02314_02341_02431_03214_03241_20314_20341_20431_23014_23041_23401_24031_24301_30214_30241_32014_32041_32401
Counting sequence:
1, 1, 2, 6, 24, 102, 433, 1820, 7598, 31606, 131255, 544691, 2259734, 9373780, 38882437, 161281800, 668982591, 2774875014, 11509905257, 47741930299, 198028714231, 821403123731, 3407097241171, 14132295386626, 58619334447748, 243147080898776, 1008549542513540, 4183361675059359, 17352161858343594, 71975015440242360, 298545097140495460, 1238334920545288919, 5136488222812463651, 21305634546317977642, 88373620989759466880, 366564857285177586071, 1520474018056473711224, 6306772713310667153803, 26159856455950639918702, 108508443367813408381575, 450082067611180913420889, 1866894974232434450802843, 7743691863380829067319447, 32120052012912349419872497, 133230732771146749117106794, 552627627987681813649741778, 2292243605233929352853129944, 9507995039750280821197400158, 39438203456866091131719152329, 163585686088664070601650042320, 678536909582275745759393668226, 2814502592946428052079963767966, 11674272591271112559346056616551, 48423704023888276898142254105343, 200856635225940214924878438759430, 833133043568585640934284609659192, 3455751748031930969674994776941485, 14334109343296779748968917803476676, 59456438322747695435741112550379843, 246619303185366330291697977864030074, 1022951969868767593682230669158045245, 4243101489390973790613513232814747983, 17599956576242367195368645427702169279, 73002842911041845642131409348217850275, 302808421714418542875280449501749339907, 1256018760432525265895441226034523754930, 5209839005225193871793344975855866960248, 21609886185950770265894761716076219749760, 89635626072395405049215473391419584919060, 371799526950483796468121754508183030436735, 1542186899313407836980888509539260682115710, 6396835552538640353755454264210816503002508, 26533428019937126926768836506544658815541084, 110057980497839594067633492432787250266042007, 456509391178605144682469824315900546002202439, 1893554863459915838171339404711374640121407866, 7854274392199495188253499724452408150734569108, 32578737177565090885517974824051215461473974847, 135133312523301946106618882268427972396659576604, 560519336706997807043362025862351768642137438999, 2324977616220843221780531602694933817580071752210, 9643772412357650768816222797207467130095137215627, 40001394289774730540176375375484367910263893814197, 165921744801403592013832292891740448853130305241955, 688226645264197773453702800160269209871407882911791, 2854694638237706700843854879016877519765134299790625, 11840985137177810405679635586900037777723464858090802, 49115210832294558989026806003506402117500835477384574, 203724935649711927551267437719096183711458402121291912, 845030464130459960663613500266683996495208945704843654, 3505101047307903769828791627830999022823248006443402561, 14538805254176294287472359330555282862653132565055123652, 60305496294097546880675954026653149688183228014160434854, 250141109925985842068577772209277078946648060024708037830, 1037560068652121886737832283066793002757629400476211003911, 4303694408247929340130820756777550261246862082309379227563, 17851289885939671545203293284391243500645715556331448408966, 74045348103975787035232052943454137871890144460079475058508, 307132627998906471674955651433699508445424952333115582608837, 1273955131510141327138270458387059820417343824171899331346608, 5284237261522080769835602565128712865532500677115027428529015
Generating function in Maple syntax:
(2*x-1)*(x^4-2*x^3-4*x^2+5*x-1)/(x^2+x-1)/(9*x^3-14*x^2+7*x-1)
Generating function in latex syntax:
\frac{\left(2 x -1\right) \left(x^{4}-2 x^{3}-4 x^{2}+5 x -1\right)}{\left(x^{2}+x -1\right) \left(9 x^{3}-14 x^{2}+7 x -1\right)}
Generating function in sympy syntax:
