0231_1032_1230_2031
Counting sequence:
1, 1, 2, 6, 20, 66, 215, 695, 2235, 7159, 22859, 72804, 231395, 734208, 2326397, 7363016, 23282106, 73562191, 232279691, 733060566, 2312489960, 7292285298, 22988889695, 72454438832, 228308951682, 719294874364, 2265841984412, 7136763481311, 22476601588421, 70782322905237, 222889566628169, 701827483247831, 2209788991308216, 6957519804143581, 21905044456679468, 68963964875915187, 217115413617943490, 683519749870920720, 2151814392536228591, 6774121795671265823, 21325370270480347632, 67133041572521799700, 211335705214018306484, 665283538743012850689, 2094297969964891426910, 6592776163697640217554, 20753753979135810562760, 65331665287052851637546, 205659955353917619793647, 647403239580258110355019, 2037976957706747555553419, 6415390007874768501042171, 20195116019102579296286423, 63572489933488593792741624, 200120574832365419600233499, 629961446068634683215078824, 1983060478124695674723522153, 6242488433846001682566499552, 19650760672827062623591586582, 61858708360419708210516183939, 194725224408869439686952841895, 612976016389998308750017687230, 1929588365630836667147121895496, 6074153949410364699007404542270, 19120835387146345611286928221743, 60190490764359177022136578131340, 189473670270522793466336145277526, 596444199753130208941287456587520, 1877546686271107536468831800722796, 5910328882435979804228396792978319, 18605122462399183387499612837974961, 58567057197365853895225197794043173, 184363209419404245315908430904650045, 580356838643219851023848882402361883, 1826904914663233866124790771223865436, 5750912695500982940930819738868084477, 18103293775581157024852744798493953628, 56987344283897731383995983701192918615, 179390414665663185117634549731659524202, 564702935717072128247984408419460680940, 1777627885385476216021496185994277602667, 5595793259616658820550483306083142104395, 17614992607477920703659414569857238394656, 55450219294238801236738843794805176968172, 174551694598062315718447047023538208989176, 549471118310991803385258228775381393934961, 1729679622342037924114592658065270603008778, 5444856864633314147979501956181353020536158, 17139859803020342404342702928734056933735228, 53954548484530012895738084089521788495070370, 169843472032509774131094071433830308589117447, 534650104151915159282884576527717493754781231, 1683024553373181169144943354389819569206699435, 5297991384532602738353681454750484730581353615, 16677542012173604060226234239890864856289587267, 52499218527039139794387729976953297619679675180, 165262239661865580078459126817114831943777865219, 520228845617040845421200342072910080865343053136, 1637627883419475572191480861129284717225314810981, 5155087240179732364993488184556210453082816475944, 16227694165740934895111161271919923134046493583682
Generating function in Maple syntax:
(x^5-2*x^4+6*x^3-11*x^2+6*x-1)/(x^2-3*x+1)/(x^3-3*x^2+4*x-1)
Generating function in latex syntax:
\frac{x^{5}-2 x^{4}+6 x^{3}-11 x^{2}+6 x -1}{\left(x^{2}-3 x +1\right) \left(x^{3}-3 x^{2}+4 x -1\right)}
Generating function in sympy syntax:
(x**5 - 2*x**4 + 6*x**3 - 11*x**2 + 6*x - 1)/((x**2 - 3*x + 1)*(x**3 - 3*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x^3-3*x^2+4*x-1)*F(x)-x^5+2*x^4-6*x^3+11*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x^{3}-3 x^{2}+4 x -1\right) F \! \left(x \right)-x^{5}+2 x^{4}-6 x^{3}+11 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/11160*(-15*2^(2/3)*((I*3^(1/3)-1/3*3^(5/6))*31^(1/2)+31*I*3^(5/6)-31*3^(1/3))*(9+31^(1/2)*3^(1/2))^(1/3)+7440-255*((I*3^(2/3)+3^(1/6))*31^(1/2)-155/17*I*3^(1/6)-155/51*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)+1/11160*(15*((I*3^(1/3)+1/3*3^(5/6))*31^(1/2)+31*I*3^(5/6)+31*3^(1/3))*2^(2/3)*(9+31^(1/2)*3^(1/2))^(1/3)+7440+255*((I*3^(2/3)-3^(1/6))*31^(1/2)-155/17*I*3^(1/6)+155/51*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)+1/11160*(-10*2^(2/3)*(31^(1/2)*3^(5/6)+93*3^(1/3))*(9+31^(1/2)*3^(1/2))^(1/3)+7440+510*2^(1/3)*(3^(1/6)*31^(1/2)-155/51*3^(2/3))*(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)+1/11160*(4464*5^(1/2)-11160)*(3/2-1/2*5^(1/2))^(-n)-2/5*(3/2+1/2*5^(1/2))^(-n)*(5^(1/2)+5/2))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(-15 \,2^{\frac{2}{3}} \left(\left(\mathrm{I} \,3^{\frac{1}{3}}-\frac{3^{\frac{5}{6}}}{3}\right) \sqrt{31}+31 \,\mathrm{I} \,3^{\frac{5}{6}}-31 \,3^{\frac{1}{3}}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+7440-255 \left(\left(\mathrm{I} \,3^{\frac{2}{3}}+3^{\frac{1}{6}}\right) \sqrt{31}-\frac{155 \,\mathrm{I} \,3^{\frac{1}{6}}}{17}-\frac{155 \,3^{\frac{2}{3}}}{51}\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}}{11160}\\+\\\frac{\left(15 \left(\left(\mathrm{I} \,3^{\frac{1}{3}}+\frac{3^{\frac{5}{6}}}{3}\right) \sqrt{31}+31 \,\mathrm{I} \,3^{\frac{5}{6}}+31 \,3^{\frac{1}{3}}\right) 2^{\frac{2}{3}} \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+7440+255 \left(\left(\mathrm{I} \,3^{\frac{2}{3}}-3^{\frac{1}{6}}\right) \sqrt{31}-\frac{155 \,\mathrm{I} \,3^{\frac{1}{6}}}{17}+\frac{155 \,3^{\frac{2}{3}}}{51}\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}}{11160}\\+\\\frac{\left(-10 \,2^{\frac{2}{3}} \left(\sqrt{31}\, 3^{\frac{5}{6}}+93 \,3^{\frac{1}{3}}\right) \left(9+\sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+7440+510 \,2^{\frac{1}{3}} \left(3^{\frac{1}{6}} \sqrt{31}-\frac{155 \,3^{\frac{2}{3}}}{51}\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}}}{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}}{11160}\\+\frac{\left(4464 \sqrt{5}-11160\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{11160}-\frac{2 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \left(\sqrt{5}+\frac{5}{2}\right)}{5} & \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(5) = 66
a(n+5) = a(n)-6*a(n+1)+14*a(n+2)-16*a(n+3)+7*a(n+4), 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) = 20
a \! \left(5\right) = 66
a \! \left(n +5\right) = a \! \left(n \right)-6 a \! \left(n +1\right)+14 a \! \left(n +2\right)-16 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21438/
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[10,x]*F[4,x]
F[4,x] = F[13,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[10,x]*F[7,x]
F[7,x] = F[5,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[11,x]*F[7,x]
F[10,x] = x
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[10,x]*F[11,x]
F[13,x] = F[14,x]
F[14,x] = F[10,x]*F[15,x]*F[5,x]
F[15,x] = F[16,x]+F[27,x]
F[16,x] = F[11,x]+F[17,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[10,x]*F[20,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[23,x]+F[26,x]
F[22,x] = 0
F[23,x] = F[10,x]*F[24,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[12,x]
F[26,x] = F[10,x]*F[17,x]
F[27,x] = F[28,x]+F[70,x]
F[28,x] = F[29,x]+F[47,x]
F[29,x] = F[30,x]
F[30,x] = F[10,x]*F[31,x]
F[31,x] = F[20,x]+F[32,x]
F[32,x] = F[29,x]+F[33,x]
F[33,x] = F[22,x]+F[34,x]+F[45,x]
F[34,x] = F[10,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[10,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[10,x]*F[18,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = F[22,x]+F[34,x]+F[41,x]
F[41,x] = F[10,x]*F[29,x]
F[42,x] = F[43,x]
F[43,x] = F[10,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[10,x]*F[46,x]
F[46,x] = F[29,x]+F[44,x]
F[47,x] = F[22,x]+F[48,x]+F[69,x]
F[48,x] = F[10,x]*F[49,x]
F[49,x] = F[24,x]+F[50,x]
F[50,x] = F[47,x]+F[51,x]
F[51,x] = F[22,x]+F[52,x]+F[65,x]+F[67,x]
F[52,x] = F[10,x]*F[53,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[56,x]
F[56,x] = F[10,x]*F[25,x]
F[57,x] = F[58,x]
F[58,x] = F[10,x]*F[21,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = 2*F[22,x]+F[52,x]+F[61,x]
F[61,x] = F[10,x]*F[47,x]
F[62,x] = F[63,x]
F[63,x] = F[10,x]*F[64,x]
F[64,x] = 2*F[22,x]+F[65,x]+F[67,x]
F[65,x] = F[10,x]*F[66,x]
F[66,x] = F[47,x]+F[64,x]
F[67,x] = F[10,x]*F[68,x]
F[68,x] = F[44,x]+F[64,x]
F[69,x] = F[10,x]*F[28,x]
F[70,x] = F[33,x]+F[51,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{13}\! \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_{10}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{10}\! \left(x \right) = x
