0132_0213_0231_2031_2130
Counting sequence:
1, 1, 2, 6, 19, 57, 163, 453, 1239, 3357, 9040, 24237, 64762, 172573, 458811, 1217454, 3225137, 8531368, 22539608, 59484128, 156834905, 413164254, 1087641254, 2861344475, 7523323925, 19771236004, 51935931636, 136374915874, 357975400478, 939379872620, 2464415166522, 6463747884711, 16949801949658, 44439064783985, 116491548195104, 305324207002320, 800152049648911, 2096691773846366, 5493549441122895, 14392386370253557, 37703206625267991, 98762790900211256, 258691074168819067, 677556638052914311, 1774551200537683184, 4647427540403529712, 12170824636554239053, 31872237223764157083, 83462603743333869329, 218554435638895756087, 572291045508642009805, 1498528721336175132667, 3923783356809399049602, 10273956365457567892503, 26900724332490055793476, 70434350616371276893259, 184416587300211850647477, 482848561259237898687548, 1264206160819605242213223, 3309949074059528846830658, 8666057541229601184956570, 22689191747863335727113434, 59403768490181300299129719, 155527346169545745927042680, 407190433981643752165881540, 1066072233559039487411463609, 2791092004566926191980094751, 7307356602151973395265736854, 19131333069960447927045555118, 50087468505794715053993999400, 131132992427487057679585693312, 343315972188797303915693128666, 898825300313236015639108407448, 2353184050429705896299265391865, 6160782927075735655939288281244, 16129295091913803874536749109475, 42227405401493671564661840291926, 110553625624918445987065716698346, 289435109265775683508422531767285, 757755509578076181135620535876612, 1983840270612778790634537548685481, 5193785878674416846893337436066511, 13597565199769957433546732448801257, 35599020922029925122736040799248366, 93199756078198412230751762562989349, 244000848279771640803313260643321117, 638804185840372778957378496288598318, 1672414957056581438231896004094189338, 4378448235583769553904943903519468919, 11462947301906708062434881794218908317, 30010434474078735856085344743222045695, 78568450977987079514140824439717715097, 205695138977182461104876804148327670067, 538517478594087400262154913977998823433, 1409858488549718692237824236563346730516, 3691060757525231299615235715672004672689, 9663330224587712267448829398749934868942, 25298944888727430391482492404327353999353, 66233539248409842074734392528846217466463, 173401753772530572619266385966851728862938, 453971910176126304695981618220151633901485
Generating function in Maple syntax:
-(2*x-1)*(x^5-4*x^4+7*x^3-9*x^2+5*x-1)/(x^2-3*x+1)/(x^3-2*x^2+3*x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(x^{5}-4 x^{4}+7 x^{3}-9 x^{2}+5 x -1\right)}{\left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(1 - 2*x)*(x**5 - 4*x**4 + 7*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**2*(x**2 - 3*x + 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x^3-2*x^2+3*x-1)*(x-1)^2*F(x)+(2*x-1)*(x^5-4*x^4+7*x^3-9*x^2+5*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+\left(2 x -1\right) \left(x^{5}-4 x^{4}+7 x^{3}-9 x^{2}+5 x -1\right) = 0
Explicit closed form in Maple syntax:
1/13800*(-115*2^(2/3)*((3/23*I-1/23*3^(1/2))*23^(1/2)+I*3^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3)-4600+46*2^(1/3)*((-12/23*I-4/23*3^(1/2))*23^(1/2)+I*3^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(11/600*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*(115*2^(2/3)*((3/23*I+1/23*3^(1/2))*23^(1/2)+I*3^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)-4600-46*2^(1/3)*((-12/23*I+4/23*3^(1/2))*23^(1/2)+I*3^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*((-10*3^(1/2)*2^(2/3)*23^(1/2)-230*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)-4600+(16*23^(1/2)*3^(1/2)*2^(1/3)-92*2^(1/3))*(11+3*23^(1/2)*3^(1/2))^(2/3))*(1/300*2^(1/3)*(3*23^(1/2)*3^(1/2)-11)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/6*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*(1380*5^(1/2)+6900)*(3/2-1/2*5^(1/2))^(-n)+1/13800*(-1380*5^(1/2)+6900)*(3/2+1/2*5^(1/2))^(-n)-n+1
Explicit closed form in latex syntax:
\frac{\left(-115 \,2^{\frac{2}{3}} \left(\left(\frac{3 \,\mathrm{I}}{23}-\frac{\sqrt{3}}{23}\right) \sqrt{23}+\mathrm{I} \sqrt{3}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-4600+46 \,2^{\frac{1}{3}} \left(\left(-\frac{12 \,\mathrm{I}}{23}-\frac{4 \sqrt{3}}{23}\right) \sqrt{23}+\mathrm{I} \sqrt{3}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{11 \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}-\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}+\frac{\left(115 \,2^{\frac{2}{3}} \left(\left(\frac{3 \,\mathrm{I}}{23}+\frac{\sqrt{3}}{23}\right) \sqrt{23}+\mathrm{I} \sqrt{3}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-4600-46 \,2^{\frac{1}{3}} \left(\left(-\frac{12 \,\mathrm{I}}{23}+\frac{4 \sqrt{3}}{23}\right) \sqrt{23}+\mathrm{I} \sqrt{3}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}+\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}+\frac{\left(\left(-10 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{23}-230 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-4600+\left(16 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}-92 \,2^{\frac{1}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(3 \sqrt{23}\, \sqrt{3}-11\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{300}-\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{13800}+\frac{\left(1380 \sqrt{5}+6900\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{13800}+\frac{\left(-1380 \sqrt{5}+6900\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{13800}-n +1
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 57
a(6) = 163
a(n+5) = a(n)-5*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4)-n-1, 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) = 19
a \! \left(5\right) = 57
a \! \left(6\right) = 163
