0132_0231_0321_1320_2130
Counting sequence:
1, 1, 2, 6, 19, 57, 164, 462, 1289, 3581, 9930, 27514, 76211, 211069, 584532, 1618762, 4482849, 12414345, 34378978, 95205470, 263651811, 730128977, 2021940628, 5599344758, 15506222665, 42941263909, 118916913866, 329315700402, 911971451299, 2525515567413, 6993890951396, 19368128738130, 53636010830465, 148533794704721, 411333502021890, 1139102722191478, 3154508459257331, 8735756157602473, 24191862735741636, 66994340508879838, 185526914948500425, 513778267072363149, 1422802226777468938, 3940155328208544170, 10911442024920526803, 30216972973330505261, 83679632223279533236, 231733365721428621338, 641737437914336836129, 1777158580244861420377, 4921471668541676046434, 13628993863294503555150, 37742668501586696039491, 104520483310007260609857, 289447775291729589345332, 801565511066768203465734, 2219769241218582281661833, 6147189987880708230865205, 17023366233490310614399626, 47142677953808805893995618, 130551857615816815298452547, 361536261127131950615761765, 1001199603719387842442828484, 2772614407646848392011176354, 7678179880348289284206462465, 21263124837117407303051039649, 58883809038650781016957832962, 163066482159183225032028921830, 451578762276016301382179972307, 1250553613707516460131468828185, 3463148561005716304044255434212, 9590470831585648753383477446894, 26558817547458746416237645734793, 73549130371796306799373715191837, 203679044399515822735266977287754, 564046820374209907822664862406362, 1562010547094910207532101325123315, 4325663865310036537508906090251485, 11979027869209409312817281808037652, 33173430289413101608475040658984938, 91866926864339932050116746259168801, 254406378172816103854692479926559273, 704525637943521481122435734179494114, 1951037462522088271562731468871092030, 5402993127795559437420451152360341411, 14962467558808111521821057722389426481, 41435447011150863399605453483679030228, 114746866602440038114415753881008005782, 317767620354977362465462865881734413769, 879991441473642912681578297247874265925, 2436953570668391413693687779742896389962, 6748636890886508690864947907862549317906, 18688948543464777571582734241092625829859, 51755162310176215437576942595158224561813, 143325175277950377432013041452244597173668, 396909312067139694430044916002668192789234, 1099157923233644921295698649150918205756033, 3043889632911745446889064072902331021652721, 8429420287568731113801538485558743051991554, 23343529153028092815811250032924816340078166, 64645056804427292780521275686118036989895859
Generating function in Maple syntax:
-(2*x^4-2*x^3+5*x^2-4*x+1)/(x^3-x^2+3*x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{2 x^{4}-2 x^{3}+5 x^{2}-4 x +1}{\left(x^{3}-x^{2}+3 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-2*x**4 + 2*x**3 - 5*x**2 + 4*x - 1)/((x - 1)**2*(x**3 - x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^3-x^2+3*x-1)*(x-1)^2*F(x)+2*x^4-2*x^3+5*x^2-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-x^{2}+3 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+2 x^{4}-2 x^{3}+5 x^{2}-4 x +1 = 0
Explicit closed form in Maple syntax:
1/14592*(((-3*I+3^(1/2))*19^(1/2)+171*I*3^(1/2)-171)*(1+3*19^(1/2)*3^(1/2))^(2/3)-192*19^(1/2)*(I+1/3*3^(1/2))*(1+3*19^(1/2)*3^(1/2))^(1/3))*(1/384*((I+3*19^(1/2))*3^(1/2)-9*I*19^(1/2)-1)*(1+3*19^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(1+3*19^(1/2)*3^(1/2))^(1/3)-1/6*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)+1/14592*(((3*I+3^(1/2))*19^(1/2)-171*I*3^(1/2)-171)*(1+3*19^(1/2)*3^(1/2))^(2/3)+192*19^(1/2)*(I-1/3*3^(1/2))*(1+3*19^(1/2)*3^(1/2))^(1/3))*(1/384*((-I+3*19^(1/2))*3^(1/2)+9*I*19^(1/2)-1)*(1+3*19^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(1+3*19^(1/2)*3^(1/2))^(1/3)-1/6*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)+1/14592*(128*(1+3*19^(1/2)*3^(1/2))^(1/3)*19^(1/2)*3^(1/2)-2*(1+3*19^(1/2)*3^(1/2))^(2/3)*19^(1/2)*3^(1/2)+342*(1+3*19^(1/2)*3^(1/2))^(2/3))*(1/3*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3+1/192*(1+3*19^(1/2)*3^(1/2))^(2/3)-1/64*(1+3*19^(1/2)*3^(1/2))^(2/3)*19^(1/2)*3^(1/2))^(-n)-n+1
Explicit closed form in latex syntax:
\frac{\left(\left(\left(-3 \,\mathrm{I}+\sqrt{3}\right) \sqrt{19}+171 \,\mathrm{I} \sqrt{3}-171\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}-192 \sqrt{19}\, \left(\mathrm{I}+\frac{\sqrt{3}}{3}\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(\mathrm{I}+3 \sqrt{19}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{19}-1\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}-\frac{\mathrm{I} \sqrt{3}\, \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{14592}+\frac{\left(\left(\left(3 \,\mathrm{I}+\sqrt{3}\right) \sqrt{19}-171 \,\mathrm{I} \sqrt{3}-171\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}+192 \sqrt{19}\, \left(\mathrm{I}-\frac{\sqrt{3}}{3}\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-\mathrm{I}+3 \sqrt{19}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{19}-1\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}+\frac{\mathrm{I} \sqrt{3}\, \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{14592}+\frac{\left(128 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{19}\, \sqrt{3}-2 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{19}\, \sqrt{3}+342 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}+\frac{1}{3}+\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{192}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{19}\, \sqrt{3}}{64}\right)^{-n}}{14592}-n +1
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+3) = a(n)-a(n+1)+3*a(n+2)+2*n, n >= 5
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(n +3\right) = a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)+2 n, \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18695/
