0132_0321_1032_1230
Counting sequence:
1, 1, 2, 6, 20, 64, 202, 636, 2002, 6302, 19838, 62448, 196580, 618814, 1947964, 6131994, 19302898, 60763574, 191277596, 602122560, 1895421026, 5966594020, 18782235562, 59124581214, 186118212190, 585881340680, 1844295307364, 5805655419606, 18275617097012, 57529797436594, 181097993874946, 570078200287014, 1794548616959812, 5649057860853152, 17782663792820186, 55978030205681100, 176213187305116994, 554701322396244862, 1746143757875309566, 5496684251617620672, 17303007055240798852, 54468119223985642958, 171460139981837795948, 539739209310635053770, 1699044536521012470194, 5348420658133982515414, 16836288232283527704844, 52998935491253175743328, 166835297926296102374194, 525180673463708409971636, 1653215735567198508507290, 5204156219803964906488446, 16382158345977972510403550, 51569380460067193830656152, 162335203022138822697902404, 511014829054331681810044710, 1608623087610977452977127780, 5063783066303053589176279394, 15940277831433613679583778946, 50178385214436271403783405382, 157956490429747298165558564084, 497231083907113992130467819136, 1565233249553650345428978989674, 4927196236923006703490071065372, 15510316282938189769803815111602, 48824909670537389314174026239966, 153695886070257994650774730690430, 483819131552358000430380659153424, 1523013777669195407083372470782372, 4794293602089965621693122636359646, 15091952206904634265952753792244892, 47507941799017835605815019730683002, 149550204177447405247094940182356978, 470768943519640748436887455329623798, 1481933103345238613612080020502107260, 4664975786999479614384752656201914624, 14684872781481843365139658018630960514, 46226496868274173231016454126420205444, 145516344915650642443031595105989854858, 458070761839261893444216676063329763614, 1441960509478369819678788373061769695326, 4539146097311344240825535059163079345320, 14288773622649529397709991793530338058916, 44979616708142454688042150369693883895030, 141591292061932574799864161157347600748692, 445715091745952464533040185313839089368594, 1403066107506154588420610408153007439123330, 4416710446848693534883185237827860089136230, 13903358556622262838803949912166257128543524, 43766368993449125338986854343334455685888736, 137772110750778406374418752874666911447060602, 433692694579388512319518398380830535859119724, 1365220815058667955493804189242655864781185826, 4297577287247284691391080314702798762994444734, 13528339398392523411402427089464057993493341182, 42585846546886907526930271602990491549771216352, 134055945279617344564904885458272590981599286596, 421994580876201179090231154113582947270576838510, 1328396334212839590193140231682504507687280710604, 4181657539502372168066772349847541779918991613482, 13163435736247171080777899858456236543884701160626
Generating function in Maple syntax:
-(x-1)*(x^3+x^2+2*x-1)/(x^3-3*x^2+4*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(x^{3}+x^{2}+2 x -1\right)}{x^{3}-3 x^{2}+4 x -1}
Generating function in sympy syntax:
(1 - x)*(x**3 + x**2 + 2*x - 1)/(x**3 - 3*x**2 + 4*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^3-3*x^2+4*x-1)*F(x)+(x-1)*(x^3+x^2+2*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-3 x^{2}+4 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{3}+x^{2}+2 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/1116*(-39*((I*3^(1/3)-1/3*3^(5/6))*31^(1/2)-31/13*I*3^(5/6)+31/13*3^(1/3))*2^(2/3)*(9+31^(1/2)*3^(1/2))^(1/3)+1488-12*((I*3^(2/3)+3^(1/6))*31^(1/2)-31/2*I*3^(1/6)-31/6*3^(2/3))*2^(1/3)*(9+31^(1/2)*3^(1/2))^(2/3))*(1/12*(108+12*31^(1/2)*3^(1/2))^(1/3)-1/12*I*(36+4*31^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1+1/24*((-I*31^(1/2)+3)*18^(1/3)+9*I*2^(1/3)*3^(1/6)-31^(1/2)*3^(1/6)*2^(1/3))*(9+31^(1/2)*3^(1/2))^(2/3))^(-n)+1/1116*(39*2^(2/3)*((I*3^(1/3)+1/3*3^(5/6))*31^(1/2)-31/13*I*3^(5/6)-31/13*3^(1/3))*(9+31^(1/2)*3^(1/2))^(1/3)+1488+12*2^(1/3)*((I*3^(2/3)-3^(1/6))*31^(1/2)-31/2*I*3^(1/6)+31/6*3^(2/3))*(9+31^(1/2)*3^(1/2))^(2/3))*(1/12*(108+12*31^(1/2)*3^(1/2))^(1/3)+1/12*I*(36+4*31^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1+1/24*((I*31^(1/2)+3)*18^(1/3)-9*I*2^(1/3)*3^(1/6)-31^(1/2)*3^(1/6)*2^(1/3))*(9+31^(1/2)*3^(1/2))^(2/3))^(-n)-13/558*(2^(2/3)*(31^(1/2)*3^(5/6)-93/13*3^(1/3))*(9+31^(1/2)*3^(1/2))^(1/3)-744/13-12/13*(3^(1/6)*31^(1/2)-31/6*3^(2/3))*2^(1/3)*(9+31^(1/2)*3^(1/2))^(2/3))*(-1/6*(108+12*31^(1/2)*3^(1/2))^(1/3)+1+1/12*(31^(1/2)*3^(1/6)*2^(1/3)-3*18^(1/3))*(9+31^(1/2)*3^(1/2))^(2/3))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-39 \left(\left(\mathrm{I} \,3^{\frac{1}{3}}-\frac{3^{\frac{5}{6}}}{3}\right) \sqrt{31}-\frac{31 \,\mathrm{I} \,3^{\frac{5}{6}}}{13}+\frac{31 \,3^{\frac{1}{3}}}{13}\right) 2^{\frac{2}{3}} \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+1488-12 \left(\left(\mathrm{I} \,3^{\frac{2}{3}}+3^{\frac{1}{6}}\right) \sqrt{31}-\frac{31 \,\mathrm{I} \,3^{\frac{1}{6}}}{2}-\frac{31 \,3^{\frac{2}{3}}}{6}\right) 2^{\frac{1}{3}} \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(108+12 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\mathrm{I} \left(36+4 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}}{12}+1+\frac{\left(\left(-\mathrm{I} \sqrt{31}+3\right) 18^{\frac{1}{3}}+9 \,\mathrm{I} \,2^{\frac{1}{3}} 3^{\frac{1}{6}}-\sqrt{31}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}\right)^{-n}}{1116}\\+\\\frac{\left(39 \,2^{\frac{2}{3}} \left(\left(\mathrm{I} \,3^{\frac{1}{3}}+\frac{3^{\frac{5}{6}}}{3}\right) \sqrt{31}-\frac{31 \,\mathrm{I} \,3^{\frac{5}{6}}}{13}-\frac{31 \,3^{\frac{1}{3}}}{13}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+1488+12 \,2^{\frac{1}{3}} \left(\left(\mathrm{I} \,3^{\frac{2}{3}}-3^{\frac{1}{6}}\right) \sqrt{31}-\frac{31 \,\mathrm{I} \,3^{\frac{1}{6}}}{2}+\frac{31 \,3^{\frac{2}{3}}}{6}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(108+12 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\mathrm{I} \left(36+4 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}}{12}+1+\frac{\left(\left(\mathrm{I} \sqrt{31}+3\right) 18^{\frac{1}{3}}-9 \,\mathrm{I} \,2^{\frac{1}{3}} 3^{\frac{1}{6}}-\sqrt{31}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}\right)^{-n}}{1116}\\-\\\frac{13 \left(2^{\frac{2}{3}} \left(\sqrt{31}\, 3^{\frac{5}{6}}-\frac{93 \,3^{\frac{1}{3}}}{13}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{744}{13}-\frac{12 \left(3^{\frac{1}{6}} \sqrt{31}-\frac{31 \,3^{\frac{2}{3}}}{6}\right) 2^{\frac{1}{3}} \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{13}\right) \left(-\frac{\left(108+12 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+1+\frac{\left(\sqrt{31}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}-3 \,18^{\frac{1}{3}}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}\right)^{-n}}{558} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+3) = a(n)-3*a(n+1)+4*a(n+2), 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) = 20
a \! \left(n +3\right) = a \! \left(n \right)-3 a \! \left(n +1\right)+4 a \! \left(n +2\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15423/
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[24,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[12,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[10,x]*F[12,x]
F[23,x] = F[12,x]*F[13,x]
F[24,x] = F[25,x]+F[45,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[16,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = F[18,x]+F[33,x]+F[43,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[12,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = x^2
F[38,x] = F[39,x]+F[41,x]
F[39,x] = F[18,x]+F[33,x]+F[40,x]
F[40,x] = F[12,x]*F[25,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[39,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[25,x]+F[39,x]
F[45,x] = F[18,x]+F[46,x]+F[75,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[55,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[18,x]+F[50,x]+F[53,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[10,x]+F[52,x]
F[52,x] = F[18,x]+F[22,x]+F[53,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[12,x]+F[52,x]
F[55,x] = F[56,x]+F[59,x]
F[56,x] = F[18,x]+F[46,x]+F[57,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[25,x]+F[56,x]
F[59,x] = F[18,x]+F[60,x]+F[71,x]+F[73,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[21,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[12,x]*F[52,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = 2*F[18,x]+F[60,x]+F[67,x]
