0132_0231_1203_1302_2130
Counting sequence:
1, 1, 2, 6, 19, 56, 156, 419, 1097, 2817, 7124, 17795, 44002, 107892, 262683, 635723, 1530655, 3669218, 8762291, 20855924, 49498840, 117185363, 276822205, 652672617, 1536238868, 3610602279, 8474916278, 19869806568, 46538624883, 108904825919, 254647885247, 595021439026, 1389505210711, 3243052751200, 7565570365860, 17641986737027, 41123771576481, 95829005280385, 223242236678084, 519931205424875, 1210649976687034, 2818422132342556, 6560219840938187, 15267384496442851, 35526524218861359, 82658899574397586, 192300985944690491, 447335983276203964, 1040522274350783312, 2420128228304986547, 5628576075582393909, 13089864325417763465, 30440450352741387492, 70786242556643536847, 164600342387164035118, 382735420495450133968, 889926927257486983395, 2069185002745994317623, 4810995020572253061551, 11185676890588354897794, 26006531476375766581855, 60463919412135308327368, 140573883776655753203740, 326819655417274574225187, 759814317441804157392633, 1766457076851336949372609, 4106723660098322066134388, 9547398573741404801591763, 22195869560665560765737298, 51600881806929575557430724, 119961034991321918956048507, 278882744943994279384506171, 648338262276665391206234751, 1507233058322028343973331330, 3503951438429956507932864195, 8145819727660514902551135172, 18936978259102974821569556296, 44023629272102963608801572115, 102343525493866646707631785069, 237921864022169300449072714345, 553105343781154059942339748724, 1285822251211406928353996229111, 2989190926046642822890009995622, 6949059913634845290088927136696, 16154673332758720196524444719699, 37555198691451058534282038730991, 87305526929118111133137601001951, 202961296786209276252392763311634, 471828924961245901392257710407527, 1096871507122056849373337168391152, 2549921604678753422392446363847444, 5927858075022375726768304678717635, 13780617378112148609456657266339857, 32036087609016400467697475109194177, 74474946804909204894580885530707428, 173133405130870851610451578653371963, 402486656979818402585945419832740010, 935668607610398580725145046968370028, 2175166924161501845484300197578368811, 5056652254368711519895248952387827539, 11755295642257980191187846373260532495
Generating function in Maple syntax:
(3*x^5-4*x^4+11*x^3-13*x^2+6*x-1)/(x^3-2*x^2+3*x-1)/(2*x-1)^2
Generating function in latex syntax:
\frac{3 x^{5}-4 x^{4}+11 x^{3}-13 x^{2}+6 x -1}{\left(x^{3}-2 x^{2}+3 x -1\right) \left(2 x -1\right)^{2}}
Generating function in sympy syntax:
(3*x**5 - 4*x**4 + 11*x**3 - 13*x**2 + 6*x - 1)/((2*x - 1)**2*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^3-2*x^2+3*x-1)*(2*x-1)^2*F(x)-3*x^5+4*x^4-11*x^3+13*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-2 x^{2}+3 x -1\right) \left(2 x -1\right)^{2} F \! \left(x \right)-3 x^{5}+4 x^{4}-11 x^{3}+13 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/6900*(-276*2^(1/3)*((1/138*23^(1/2)+I)*3^(1/2)+1/46*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+6900-345*((17/69*23^(1/2)+I)*3^(1/2)-17/23*I*23^(1/2)-1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(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)+1/6900*(345*((-17/69*23^(1/2)+I)*3^(1/2)-17/23*I*23^(1/2)+1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)+6900+276*((-1/138*23^(1/2)+I)*3^(1/2)+1/46*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*2^(1/3)*(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)+1/6900*((170*2^(2/3)*23^(1/2)*3^(1/2)-690*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+6900+(4*23^(1/2)*3^(1/2)*2^(1/3)+552*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)-1/4*2^n*(n+11))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(-276 \,2^{\frac{1}{3}} \left(\left(\frac{\sqrt{23}}{138}+\mathrm{I}\right) \sqrt{3}+\frac{\mathrm{I} \sqrt{23}}{46}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+6900-345 \left(\left(\frac{17 \sqrt{23}}{69}+\mathrm{I}\right) \sqrt{3}-\frac{17 \,\mathrm{I} \sqrt{23}}{23}-1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{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}}{6900}\\+\\\frac{\left(345 \left(\left(-\frac{17 \sqrt{23}}{69}+\mathrm{I}\right) \sqrt{3}-\frac{17 \,\mathrm{I} \sqrt{23}}{23}+1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+6900+276 \left(\left(-\frac{\sqrt{23}}{138}+\mathrm{I}\right) \sqrt{3}+\frac{\mathrm{I} \sqrt{23}}{46}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) 2^{\frac{1}{3}} \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}}{6900}\\+\\\frac{\left(\left(170 \,2^{\frac{2}{3}} \sqrt{23}\, \sqrt{3}-690 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+6900+\left(4 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+552 \,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}}{6900}\\-\frac{2^{n} \left(n +11\right)}{4} & \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) = 56
