0132_0231_1023_2103_3021
Counting sequence:
1, 1, 2, 6, 19, 50, 121, 285, 666, 1552, 3612, 8401, 19534, 45415, 105581, 245450, 570606, 1326502, 3083747, 7168846, 16665549, 38742705, 90065866, 209377740, 486744196, 1131542977, 2630518282, 6115213091, 14216145689, 33048529170, 76828509226, 178604615030, 415205355811, 965235346602, 2243899943217, 5216434492261, 12126738936954, 28191247769560, 65536699927036, 152354343178945, 354180877452326, 823370645926127, 1914104526052677, 4449753163758106, 10344421085095094, 24047861453821750, 55904495355033171, 129962184242551110, 302125423471408741, 702356397284157177, 1632780529152205162, 3795754216359709876, 8824057988058876484, 20513446060609414865, 47687976422070201506, 110861095133050651275, 257720778615620965681, 599128122002831796002, 1392803903910304107922, 3237876246340869697446, 7527149053204832672499, 17498498570843062730530, 40679073852460392544041, 94567373468899884843565, 219842471272621932173146, 511071740732526419376352, 1188097653121235278626332, 2761991949171274929299441, 6420852282003880650022014, 14926670600790327370093495, 34700299187534495739535901, 80668408643026713128442730, 187531298154801475276349886, 435957376365885495311700102, 1013477941431080248510843267, 2356050369716271230185479486, 5477152602652538688846452029, 12732835009956153854679240385, 29600250194279655416530296586, 68812233165579197229078861020, 159969034118134434708855230276, 371882886217524565084938265377, 864522823581884023066183196602, 2009771732428737373737528289331, 4672152436339968640165156740169, 10861436667744315196086596838450, 25249776862981745681667005324346, 58698609689796575292992979036310, 136457712011170549711731523298691, 317225693516900244230875617147802, 737460266218156208562156783882337, 1714387123631838686936450640650101, 3985466531976103887915913971333434, 9265085614882790498436997416582440, 21538710904328002406415614947730556, 50071428015194530110288763981360225, 116401947851810376016472059465202006, 270601698429370070235254265380616127, 629072627599683988783107441192804597, 1462416433792122201895285852282383546, 3399705744606368698354896939842157574
Generating function in Maple syntax:
-(x^5-3*x^4-3*x^2+3*x-1)/(x-1)/(x^3-2*x^2+3*x-1)
Generating function in latex syntax:
-\frac{x^{5}-3 x^{4}-3 x^{2}+3 x -1}{\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(-x**5 + 3*x**4 + 3*x**2 - 3*x + 1)/((x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^3-2*x^2+3*x-1)*F(x)+x^5-3*x^4-3*x^2+3*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) F \! \left(x \right)+x^{5}-3 x^{4}-3 x^{2}+3 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,0,1/13800*(437*((I-101/437*23^(1/2))*3^(1/2)-303/437*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+18400-1610*((I-2/161*23^(1/2))*3^(1/2)+6/161*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)+1/13800*(1610*2^(2/3)*((I+2/161*23^(1/2))*3^(1/2)+6/161*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+18400-437*2^(1/3)*((I+101/437*23^(1/2))*3^(1/2)-303/437*I*23^(1/2)-1)*(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)-3+1/13800*((-40*3^(1/2)*2^(2/3)*23^(1/2)-3220*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+18400+(202*23^(1/2)*3^(1/2)*2^(1/3)-874*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))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}0 & n =0 \\ \frac{\left(437 \left(\left(\mathrm{I}-\frac{101 \sqrt{23}}{437}\right) \sqrt{3}-\frac{303 \,\mathrm{I} \sqrt{23}}{437}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+18400-1610 \left(\left(\mathrm{I}-\frac{2 \sqrt{23}}{161}\right) \sqrt{3}+\frac{6 \,\mathrm{I} \sqrt{23}}{161}-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}}{13800}\\+\\\frac{\left(1610 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{2 \sqrt{23}}{161}\right) \sqrt{3}+\frac{6 \,\mathrm{I} \sqrt{23}}{161}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+18400-437 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{101 \sqrt{23}}{437}\right) \sqrt{3}-\frac{303 \,\mathrm{I} \sqrt{23}}{437}-1\right) \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}}{13800}\\-3+\\\frac{\left(\left(-40 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{23}-3220 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+18400+\left(202 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}-874 \,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} & \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) = 50
a(n+3) = a(n)-2*a(n+1)+3*a(n+2)+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) = 50
a \! \left(n +3\right) = a \! \left(n \right)-2 a \! \left(n +1\right)+3 a \! \left(n +2\right)+3, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18818/