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[18,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[12,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[17,x]
F[15,x] = 0
F[16,x] = F[10,x]*F[12,x]
F[17,x] = F[12,x]*F[13,x]
F[18,x] = F[19,x]+F[25,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[9,x]
F[22,x] = F[19,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[22,x]
F[25,x] = F[15,x]+F[26,x]+F[57,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[35,x]
F[28,x] = F[29,x]+F[6,x]
F[29,x] = F[15,x]+F[30,x]+F[33,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[10,x]+F[32,x]
F[32,x] = F[30,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[13,x]
F[35,x] = F[25,x]+F[36,x]
F[36,x] = 2*F[15,x]+F[37,x]+F[55,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[54,x]
F[39,x] = F[15,x]+F[40,x]+F[52,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[10,x]+F[43,x]
F[43,x] = F[15,x]+F[17,x]+F[30,x]
F[44,x] = F[39,x]+F[45,x]
F[45,x] = 2*F[15,x]+F[37,x]+F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[19,x]
F[50,x] = 2*F[15,x]+F[46,x]+F[51,x]
F[51,x] = F[12,x]*F[39,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[19,x]+F[39,x]
F[54,x] = F[37,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[47,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[53,x]+F[59,x]
F[59,x] = F[60,x]+F[69,x]
F[60,x] = F[15,x]+F[49,x]+F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[63,x]+F[66,x]
F[63,x] = F[12,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]*F[63,x]
F[66,x] = F[48,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[12,x]*F[66,x]
F[69,x] = F[15,x]+F[51,x]+F[70,x]+F[84,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[78,x]
F[72,x] = F[14,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[16,x]
F[77,x] = F[74,x]
F[78,x] = F[50,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[51,x]
F[83,x] = F[80,x]
F[84,x] = F[12,x]*F[59,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_{18}\! \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_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{25}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)+F_{57}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right)
F_{35}\! \left(x \right) = F_{25}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{55}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{54}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right)+F_{40}\! \left(x \right)+F_{52}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{10}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)+F_{30}\! \left(x \right)
F_{44}\! \left(x \right) = F_{39}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right)+F_{39}\! \left(x \right)
F_{54}\! \left(x \right) = F_{37}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{47}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{53}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{60}\! \left(x \right) = F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{66}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{70}\! \left(x \right)+F_{84}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right)
F_{77}\! \left(x \right) = F_{74}\! \left(x \right)
F_{78}\! \left(x \right) = F_{50}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{51}\! \left(x \right)
F_{83}\! \left(x \right) = F_{80}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \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_18(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_12(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_17(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_10(x)*F_12(x))
Eq(F_17(x), F_12(x)*F_13(x))
Eq(F_18(x), F_19(x) + F_25(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_9(x))
Eq(F_22(x), F_19(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_22(x))
Eq(F_25(x), F_15(x) + F_26(x) + F_57(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_35(x))
Eq(F_28(x), F_29(x) + F_6(x))
Eq(F_29(x), F_15(x) + F_30(x) + F_33(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_10(x) + F_32(x))
Eq(F_32(x), F_30(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_13(x))
Eq(F_35(x), F_25(x) + F_36(x))
Eq(F_36(x), 2*F_15(x) + F_37(x) + F_55(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_54(x))
Eq(F_39(x), F_15(x) + F_40(x) + F_52(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_10(x) + F_43(x))
Eq(F_43(x), F_15(x) + F_17(x) + F_30(x))
Eq(F_44(x), F_39(x) + F_45(x))
Eq(F_45(x), 2*F_15(x) + F_37(x) + F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_19(x))
Eq(F_50(x), 2*F_15(x) + F_46(x) + F_51(x))
Eq(F_51(x), F_12(x)*F_39(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_19(x) + F_39(x))
Eq(F_54(x), F_37(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_47(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_53(x) + F_59(x))
Eq(F_59(x), F_60(x) + F_69(x))
Eq(F_60(x), F_15(x) + F_49(x) + F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_66(x))
Eq(F_63(x), F_12(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x)*F_63(x))
Eq(F_66(x), F_48(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_12(x)*F_66(x))
Eq(F_69(x), F_15(x) + F_51(x) + F_70(x) + F_84(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_78(x))
Eq(F_72(x), F_14(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_16(x))
Eq(F_77(x), F_74(x))
Eq(F_78(x), F_50(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_51(x))
Eq(F_83(x), F_80(x))
Eq(F_84(x), F_12(x)*F_59(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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