0213_0231_1032_1302_3012
Counting sequence:
1, 1, 2, 6, 19, 54, 147, 395, 1056, 2814, 7480, 19843, 52552, 138981, 367105, 968642, 2553484, 6725896, 17703443, 46568640, 122430705, 321718983, 845040518, 2218782604, 5823814352, 15281735833, 40088985206, 105142352257, 275703360243, 722816921620, 1894721539176, 4965937001966, 13013758308925, 34100139973860, 89344319381459, 234066856221029, 613167849944606, 1606161077269502, 4206999369558594, 11018751827839913, 28858356911529368, 75577475694280287, 197923253735204967, 518306623425519066, 1357262419943650734, 3554098554347853214, 9306469728036756587, 24368650052090417930, 63807243643287226071, 167071128163210291799, 437448095694883287520, 1145370692111233151178, 2998890717796556662392, 7851828561220610802491, 20557820324566110232220, 53824481025853615918977, 140922244975662930591349, 368957648701088797492506, 965986489695503836690008, 2529085018711884786780800, 6621461979083689618291995, 17335750548384777578411268, 45386834928646807532814133, 118827184178236490341655539, 311100366532798464135597142, 814487047581580777768093368, 2132391304783418740312290496, 5582757837086992105837130417, 14616047192450979698619900058, 38265767286121054900091870605, 100182146301848981151690367991, 262282744421499483306365399676, 686670905642851768631564318340, 1797741174579452328828065340870, 4706578659754363731594914252549, 12322055344195623694568207977864, 32259728110123141316699474053271, 84457456160680591005818728724737, 221113400960369720851054257565934, 578884514874058891462249415594698, 1515544254120302525730103527735858, 3967757803143525851631776585367697, 10387751369516945702402458776217932, 27195547947172464515674276089846251, 71199012524539243444345648855054699, 186401768714738016769578388415249874, 488006942421240621781684787833583402, 1277620566829634587022655632896035590, 3344858264394776475745446259340284211, 8756962377576299187614111546403917534, 22926047817625358194827024944547783435, 60021225127057391361715680327195937763, 157137729971458793916806322428836015232, 411392202856830929646194908619463369126, 1077039432043503472706129372666372409960, 2819727379875976021036749180161602277187, 7382145698571887171986575763350794296464, 19326716669041949652225589924160781721741, 50598020472788125625997670231658782864073, 132467382326607853016667083405389620512210, 346804213863625647271390227257447776716660
Generating function in Maple syntax:
-(x^7-4*x^6+6*x^5-6*x^4+12*x^3-13*x^2+6*x-1)/(x-1)/(x^2-3*x+1)/(x^3-2*x^2+3*x-1)
Generating function in latex syntax:
-\frac{x^{7}-4 x^{6}+6 x^{5}-6 x^{4}+12 x^{3}-13 x^{2}+6 x -1}{\left(x -1\right) \left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(-x**7 + 4*x**6 - 6*x**5 + 6*x**4 - 12*x**3 + 13*x**2 - 6*x + 1)/((x - 1)*(x**2 - 3*x + 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2-3*x+1)*(x^3-2*x^2+3*x-1)*F(x)+x^7-4*x^6+6*x^5-6*x^4+12*x^3-13*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right) F \! \left(x \right)+x^{7}-4 x^{6}+6 x^{5}-6 x^{4}+12 x^{3}-13 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/13800*(-460*2^(2/3)*((I-7/46*23^(1/2))*3^(1/2)+21/46*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200+391*2^(1/3)*((I-43/391*23^(1/2))*3^(1/2)-129/391*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(11/600*2^(1/3)*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*(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*(460*2^(2/3)*((I+7/46*23^(1/2))*3^(1/2)+21/46*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200-391*((I+43/391*23^(1/2))*3^(1/2)-129/391*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*2^(1/3)*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*(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*((-140*3^(1/2)*2^(2/3)*23^(1/2)-920*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200+(86*23^(1/2)*3^(1/2)*2^(1/3)-782*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*(-2760*5^(1/2)+13800)*(3/2-1/2*5^(1/2))^(-n)-1+1/13800*(2760*5^(1/2)+13800)*(3/2+1/2*5^(1/2))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-460 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{7 \sqrt{23}}{46}\right) \sqrt{3}+\frac{21 \,\mathrm{I} \sqrt{23}}{46}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200+391 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{43 \sqrt{23}}{391}\right) \sqrt{3}-\frac{129 \,\mathrm{I} \sqrt{23}}{391}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) \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(460 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{7 \sqrt{23}}{46}\right) \sqrt{3}+\frac{21 \,\mathrm{I} \sqrt{23}}{46}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200-391 \left(\left(\mathrm{I}+\frac{43 \sqrt{23}}{391}\right) \sqrt{3}-\frac{129 \,\mathrm{I} \sqrt{23}}{391}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) \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(-140 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{23}-920 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200+\left(86 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}-782 \,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(-2760 \sqrt{5}+13800\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{13800}-1+\\\frac{\left(2760 \sqrt{5}+13800\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{13800} & \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) = 54
a(6) = 147
a(7) = 395
a(n+5) = a(n)-5*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4)-1, n >= 8
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) = 54
a \! \left(6\right) = 147
a \! \left(7\right) = 395
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)-1, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/20313/
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[17,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[6,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[11,x]
F[17,x] = F[18,x]+F[37,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[35,x]
F[23,x] = 0
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]+F[4,x]
F[27,x] = F[28,x]
F[28,x] = F[14,x]*F[4,x]
F[29,x] = F[30,x]+F[32,x]
F[30,x] = F[23,x]+F[24,x]+F[31,x]
F[31,x] = F[18,x]*F[4,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[18,x]+F[34,x]
F[37,x] = F[23,x]+F[38,x]+F[65,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[49,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[1,x]+F[41,x]
F[44,x] = F[23,x]+F[45,x]+F[47,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[41,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[14,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[23,x]+F[38,x]+F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[18,x]+F[50,x]
F[53,x] = F[23,x]+F[54,x]+F[61,x]+F[63,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[58,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[41,x]
F[58,x] = F[59,x]
F[59,x] = 2*F[23,x]+F[54,x]+F[60,x]
F[60,x] = F[4,x]*F[50,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[50,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[34,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[17,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[36,x]+F[70,x]
F[70,x] = F[68,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_{17}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{23}\! \left(x \right) = 0
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_{29}\! \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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \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_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{65}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{49}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{23}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{41}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right)+F_{54}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{50}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{17}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{36}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \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_17(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_6(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_11(x))
Eq(F_17(x), F_18(x) + F_37(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_35(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x) + F_4(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_14(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_32(x))
Eq(F_30(x), F_23(x) + F_24(x) + F_31(x))
Eq(F_31(x), F_18(x)*F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_18(x) + F_34(x))
Eq(F_37(x), F_23(x) + F_38(x) + F_65(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_49(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_41(x))
Eq(F_44(x), F_23(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_41(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_14(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_23(x) + F_38(x) + F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_18(x) + F_50(x))
Eq(F_53(x), F_23(x) + F_54(x) + F_61(x) + F_63(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_58(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_41(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), 2*F_23(x) + F_54(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_50(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_50(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_34(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_17(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_36(x) + F_70(x))
Eq(F_70(x), F_68(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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