0132_0213_1302_2103_3021
Counting sequence:
1, 1, 2, 6, 19, 54, 143, 367, 931, 2350, 5910, 14811, 37000, 92187, 229205, 568933, 1410364, 3492598, 8641755, 21367890, 52806115, 130441347, 322100627, 795138406, 1962423106, 4842399427, 11947091700, 29472027591, 72696627361, 179301201021, 442204858916, 1090537530370, 2689297865419, 6631655257486, 16352818035783, 40323036935607, 99427318303267, 245161132576974, 604494229467566, 1490487569633563, 3675031248404080, 9061307272804675, 22341810436005933, 55086348881026485, 135821364674118076, 334881344622613230, 825681999809453099, 2035794166240122682, 5019428291967109339, 12375823520468272075, 30513605489502087315, 75233729969056672230, 185494644465097779226, 457351307433567439011, 1127634323215857719228, 2780266940890700704783, 6854954573383843910521, 16901395565928700016845, 41671628233866192111108, 102744434854769819055738, 253323857005128453645883, 624588282563451371494038, 1539967438022848826625695, 3796900486750276113393727, 9361530757498719041775523, 23081525216155051293704494, 56909153149063456733509446, 140313588011346764445617691, 345953180395279001705588632, 852972277865060702213897643, 2103064047304864388502706949, 5185254488653943637734518405, 12784614846834539894419057660, 31521379676278844913217411174, 77718209117496131811389215035, 191619784990277163797549584098, 472452238124831013742549708435, 1164864664345159597155908985747, 2872056840616780742782117007891, 7081260792894749889533733937702, 17459353037088438361606401087730, 43047278856846073678931932524355, 106136132922857807479954220148420, 261686197122929086417291008588183, 645205961656891348920817905889873, 1590801262199345025265937590476189, 3922233836717413894170050557044644, 9670546930515011054030001391116658, 23843422344413822934901632345970795, 58787656273918104379634807690031454, 144945154242519588461457340384817079, 357372602788471805663032754489413959, 881127609072528603305093807828445859, 2172482885694284169932273617470726990, 5356411307017849119478103969108044766, 13206613629293441516737089762362130139, 32561846644119133136496181155916974592, 80283552360966392635016629918374375763, 197944817130957270036362967579385008093, 488047046690968597636989432990191052501, 1203314758271215380785457121412506247164
Generating function in Maple syntax:
-(2*x^5-2*x^4+6*x^3-9*x^2+5*x-1)/(2*x-1)/(3*x^3-5*x^2+4*x-1)
Generating function in latex syntax:
-\frac{2 x^{5}-2 x^{4}+6 x^{3}-9 x^{2}+5 x -1}{\left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right)}
Generating function in sympy syntax:
(-2*x**5 + 2*x**4 - 6*x**3 + 9*x**2 - 5*x + 1)/((2*x - 1)*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(3*x^3-5*x^2+4*x-1)*F(x)+2*x^5-2*x^4+6*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) F \! \left(x \right)+2 x^{5}-2 x^{4}+6 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/810216*(-2635*2^(1/3)*((-381/2635*31^(1/2)+I)*3^(1/2)-1143/2635*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)+510136+8866*((-12/403*31^(1/2)+I)*3^(1/2)+36/403*I*31^(1/2)-1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3))*(47/8712*2^(1/3)*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/810216*(-8866*((12/403*31^(1/2)+I)*3^(1/2)+36/403*I*31^(1/2)+1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)+510136+2635*2^(1/3)*((381/2635*31^(1/2)+I)*3^(1/2)-1143/2635*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(-47/8712*((I+9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)-1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)+1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/810216*((528*3^(1/2)*2^(2/3)*31^(1/2)+17732*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)+510136+(-762*31^(1/2)*3^(1/2)*2^(1/3)+5270*2^(1/3))*(47+9*31^(1/2)*3^(1/2))^(2/3))*(1/4356*2^(1/3)*(9*31^(1/2)*3^(1/2)-47)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/18*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)-2^(-1+n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-2635 \,2^{\frac{1}{3}} \left(\left(-\frac{381 \sqrt{31}}{2635}+\mathrm{I}\right) \sqrt{3}-\frac{1143 \,\mathrm{I} \sqrt{31}}{2635}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+510136+8866 \left(\left(-\frac{12 \sqrt{31}}{403}+\mathrm{I}\right) \sqrt{3}+\frac{36 \,\mathrm{I} \sqrt{31}}{403}-1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{47 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}-\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{810216}\\+\\\frac{\left(-8866 \left(\left(\frac{12 \sqrt{31}}{403}+\mathrm{I}\right) \sqrt{3}+\frac{36 \,\mathrm{I} \sqrt{31}}{403}+1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+510136+2635 \,2^{\frac{1}{3}} \left(\left(\frac{381 \sqrt{31}}{2635}+\mathrm{I}\right) \sqrt{3}-\frac{1143 \,\mathrm{I} \sqrt{31}}{2635}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{47 \left(\left(\mathrm{I}+\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}-1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}+\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{810216}\\+\\\frac{\left(\left(528 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{31}+17732 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+510136+\left(-762 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}+5270 \,2^{\frac{1}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(9 \sqrt{31}\, \sqrt{3}-47\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{4356}-\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{18}+\frac{5}{9}\right)^{-n}}{810216}\\-2^{-1+n} & \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(n+4) = -6*a(n)+13*a(n+1)-13*a(n+2)+6*a(n+3), 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) = 54