(2*x - 1)*(x**4 - 2*x**3 - 4*x**2 + 5*x - 1)/((x**2 + x - 1)*(9*x**3 - 14*x**2 + 7*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+x-1)*(9*x^3-14*x^2+7*x-1)*F(x)-(2*x-1)*(x^4-2*x^3-4*x^2+5*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+x -1\right) \left(9 x^{3}-14 x^{2}+7 x -1\right) F \! \left(x \right)-\left(2 x -1\right) \left(x^{4}-2 x^{3}-4 x^{2}+5 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/1640520*(4805*((I-45/961*31^(1/2))*3^(1/2)-135/961*I*31^(1/2)+1)*2^(1/3)*(263+27*31^(1/2)*3^(1/2))^(2/3)+607600-49910*2^(2/3)*((I+72/713*31^(1/2))*3^(1/2)-216/713*I*31^(1/2)-1)*(263+27*31^(1/2)*3^(1/2))^(1/3))*(263/10584*2^(1/3)*((I-27/263*31^(1/2))*3^(1/2)-81/263*I*31^(1/2)+1)*(263+27*31^(1/2)*3^(1/2))^(2/3)-1/108*I*3^(1/2)*(1052+108*31^(1/2)*3^(1/2))^(1/3)+1/108*(1052+108*31^(1/2)*3^(1/2))^(1/3)+14/27)^(-n)+1/1640520*(49910*2^(2/3)*((I-72/713*31^(1/2))*3^(1/2)-216/713*I*31^(1/2)+1)*(263+27*31^(1/2)*3^(1/2))^(1/3)+607600-4805*((I+45/961*31^(1/2))*3^(1/2)-135/961*I*31^(1/2)-1)*2^(1/3)*(263+27*31^(1/2)*3^(1/2))^(2/3))*(-263/10584*2^(1/3)*((I+27/263*31^(1/2))*3^(1/2)-81/263*I*31^(1/2)-1)*(263+27*31^(1/2)*3^(1/2))^(2/3)+1/108*I*3^(1/2)*(1052+108*31^(1/2)*3^(1/2))^(1/3)+1/108*(1052+108*31^(1/2)*3^(1/2))^(1/3)+14/27)^(-n)+1/1640520*((10080*2^(2/3)*31^(1/2)*3^(1/2)-99820*2^(2/3))*(263+27*31^(1/2)*3^(1/2))^(1/3)+607600+(450*31^(1/2)*3^(1/2)*2^(1/3)-9610*2^(1/3))*(263+27*31^(1/2)*3^(1/2))^(2/3))*(1/5292*2^(1/3)*(27*31^(1/2)*3^(1/2)-263)*(263+27*31^(1/2)*3^(1/2))^(2/3)-1/54*(1052+108*31^(1/2)*3^(1/2))^(1/3)+14/27)^(-n)+1/1640520*(164052*5^(1/2)-273420)*(-1/2*5^(1/2)-1/2)^(-n)-1/10*(1/2*5^(1/2)-1/2)^(-n)*(5^(1/2)+5/3))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(4805 \left(\left(i-\frac{45 \sqrt{31}}{961}\right) \sqrt{3}-\frac{135 i \sqrt{31}}{961}+1\right) 2^{\frac{1}{3}} \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+607600-49910 \,2^{\frac{2}{3}} \left(\left(i+\frac{72 \sqrt{31}}{713}\right) \sqrt{3}-\frac{216 i \sqrt{31}}{713}-1\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{263 \,2^{\frac{1}{3}} \left(\left(i-\frac{27 \sqrt{31}}{263}\right) \sqrt{3}-\frac{81 i \sqrt{31}}{263}+1\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{10584}-\frac{i \sqrt{3}\, \left(1052+108 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{108}+\frac{\left(1052+108 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{108}+\frac{14}{27}\right)^{-n}}{1640520}\\+\\\frac{\left(49910 \,2^{\frac{2}{3}} \left(\left(i-\frac{72 \sqrt{31}}{713}\right) \sqrt{3}-\frac{216 i \sqrt{31}}{713}+1\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+607600-4805 \left(\left(i+\frac{45 \sqrt{31}}{961}\right) \sqrt{3}-\frac{135 i \sqrt{31}}{961}-1\right) 2^{\frac{1}{3}} \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{263 \,2^{\frac{1}{3}} \left(\left(i+\frac{27 \sqrt{31}}{263}\right) \sqrt{3}-\frac{81 i \sqrt{31}}{263}-1\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{10584}+\frac{i \sqrt{3}\, \left(1052+108 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{108}+\frac{\left(1052+108 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{108}+\frac{14}{27}\right)^{-n}}{1640520}\\+\\\frac{\left(\left(10080 \,2^{\frac{2}{3}} \sqrt{31}\, \sqrt{3}-99820 \,2^{\frac{2}{3}}\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+607600+\left(450 \sqrt{31}\, \sqrt{3}\, 2^{\frac{1}{3}}-9610 \,2^{\frac{1}{3}}\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(27 \sqrt{31}\, \sqrt{3}-263\right) \left(263+27 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{5292}-\frac{\left(1052+108 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{54}+\frac{14}{27}\right)^{-n}}{1640520}\\+\frac{\left(164052 \sqrt{5}-273420\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{1640520}-\frac{\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n} \left(\sqrt{5}+\frac{5}{3}\right)}{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) = 24
a(5) = 102
