0231_0312_1320_2103_3021
Counting sequence:
1, 1, 2, 6, 19, 51, 125, 293, 675, 1554, 3606, 8462, 20085, 48152, 116371, 282952, 691022, 1692833, 4155854, 10217218, 25143470, 61915270, 152530272, 375869505, 926401213, 2283570685, 5629435858, 13878366177, 34215819928, 84357850575, 207984316937, 512790483620, 1264305825195, 3117210765015, 7685664238947, 18949486390541, 46721201299347, 115194276381176, 284019413254558, 700269640483354, 1726563945330323, 4256965204665464, 10495849019981771, 25878260285107390, 63804689053553030, 157314997640170765, 387871319338823868, 956324345297232258, 2357885759588034622, 5813535241037290156, 14333685155428235344, 35340721619772983805, 87135066302872566163, 214837712381202374853, 529697682549867876914, 1306007366684471908343, 3220054190294652202944, 7939272974050744302915, 19574843042590520149575, 48263169867444595318028, 118996283173237681281651, 293393812474211256454757, 723383343617962020678355, 1783553161596188407062745, 4397477365678232472310049, 10842293685522212656821008, 26732447398383247405862630, 65910753262789956416070088, 162507657115540553184159491, 400674204342925832112393148, 987890791581664417594226217, 2435715115957507814423169774, 6005429118948638296931713870, 14806813270749016644322417075, 36507252836120559442702319524, 90011232347575239622722770214, 221929105021932542299878874204, 547182016858195150686271172340, 1349116239365810442475653328928, 3326342188238009977004951336555, 8201333606697486313696204170219, 20220972203697186196816929187953, 49856247346015115815427311056360, 122924129185666623383968881136439, 303078196623681877880071188304728, 747260882604438779042859382513409, 1842424934856344038750006765214191, 4542629916274225372249099348276504, 11200177638628493553025115882912633, 27614835777711872866578316889310149, 68086344666527689138058490159233219, 167871732693436855598014557614234983, 413899714774244567341221068075534369, 1020499229629377013548304126230595852, 2516113542726595711080192346656168564, 6203657167082231360161266640488971856, 15295558643584077734246409397426245763, 37712289367104940959335628298078704346, 92982335751746068744867405187559979873, 229254572102211802573719593383884672642, 565243477751431688135010257484643904260
Generating function in Maple syntax:
(3*x^10-5*x^9+2*x^8+5*x^7-3*x^6+5*x^5-18*x^4+28*x^3-20*x^2+7*x-1)/(x^2+x-1)/(3*x^3-5*x^2+4*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{3 x^{10}-5 x^{9}+2 x^{8}+5 x^{7}-3 x^{6}+5 x^{5}-18 x^{4}+28 x^{3}-20 x^{2}+7 x -1}{\left(x^{2}+x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**10 - 5*x**9 + 2*x**8 + 5*x**7 - 3*x**6 + 5*x**5 - 18*x**4 + 28*x**3 - 20*x**2 + 7*x - 1)/((x - 1)**3*(x**2 + x - 1)*(3*x**3 - 5*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^2+x-1)*(3*x^3-5*x^2+4*x-1)*(x-1)^3*F(x)+3*x^10-5*x^9+2*x^8+5*x^7-3*x^6+5*x^5-18*x^4+28*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{2}+x -1\right) \left(3 x^{3}-5 x^{2}+4 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+3 x^{10}-5 x^{9}+2 x^{8}+5 x^{7}-3 x^{6}+5 x^{5}-18 x^{4}+28 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/1350360*(-2945*2^(1/3)*((-51/589*31^(1/2)+I)*3^(1/2)-153/589*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)+300080+3410*((-6/31*31^(1/2)+I)*3^(1/2)+18/31*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)+1/1350360*(-3410*((6/31*31^(1/2)+I)*3^(1/2)+18/31*I*31^(1/2)+1)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)+300080+2945*((51/589*31^(1/2)+I)*3^(1/2)-153/589*I*31^(1/2)-1)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3))*(-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)+1/1350360*((1320*3^(1/2)*2^(2/3)*31^(1/2)+6820*2^(2/3))*(47+9*31^(1/2)*3^(1/2))^(1/3)+300080+(-510*31^(1/2)*3^(1/2)*2^(1/3)+5890*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)+1/1350360*(-1890504*5^(1/2)+4051080)*(-1/2*5^(1/2)-1/2)^(-n)+1/1350360*(1890504*5^(1/2)+4051080)*(1/2*5^(1/2)-1/2)^(-n)-3/2*n^2-1/2*n-10)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(-2945 \,2^{\frac{1}{3}} \left(\left(-\frac{51 \sqrt{31}}{589}+\mathrm{I}\right) \sqrt{3}-\frac{153 \,\mathrm{I} \sqrt{31}}{589}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+300080+3410 \left(\left(-\frac{6 \sqrt{31}}{31}+\mathrm{I}\right) \sqrt{3}+\frac{18 \,\mathrm{I} \sqrt{31}}{31}-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}}{1350360}\\+\\\frac{\left(-3410 \left(\left(\frac{6 \sqrt{31}}{31}+\mathrm{I}\right) \sqrt{3}+\frac{18 \,\mathrm{I} \sqrt{31}}{31}+1\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+300080+2945 \left(\left(\frac{51 \sqrt{31}}{589}+\mathrm{I}\right) \sqrt{3}-\frac{153 \,\mathrm{I} \sqrt{31}}{589}-1\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{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}}{1350360}\\+\\\frac{\left(\left(1320 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{31}+6820 \,2^{\frac{2}{3}}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+300080+\left(-510 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}+5890 \,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}}{1350360}\\+\frac{\left(-1890504 \sqrt{5}+4051080\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{1350360}+\\\frac{\left(1890504 \sqrt{5}+4051080\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{1350360}-\frac{3 n^{2}}{2}-\frac{n}{2}-10 & \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) = 51
