424, 24162731404965933166506961, 71698638196441445313522289, 212753046543723727357430577, 631307092466958674588524850, 1873292305204089230665122422, 5558664083788217894231666691, 16494353983390108395987843338, 48944082468096594751788979581, 145232920977453468549822947473, 430953044209013691716532857313, 1278777050430928786420450401456, 3794545059335314298109337882748, 11259642329735226248107114529215, 33411000109660873936085747880396, 99141242291486618551538629508825, 294184127707604271694443982620069, 872939444723053322429880879439697, 2590293637156330410908384842453806, 7686238910674095424381894918288214, 22807556542824102368040777588545479, 67677396123053569956625248311570850, 200820720860506879539005063683952017, 595900023304767780420168084179326697, 1768228080514054306450868944245954005, 5246904551838437275151234160595339912, 15569262630474381906479585302563142552, 46199037253641680543784848380113697895, 137087484090975219848644053931921613800, 406782898769432919970175212898571705369, 1207056412396119897486150829864973657321, 3581726732156506270972529366583822093865, 10628141528512510714551180580019300946378, 31537133007933919766651526184370186290446, 93580872600528468043802994900188605705915, 277684712636155338878773038066612732064466, 823980344369953238196256100005371585453029, 2445016153257355592349240886851250345327929, 7255153633865480884971106792867534816277529, 21528387115506734014241261880914828513798936, 63881686754603281394810859950804166972680852, 189557623649095229823038727871314079524485351, 562478771443879870463013391418767851277665204, 1669056417961307153615061078954180294233240561, 4952630157377898274696737335685702671936875565, 14696055335103512147287517333261883152095731129, 43607948816991592310568328563619809031581964086
Generating function in Maple syntax:
-(x-1)*(x^3+2*x-1)/(x^5-x^4+3*x^3-4*x^2+4*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(x^{3}+2 x -1\right)}{x^{5}-x^{4}+3 x^{3}-4 x^{2}+4 x -1}
Generating function in sympy syntax:
(1 - x)*(x**3 + 2*x - 1)/(x**5 - x**4 + 3*x**3 - 4*x**2 + 4*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^5-x^4+3*x^3-4*x^2+4*x-1)*F(x)+(x-1)*(x^3+2*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}-x^{4}+3 x^{3}-4 x^{2}+4 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{3}+2 x -1\right) = 0
Explicit closed form in Maple syntax:
-555/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+3)-555/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+3)-555/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+3)-555/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n+3)-555/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n+3)+257/2519*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+2)+257/2519*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+2)+257/2519*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+2)+257/2519*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n+2)+257/2519*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n+2)-105/458*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+1)-105/458*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+1)-105/458*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+1)-105/458*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n+1)-105/458*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n+1)-263/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n-1)-263/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n-1)-263/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n-1)-263/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n-1)-263/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n-1)+2407/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n)+2407/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n)+2407/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n)+2407/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n)+2407/5038*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{555 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{5038}-\frac{555 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{5038}-\frac{555 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{5038}-\frac{555 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{5038}-\frac{555 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{5038}+\frac{257 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{2519}+\frac{257 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{2519}+\frac{257 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{2519}+\frac{257 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{2519}+\frac{257 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{2519}-\frac{105 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{458}-\frac{105 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{458}-\frac{105 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{458}-\frac{105 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{458}-\frac{105 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{458}-\frac{263 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{5038}-\frac{263 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{5038}-\frac{263 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{5038}-\frac{263 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{5038}-\frac{263 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{5038}+\frac{2407 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{5038}+\frac{2407 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{5038}+\frac{2407 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{5038}+\frac{2407 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{5038}+\frac{2407 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{5038}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = a(n)-a(n+1)+3*a(n+2)-4*a(n+3)+4*a(n+4), n >= 5
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) = 19
a \! \left(n +5\right) = a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)-4 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18139/
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[14,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[7,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]+F[17,x]+F[45,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[31,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[16,x]+F[24,x]+F[29,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]+F[4,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[4,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[23,x]+F[7,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[2,x]+F[32,x]
F[35,x] = 2*F[16,x]+F[36,x]+F[43,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]+F[41,x]
F[39,x] = F[40,x]
F[40,x] = F[2,x]*F[4,x]
F[41,x] = F[42,x]
F[42,x] = F[38,x]*F[4,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[15,x]+F[35,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[58,x]
F[47,x] = F[2,x]+F[48,x]
F[48,x] = F[16,x]+F[49,x]+F[57,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[4,x]+F[52,x]
F[52,x] = F[16,x]+F[24,x]+F[53,x]
F[53,x] = F[4,x]*F[7,x]
F[54,x] = F[39,x]+F[55,x]
F[55,x] = 2*F[16,x]+F[36,x]+F[56,x]
F[56,x] = F[15,x]*F[4,x]
F[57,x] = F[4,x]*F[47,x]
F[58,x] = F[15,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_{14}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{45}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \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_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right)+F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{36}\! \left(x \right)+F_{43}\! \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_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{58}\! \left(x \right)
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{16}\! \left(x \right)+F_{49}\! \left(x \right)+F_{57}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)+F_{24}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{54}\! \left(x \right) = F_{39}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{36}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \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_14(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_7(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_45(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_31(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_16(x) + F_24(x) + F_29(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x) + F_4(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_4(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_23(x) + F_7(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_2(x) + F_32(x))
Eq(F_35(x), 2*F_16(x) + F_36(x) + F_43(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x) + F_41(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_2(x)*F_4(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_38(x)*F_4(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_15(x) + F_35(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_58(x))
Eq(F_47(x), F_2(x) + F_48(x))
Eq(F_48(x), F_16(x) + F_49(x) + F_57(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_4(x) + F_52(x))
Eq(F_52(x), F_16(x) + F_24(x) + F_53(x))
Eq(F_53(x), F_4(x)*F_7(x))
Eq(F_54(x), F_39(x) + F_55(x))
Eq(F_55(x), 2*F_16(x) + F_36(x) + F_56(x))
Eq(F_56(x), F_15(x)*F_4(x))
Eq(F_57(x), F_4(x)*F_47(x))
Eq(F_58(x), F_15(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, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": 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