0132_0231_1320_2031_2130
Counting sequence:
1, 1, 2, 6, 19, 58, 172, 500, 1433, 4066, 11456, 32118, 89731, 250066, 695656, 1932776, 5365025, 14882530, 41264492, 114374274, 316937467, 878095834, 2432510740, 6737946716, 18662570969, 51688568386, 143153663816, 396460159854, 1097965715779, 3040691314594, 8420769714448, 23319986197712, 64580685499649, 178844450628418, 495275873808788, 1371570298748538, 3798292357967131, 10518608418765418, 29129154736685212, 80667251228472452, 223391413525927769, 618636556402856482, 1713186331544834960, 4744315501025017830, 13138400026467958339, 36384077506993458802, 100758161189676969208, 279028832476784473784, 772712466524228044193, 2139866833838692894498, 5925917078574867646076, 16410597290622603153906, 45445742471556564842107, 125852548891471819282426, 348522504871181216686948, 965160714949027836676268, 2672812202378172994735769, 7401798424078270128440962, 20497743838848860755709336, 56764245402932876190314718, 157196791010200820057459587, 435323871898864008965340994, 1205539070954015211484013344, 3338490133702764702454429088, 9245255205511907418665155841, 25602814560704501792666133634, 70901678624139420717069837860, 196347476544895783887772863210, 543743565626592664960043540251, 1505784899069702096151684905098, 4169958608348770336267298657644, 11547834492045923435379283846868, 31979329767744145781560296265625, 88560113421306171676645020562786, 245248844991762067545906283179872, 679165751328807726466938593062998, 1880808522430134382980163452212995, 5208508660981691688916675918038034, 14423883211900416808031238637528456, 39943949497263029913746074931889032, 110616473941097038213301405046434081, 306329355538381848716544864785456482, 848315542172218232214790236122854028, 2349233744921183274870549192391598946, 6505715048133340218572246093361517819, 18016226941658309167978667098864045594, 49892199521777277670069679945718692020, 138166086671835878280473369931846496508, 382622287435446694778670599149070739545, 1059592975156397540604291111861856207042, 2934322724705813919072042115169887963880, 8125997486396955138905237850399965595726, 22503262709642377493277426583098039373507, 62318113367237848170058012084476389175010, 172577074878471835975919703661555791119920, 477916373977827464891214237764938418303600, 1323490160422263262148252446281034642456577, 3665131182167463868090405653866318879167426, 10149819760058015228136064451336055571312052, 28107818258428963920709811542929272793150810, 77838766197396578086571318624330862319158811
Generating function in Maple syntax:
(x^5-2*x^4+4*x^3-8*x^2+5*x-1)/(x-1)/(2*x-1)/(x^3-x^2+3*x-1)
Generating function in latex syntax:
\frac{x^{5}-2 x^{4}+4 x^{3}-8 x^{2}+5 x -1}{\left(x -1\right) \left(2 x -1\right) \left(x^{3}-x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(x**5 - 2*x**4 + 4*x**3 - 8*x**2 + 5*x - 1)/((x - 1)*(2*x - 1)*(x**3 - x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x-1)*(x^3-x^2+3*x-1)*F(x)-x^5+2*x^4-4*x^3+8*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x -1\right) \left(x^{3}-x^{2}+3 x -1\right) F \! \left(x \right)-x^{5}+2 x^{4}-4 x^{3}+8 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/14592*(((-304*I-48*19^(1/2))*3^(1/2)-144*I*19^(1/2)-304)*(1+3*19^(1/2)*3^(1/2))^(1/3)+2432+((133*I+15*19^(1/2))*3^(1/2)-45*I*19^(1/2)-133)*(1+3*19^(1/2)*3^(1/2))^(2/3))*(1/384*((I+3*19^(1/2))*3^(1/2)-9*I*19^(1/2)-1)*(1+3*19^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(1+3*19^(1/2)*3^(1/2))^(1/3)-1/6*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)+1/14592*(((-133*I+15*19^(1/2))*3^(1/2)+45*I*19^(1/2)-133)*(1+3*19^(1/2)*3^(1/2))^(2/3)+2432+((304*I-48*19^(1/2))*3^(1/2)+144*I*19^(1/2)-304)*(1+3*19^(1/2)*3^(1/2))^(1/3))*(1/384*((-I+3*19^(1/2))*3^(1/2)+9*I*19^(1/2)-1)*(1+3*19^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(1+3*19^(1/2)*3^(1/2))^(1/3)-1/6*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)+1/14592*((-30*19^(1/2)*3^(1/2)+266)*(1+3*19^(1/2)*3^(1/2))^(2/3)+96*(1+3*19^(1/2)*3^(1/2))^(1/3)*19^(1/2)*3^(1/2)+608*(1+3*19^(1/2)*3^(1/2))^(1/3)+2432)*(1/3*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3+1/192*(1+3*19^(1/2)*3^(1/2))^(2/3)-1/64*(1+3*19^(1/2)*3^(1/2))^(2/3)*19^(1/2)*3^(1/2))^(-n)-2^(n-1)+1/2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(\left(-304 \,\mathrm{I}-48 \sqrt{19}\right) \sqrt{3}-144 \,\mathrm{I} \sqrt{19}-304\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}+2432+\left(\left(133 \,\mathrm{I}+15 \sqrt{19}\right) \sqrt{3}-45 \,\mathrm{I} \sqrt{19}-133\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(\mathrm{I}+3 \sqrt{19}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{19}-1\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}-\frac{\mathrm{I} \sqrt{3}\, \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{14592}\\+\\\frac{\left(\left(\left(-133 \,\mathrm{I}+15 \sqrt{19}\right) \sqrt{3}+45 \,\mathrm{I} \sqrt{19}-133\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}+2432+\left(\left(304 \,\mathrm{I}-48 \sqrt{19}\right) \sqrt{3}+144 \,\mathrm{I} \sqrt{19}-304\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-\mathrm{I}+3 \sqrt{19}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{19}-1\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}+\frac{\mathrm{I} \sqrt{3}\, \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{14592}\\+\\\frac{\left(\left(-30 \sqrt{19}\, \sqrt{3}+266\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}+96 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{19}\, \sqrt{3}+608 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}+2432\right) \left(\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}+\frac{1}{3}+\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{192}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{19}\, \sqrt{3}}{64}\right)^{-n}}{14592}\\-2^{n -1}+\frac{1}{2} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(n+4) = -2*a(n)+3*a(n+1)-7*a(n+2)+5*a(n+3)+1, 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) = 19
a \! \left(5\right) = 58
a \! \left(n +4\right) = -2 a \! \left(n \right)+3 a \! \left(n +1\right)-7 a \! \left(n +2\right)+5 a \! \left(n +3\right)+1, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19147/
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[22,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[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[17,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[26,x]+F[9,x]
F[26,x] = F[23,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[26,x]