a \! \left(n +5\right) = a \! \left(n \right)-5 a \! \left(n +1\right)+10 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 a \! \left(n +4\right)-n -1, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18194/
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[12,x]*F[4,x]
F[4,x] = F[19,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[36,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[5,x]
F[23,x] = F[20,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[20,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[20,x]+F[31,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[30,x]
F[36,x] = F[37,x]+F[38,x]+F[88,x]
F[37,x] = 0
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[58,x]
F[40,x] = F[41,x]+F[6,x]
F[41,x] = F[37,x]+F[42,x]+F[50,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[10,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[44,x]
F[47,x] = F[17,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[47,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[13,x]+F[52,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[54,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[14,x]+F[53,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[52,x]
F[58,x] = F[36,x]+F[59,x]
F[59,x] = 2*F[37,x]+F[60,x]+F[80,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[77,x]
F[62,x] = F[63,x]+F[75,x]
F[63,x] = F[37,x]+F[64,x]+F[73,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[10,x]+F[67,x]
F[67,x] = F[18,x]+F[37,x]+F[42,x]
F[68,x] = F[63,x]+F[69,x]
F[69,x] = 2*F[37,x]+F[60,x]+F[70,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[31,x]+F[72,x]
F[72,x] = F[70,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[20,x]+F[63,x]
F[75,x] = F[76,x]
F[76,x] = F[12,x]*F[62,x]
F[77,x] = F[72,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]*F[77,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[71,x]+F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[31,x]+F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[82,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[71,x]+F[74,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{19}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{36}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{88}\! \left(x \right)
F_{37}\! \left(x \right) = 0
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{58}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{6}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)+F_{50}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right)+F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{58}\! \left(x \right) = F_{36}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{60}\! \left(x \right)+F_{80}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{77}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{75}\! \left(x \right)
F_{63}\! \left(x \right) = F_{37}\! \left(x \right)+F_{64}\! \left(x \right)+F_{73}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{10}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{68}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{60}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{31}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{20}\! \left(x \right)+F_{63}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{77}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{71}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{31}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_19(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_36(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_5(x))
Eq(F_23(x), F_20(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_20(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_20(x) + F_31(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_30(x))
Eq(F_36(x), F_37(x) + F_38(x) + F_88(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_58(x))
Eq(F_40(x), F_41(x) + F_6(x))
Eq(F_41(x), F_37(x) + F_42(x) + F_50(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_10(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_44(x))
Eq(F_47(x), F_17(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_47(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_13(x) + F_52(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_14(x) + F_53(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_52(x))
Eq(F_58(x), F_36(x) + F_59(x))
Eq(F_59(x), 2*F_37(x) + F_60(x) + F_80(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_77(x))
Eq(F_62(x), F_63(x) + F_75(x))
Eq(F_63(x), F_37(x) + F_64(x) + F_73(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_10(x) + F_67(x))
Eq(F_67(x), F_18(x) + F_37(x) + F_42(x))
Eq(F_68(x), F_63(x) + F_69(x))
Eq(F_69(x), 2*F_37(x) + F_60(x) + F_70(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_31(x) + F_72(x))
Eq(F_72(x), F_70(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_20(x) + F_63(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_12(x)*F_62(x))
Eq(F_77(x), F_72(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x)*F_77(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_71(x) + F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_31(x) + F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_82(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_71(x) + F_74(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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"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, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 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, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], 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[[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 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, 0], [1, 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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 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