a(n+5) = 4*a(n)-12*a(n+1)+21*a(n+2)-18*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) = 19
a \! \left(5\right) = 56
a \! \left(n +5\right) = 4 a \! \left(n \right)-12 a \! \left(n +1\right)+21 a \! \left(n +2\right)-18 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/18948/
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[22,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[14,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[17,x]
F[21,x] = F[12,x]*F[13,x]
F[22,x] = F[23,x]+F[46,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[26,x]+F[33,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[9,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[30,x]
F[33,x] = F[23,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[23,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[37,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[23,x]+F[41,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[40,x]
F[46,x] = F[18,x]+F[47,x]+F[51,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[6,x]
F[50,x] = F[46,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[60,x]
F[53,x] = F[23,x]+F[54,x]
F[54,x] = F[18,x]+F[55,x]+F[59,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[10,x]
F[58,x] = F[54,x]
F[59,x] = F[12,x]*F[53,x]
F[60,x] = F[61,x]+F[68,x]
F[61,x] = F[18,x]+F[62,x]+F[66,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[14,x]
F[65,x] = F[41,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[23,x]+F[61,x]
F[68,x] = F[18,x]+F[69,x]+F[70,x]+F[72,x]
F[69,x] = 0
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[54,x]+F[68,x]
F[72,x] = F[12,x]*F[60,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_{22}\! \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_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \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_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{46}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \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_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \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_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{23}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{6}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right)+F_{55}\! \left(x \right)+F_{59}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{61}\! \left(x \right) = F_{18}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right)
F_{65}\! \left(x \right) = F_{41}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{23}\! \left(x \right)+F_{61}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = 0
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)+F_{68}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \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_22(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_14(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_17(x))
Eq(F_21(x), F_12(x)*F_13(x))
Eq(F_22(x), F_23(x) + F_46(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_33(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_9(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_30(x))
Eq(F_33(x), F_23(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_23(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_37(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_23(x) + F_41(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_40(x))
Eq(F_46(x), F_18(x) + F_47(x) + F_51(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_6(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_60(x))
Eq(F_53(x), F_23(x) + F_54(x))
Eq(F_54(x), F_18(x) + F_55(x) + F_59(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_10(x))
Eq(F_58(x), F_54(x))
Eq(F_59(x), F_12(x)*F_53(x))
Eq(F_60(x), F_61(x) + F_68(x))
Eq(F_61(x), F_18(x) + F_62(x) + F_66(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_14(x))
Eq(F_65(x), F_41(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_23(x) + F_61(x))
Eq(F_68(x), F_18(x) + F_69(x) + F_70(x) + F_72(x))
Eq(F_69(x), 0)
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_54(x) + F_68(x))
Eq(F_72(x), F_12(x)*F_60(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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