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{10}\! \left(x \right) F_{15}\! \left(x \right) F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{10}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{70}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{47}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{20}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{45}\! \left(x \right)
F_{34}\! \left(x \right) = F_{10}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{10}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right) F_{18}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right) F_{29}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{10}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{10}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{29}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)+F_{69}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right)+F_{52}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{10}\! \left(x \right) F_{25}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{10}\! \left(x \right) F_{21}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{52}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{10}\! \left(x \right) F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{10}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{10}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{47}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{10}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{44}\! \left(x \right)+F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right) F_{28}\! \left(x \right)
F_{70}\! \left(x \right) = F_{33}\! \left(x \right)+F_{51}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_13(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_10(x)*F_7(x))
Eq(F_7(x), F_5(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_11(x)*F_7(x))
Eq(F_10(x), x)
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_10(x)*F_11(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_10(x)*F_15(x)*F_5(x))
Eq(F_15(x), F_16(x) + F_27(x))
Eq(F_16(x), F_11(x) + F_17(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_10(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_26(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_10(x)*F_24(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_12(x))
Eq(F_26(x), F_10(x)*F_17(x))
Eq(F_27(x), F_28(x) + F_70(x))
Eq(F_28(x), F_29(x) + F_47(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_10(x)*F_31(x))
Eq(F_31(x), F_20(x) + F_32(x))
Eq(F_32(x), F_29(x) + F_33(x))
Eq(F_33(x), F_22(x) + F_34(x) + F_45(x))
Eq(F_34(x), F_10(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_10(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_10(x)*F_18(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_22(x) + F_34(x) + F_41(x))
Eq(F_41(x), F_10(x)*F_29(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_10(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_10(x)*F_46(x))
Eq(F_46(x), F_29(x) + F_44(x))
Eq(F_47(x), F_22(x) + F_48(x) + F_69(x))
Eq(F_48(x), F_10(x)*F_49(x))
Eq(F_49(x), F_24(x) + F_50(x))
Eq(F_50(x), F_47(x) + F_51(x))
Eq(F_51(x), F_22(x) + F_52(x) + F_65(x) + F_67(x))
Eq(F_52(x), F_10(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_10(x)*F_25(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_10(x)*F_21(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), 2*F_22(x) + F_52(x) + F_61(x))
Eq(F_61(x), F_10(x)*F_47(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_10(x)*F_64(x))
Eq(F_64(x), 2*F_22(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_10(x)*F_66(x))
Eq(F_66(x), F_47(x) + F_64(x))
Eq(F_67(x), F_10(x)*F_68(x))
Eq(F_68(x), F_44(x) + F_64(x))
Eq(F_69(x), F_10(x)*F_28(x))
Eq(F_70(x), F_33(x) + F_51(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"BasicVerificationStrategy"}}, {"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": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 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, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 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", 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{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": 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