a \! \left(n +4\right) = -6 a \! \left(n \right)+13 a \! \left(n +1\right)-13 a \! \left(n +2\right)+6 a \! \left(n +3\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18519/
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[16,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[17,x]+F[35,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[10,x]+F[20,x]
F[20,x] = F[17,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[34,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[11,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[17,x]+F[29,x]
F[32,x] = F[33,x]
F[33,x] = F[28,x]*F[4,x]
F[34,x] = F[20,x]*F[4,x]
F[35,x] = F[22,x]+F[36,x]+F[66,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[49,x]
F[38,x] = F[39,x]+F[7,x]
F[39,x] = F[22,x]+F[27,x]+F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[11,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[42,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[40,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[45,x]
F[49,x] = F[50,x]+F[56,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[31,x]+F[53,x]
F[53,x] = F[50,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[53,x]
F[56,x] = 2*F[22,x]+F[33,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[62,x]
F[59,x] = F[29,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[59,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[57,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[62,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[77,x]
F[68,x] = F[17,x]+F[69,x]
F[69,x] = F[22,x]+F[70,x]+F[76,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[74,x]
F[72,x] = F[11,x]+F[73,x]
F[73,x] = F[22,x]+F[27,x]+F[44,x]
F[74,x] = F[29,x]+F[75,x]
F[75,x] = 2*F[22,x]+F[33,x]+F[61,x]
F[76,x] = F[4,x]*F[68,x]
F[77,x] = F[50,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{16}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \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_{17}\! \left(x \right)+F_{35}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{17}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{66}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{49}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{7}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{56}\! \left(x \right)
F_{50}\! \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_{31}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{33}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{59}\! \left(x \right) = F_{29}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{57}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{77}\! \left(x \right)
F_{68}\! \left(x \right) = F_{17}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{22}\! \left(x \right)+F_{70}\! \left(x \right)+F_{76}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{33}\! \left(x \right)+F_{61}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{77}\! \left(x \right) = F_{50}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_16(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_35(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_10(x) + F_20(x))
Eq(F_20(x), F_17(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_34(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_11(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_17(x) + F_29(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_28(x)*F_4(x))
Eq(F_34(x), F_20(x)*F_4(x))
Eq(F_35(x), F_22(x) + F_36(x) + F_66(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_49(x))
Eq(F_38(x), F_39(x) + F_7(x))
Eq(F_39(x), F_22(x) + F_27(x) + F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_11(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_42(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_40(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_45(x))
Eq(F_49(x), F_50(x) + F_56(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_31(x) + F_53(x))
Eq(F_53(x), F_50(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_53(x))
Eq(F_56(x), 2*F_22(x) + F_33(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_62(x))
Eq(F_59(x), F_29(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_59(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_57(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_62(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_77(x))
Eq(F_68(x), F_17(x) + F_69(x))
Eq(F_69(x), F_22(x) + F_70(x) + F_76(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_74(x))
Eq(F_72(x), F_11(x) + F_73(x))
Eq(F_73(x), F_22(x) + F_27(x) + F_44(x))
Eq(F_74(x), F_29(x) + F_75(x))
Eq(F_75(x), 2*F_22(x) + F_33(x) + F_61(x))
Eq(F_76(x), F_4(x)*F_68(x))
Eq(F_77(x), F_50(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(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:
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"pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], 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