F[29,x] = F[18,x]+F[30,x]+F[81,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[51,x]
F[32,x] = F[33,x]+F[6,x]
F[33,x] = F[18,x]+F[34,x]+F[37,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[10,x]+F[36,x]
F[36,x] = F[34,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[43,x]
F[39,x] = F[12,x]+F[40,x]
F[40,x] = F[18,x]+F[41,x]+F[42,x]
F[41,x] = F[10,x]*F[12,x]
F[42,x] = F[12,x]*F[39,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[12,x]+F[44,x]
F[47,x] = 2*F[18,x]+F[48,x]+F[50,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[40,x]+F[47,x]
F[50,x] = F[12,x]*F[43,x]
F[51,x] = F[29,x]+F[52,x]
F[52,x] = 2*F[18,x]+F[53,x]+F[71,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[70,x]
F[55,x] = F[18,x]+F[56,x]+F[68,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[60,x]
F[58,x] = F[10,x]+F[59,x]
F[59,x] = F[18,x]+F[34,x]+F[42,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = 2*F[18,x]+F[53,x]+F[62,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]+F[66,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]*F[23,x]
F[66,x] = 2*F[18,x]+F[62,x]+F[67,x]
F[67,x] = F[12,x]*F[55,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[23,x]+F[55,x]
F[70,x] = F[53,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[63,x]+F[73,x]
F[73,x] = F[74,x]+F[77,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[64,x]+F[74,x]
F[77,x] = 3*F[18,x]+F[78,x]+F[80,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[66,x]+F[77,x]
F[80,x] = F[12,x]*F[73,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[69,x]+F[83,x]
F[83,x] = F[84,x]+F[87,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[86,x]
F[86,x] = F[23,x]+F[84,x]
F[87,x] = 2*F[18,x]+F[88,x]+F[90,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[55,x]+F[87,x]
F[90,x] = F[12,x]*F[83,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_{22}\! \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_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{81}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{51}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{10}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \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) = 2 F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{51}\! \left(x \right) = F_{29}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{71}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{70}\! \left(x \right)
F_{55}\! \left(x \right) = F_{18}\! \left(x \right)+F_{56}\! \left(x \right)+F_{68}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{10}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{23}\! \left(x \right)+F_{55}\! \left(x \right)
F_{70}\! \left(x \right) = F_{53}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{63}\! \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_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{64}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{66}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{69}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{23}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{55}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \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_22(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) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_17(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_9(x))
Eq(F_26(x), F_23(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_26(x))
Eq(F_29(x), F_18(x) + F_30(x) + F_81(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_51(x))
Eq(F_32(x), F_33(x) + F_6(x))
Eq(F_33(x), F_18(x) + F_34(x) + F_37(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_10(x) + F_36(x))
Eq(F_36(x), F_34(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_43(x))
Eq(F_39(x), F_12(x) + F_40(x))
Eq(F_40(x), F_18(x) + F_41(x) + F_42(x))
Eq(F_41(x), F_10(x)*F_12(x))
Eq(F_42(x), F_12(x)*F_39(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_12(x) + F_44(x))
Eq(F_47(x), 2*F_18(x) + F_48(x) + F_50(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_40(x) + F_47(x))
Eq(F_50(x), F_12(x)*F_43(x))
Eq(F_51(x), F_29(x) + F_52(x))
Eq(F_52(x), 2*F_18(x) + F_53(x) + F_71(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_70(x))
Eq(F_55(x), F_18(x) + F_56(x) + F_68(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_60(x))
Eq(F_58(x), F_10(x) + F_59(x))
Eq(F_59(x), F_18(x) + F_34(x) + F_42(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), 2*F_18(x) + F_53(x) + F_62(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_66(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x)*F_23(x))
Eq(F_66(x), 2*F_18(x) + F_62(x) + F_67(x))
Eq(F_67(x), F_12(x)*F_55(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_23(x) + F_55(x))
Eq(F_70(x), F_53(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_63(x) + F_73(x))
Eq(F_73(x), F_74(x) + F_77(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_64(x) + F_74(x))
Eq(F_77(x), 3*F_18(x) + F_78(x) + F_80(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_66(x) + F_77(x))
Eq(F_80(x), F_12(x)*F_73(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_69(x) + F_83(x))
Eq(F_83(x), F_84(x) + F_87(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_86(x))
Eq(F_86(x), F_23(x) + F_84(x))
Eq(F_87(x), 2*F_18(x) + F_88(x) + F_90(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_55(x) + F_87(x))
Eq(F_90(x), F_12(x)*F_83(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:
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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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "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": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 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": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 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], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": 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"Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[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": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 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], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 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": [[1, 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": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 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