a(6) = 125
a(7) = 293
a(8) = 675
a(9) = 1554
a(10) = 3606
a(n+5) = -3/2*n^2-3*a(n)+2*a(n+1)+4*a(n+2)-8*a(n+3)+5*a(n+4)+5/2*n-8, n >= 11
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) = 51
a \! \left(6\right) = 125
a \! \left(7\right) = 293
a \! \left(8\right) = 675
a \! \left(9\right) = 1554
a \! \left(10\right) = 3606
a \! \left(n +5\right) = -\frac{3 n^{2}}{2}-3 a \! \left(n \right)+2 a \! \left(n +1\right)+4 a \! \left(n +2\right)-8 a \! \left(n +3\right)+5 a \! \left(n +4\right)+\frac{5 n}{2}-8, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/20749/
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[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[7,x]
F[17,x] = F[18,x]+F[39,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[4,x]
F[24,x] = F[18,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[38,x]
F[26,x] = 0
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[22,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[29,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[18,x]+F[33,x]
F[36,x] = F[37,x]
F[37,x] = F[32,x]*F[4,x]
F[38,x] = F[24,x]*F[4,x]
F[39,x] = F[26,x]+F[40,x]+F[64,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[50,x]
F[42,x] = F[43,x]+F[7,x]
F[43,x] = F[26,x]+F[44,x]+F[45,x]
F[44,x] = F[4,x]*F[42,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[7,x]
F[50,x] = F[51,x]+F[55,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[18,x]+F[51,x]
F[55,x] = 2*F[26,x]+F[56,x]+F[57,x]
F[56,x] = F[4,x]*F[50,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[61,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[17,x]+F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[59,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[48,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[71,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_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{39}\! \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_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{38}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{28}\! \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_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{26}\! \left(x \right)+F_{40}\! \left(x \right)+F_{64}\! \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_{50}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = F_{26}\! \left(x \right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \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_{59}\! \left(x \right) = F_{4}\! \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_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{59}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{48}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \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) + F_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_7(x))
Eq(F_17(x), F_18(x) + F_39(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_4(x))
Eq(F_24(x), F_18(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_38(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_22(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_29(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_18(x) + F_33(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_32(x)*F_4(x))
Eq(F_38(x), F_24(x)*F_4(x))
Eq(F_39(x), F_26(x) + F_40(x) + F_64(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_50(x))
Eq(F_42(x), F_43(x) + F_7(x))
Eq(F_43(x), F_26(x) + F_44(x) + F_45(x))
Eq(F_44(x), F_4(x)*F_42(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_7(x))
Eq(F_50(x), F_51(x) + F_55(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_18(x) + F_51(x))
Eq(F_55(x), 2*F_26(x) + F_56(x) + F_57(x))
Eq(F_56(x), F_4(x)*F_50(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_61(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_17(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_59(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_48(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_71(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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