F[67,x] = F[12,x]*F[56,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[18,x]+F[60,x]+F[67,x]+F[71,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[39,x]+F[70,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[56,x]+F[70,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[58,x]+F[77,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = F[18,x]+F[33,x]+F[79,x]
F[79,x] = F[12,x]*F[44,x]
F[80,x] = F[18,x]+F[60,x]+F[81,x]+F[83,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[56,x]+F[66,x]
F[83,x] = F[12,x]*F[77,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_{24}\! \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_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \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_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{43}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = x^{2}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{25}\! \left(x \right)+F_{39}\! \left(x \right)
F_{45}\! \left(x \right) = F_{18}\! \left(x \right)+F_{46}\! \left(x \right)+F_{75}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{18}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{10}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)+F_{46}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \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_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{39}\! \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_{56}\! \left(x \right)+F_{70}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{58}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right)+F_{60}\! \left(x \right)+F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{56}\! \left(x \right)+F_{66}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \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_24(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_12(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_10(x)*F_12(x))
Eq(F_23(x), F_12(x)*F_13(x))
Eq(F_24(x), F_25(x) + F_45(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_16(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), F_18(x) + F_33(x) + F_43(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_12(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), x**2)
Eq(F_38(x), F_39(x) + F_41(x))
Eq(F_39(x), F_18(x) + F_33(x) + F_40(x))
Eq(F_40(x), F_12(x)*F_25(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_39(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_25(x) + F_39(x))
Eq(F_45(x), F_18(x) + F_46(x) + F_75(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_55(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_18(x) + F_50(x) + F_53(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_10(x) + F_52(x))
Eq(F_52(x), F_18(x) + F_22(x) + F_53(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_12(x) + F_52(x))
Eq(F_55(x), F_56(x) + F_59(x))
Eq(F_56(x), F_18(x) + F_46(x) + F_57(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_25(x) + F_56(x))
Eq(F_59(x), F_18(x) + F_60(x) + F_71(x) + F_73(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_21(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_52(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), 2*F_18(x) + F_60(x) + F_67(x))
Eq(F_67(x), F_12(x)*F_56(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_18(x) + F_60(x) + F_67(x) + F_71(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_39(x) + F_70(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_56(x) + F_70(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_58(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_18(x) + F_33(x) + F_79(x))
Eq(F_79(x), F_12(x)*F_44(x))
Eq(F_80(x), F_18(x) + F_60(x) + F_81(x) + F_83(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_56(x) + F_66(x))
Eq(F_83(x), F_12(x)*F_77(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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [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": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"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], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 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, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [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, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 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