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[20,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[16,x]*F[4,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]+F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[21,x]+F[35,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[10,x]+F[24,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[34,x]
F[26,x] = 0
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[17,x]+F[29,x]
F[29,x] = F[30,x]+F[32,x]
F[30,x] = F[31,x]
F[31,x] = F[21,x]*F[4,x]
F[32,x] = F[33,x]
F[33,x] = F[29,x]*F[4,x]
F[34,x] = F[24,x]*F[4,x]
F[35,x] = F[26,x]+F[36,x]+F[52,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[1,x]+F[39,x]
F[42,x] = F[19,x]+F[26,x]+F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[11,x]+F[42,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[21,x]+F[46,x]
F[49,x] = 2*F[26,x]+F[33,x]+F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[25,x]+F[49,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[65,x]
F[54,x] = F[21,x]+F[55,x]
F[55,x] = F[26,x]+F[56,x]+F[64,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[4,x]+F[59,x]
F[59,x] = F[19,x]+F[26,x]+F[60,x]
F[60,x] = F[11,x]*F[4,x]
F[61,x] = F[30,x]+F[62,x]
F[62,x] = 2*F[26,x]+F[33,x]+F[63,x]
F[63,x] = F[25,x]*F[4,x]
F[64,x] = F[4,x]*F[54,x]
F[65,x] = F[66,x]+F[73,x]
F[66,x] = F[26,x]+F[27,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[24,x]+F[69,x]
F[69,x] = F[66,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[29,x]
F[73,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_{20}\! \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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{35}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
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_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{34}\! \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_{17}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)+F_{52}\! \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_{45}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \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_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{11}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \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_{21}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{33}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{25}\! \left(x \right)+F_{49}\! \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_{65}\! \left(x \right)
F_{54}\! \left(x \right) = F_{21}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{26}\! \left(x \right)+F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{61}\! \left(x \right) = F_{30}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{33}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{73}\! \left(x \right)
F_{66}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{24}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{29}\! \left(x \right)
F_{73}\! \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_20(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_16(x)*F_4(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) + F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_35(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
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_26(x) + F_27(x) + F_34(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_17(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_32(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_21(x)*F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_29(x)*F_4(x))
Eq(F_34(x), F_24(x)*F_4(x))
Eq(F_35(x), F_26(x) + F_36(x) + F_52(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_45(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_1(x) + F_39(x))
Eq(F_42(x), F_19(x) + F_26(x) + F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_11(x) + F_42(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_21(x) + F_46(x))
Eq(F_49(x), 2*F_26(x) + F_33(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_25(x) + F_49(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_65(x))
Eq(F_54(x), F_21(x) + F_55(x))
Eq(F_55(x), F_26(x) + F_56(x) + F_64(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_4(x) + F_59(x))
Eq(F_59(x), F_19(x) + F_26(x) + F_60(x))
Eq(F_60(x), F_11(x)*F_4(x))
Eq(F_61(x), F_30(x) + F_62(x))
Eq(F_62(x), 2*F_26(x) + F_33(x) + F_63(x))
Eq(F_63(x), F_25(x)*F_4(x))
Eq(F_64(x), F_4(x)*F_54(x))
Eq(F_65(x), F_66(x) + F_73(x))
Eq(F_66(x), F_26(x) + F_27(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_24(x) + F_69(x))
Eq(F_69(x), F_66(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_29(x))
Eq(F_73(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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