a(n+5) = -9*a(n)+5*a(n+1)+16*a(n+2)-20*a(n+3)+8*a(n+4), n >= 6
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 102
a{\left(n + 5 \right)} = - 9 a{\left(n \right)} + 5 a{\left(n + 1 \right)} + 16 a{\left(n + 2 \right)} - 20 a{\left(n + 3 \right)} + 8 a{\left(n + 4 \right)}, \quad n \geq 6
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/24479/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[22,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[6,x]
F[10,x] = F[11,x]+F[6,x]
F[11,x] = F[12,x]+F[13,x]+F[20,x]
F[12,x] = 0
F[13,x] = F[14,x]*F[16,x]
F[14,x] = F[15,x]+F[19,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = x
F[17,x] = F[12,x]+F[13,x]+F[18,x]
F[18,x] = F[16,x]*F[6,x]
F[19,x] = F[17,x]
F[20,x] = F[16,x]*F[21,x]
F[21,x] = F[6,x]
F[22,x] = F[12,x]+F[23,x]+F[63,x]
F[23,x] = F[16,x]*F[24,x]
F[24,x] = F[25,x]+F[44,x]
F[25,x] = F[26,x]+F[33,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[26,x]
F[30,x] = F[16,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[26,x]
F[33,x] = F[12,x]+F[23,x]+F[34,x]
F[34,x] = F[16,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[33,x]+F[6,x]
F[37,x] = F[17,x]+F[38,x]
F[38,x] = 2*F[12,x]+F[39,x]+F[43,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[31,x]+F[38,x]
F[42,x] = F[38,x]
F[43,x] = F[16,x]*F[33,x]
F[44,x] = F[33,x]+F[45,x]
F[45,x] = F[12,x]+F[46,x]+F[56,x]+F[58,x]
F[46,x] = F[16,x]*F[47,x]
F[47,x] = F[48,x]+F[55,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[12,x]+F[32,x]+F[50,x]
F[50,x] = F[16,x]*F[51,x]
F[51,x] = F[30,x]
F[52,x] = F[12,x]+F[43,x]+F[46,x]+F[53,x]
F[53,x] = F[16,x]*F[54,x]
F[54,x] = F[37,x]
F[55,x] = F[52,x]
F[56,x] = F[16,x]*F[57,x]
F[57,x] = F[33,x]
F[58,x] = F[16,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[11,x]+F[61,x]
F[61,x] = F[12,x]+F[39,x]+F[56,x]+F[62,x]
F[62,x] = 0
F[63,x] = F[16,x]*F[64,x]
F[64,x] = F[5,x]+F[65,x]
F[65,x] = F[11,x]+F[66,x]
F[66,x] = F[12,x]+F[39,x]+F[56,x]+F[67,x]
F[67,x] = 0
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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = 0
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{6}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{6}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)+F_{23}\! \left(x \right)+F_{63}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{44}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{26}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right)+F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{17}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{33}\! \left(x \right)
F_{44}\! \left(x \right) = F_{33}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right)+F_{46}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{55}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right)+F_{32}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{16}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{30}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right)+F_{43}\! \left(x \right)+F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{16}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{37}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{33}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{11}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)+F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 0
F_{63}\! \left(x \right) = F_{16}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{5}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)+F_{56}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 0
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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_22(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_6(x))
Eq(F_10(x), F_11(x) + F_6(x))
Eq(F_11(x), F_12(x) + F_13(x) + F_20(x))
Eq(F_12(x), 0)
Eq(F_13(x), F_14(x)*F_16(x))
Eq(F_14(x), F_15(x) + F_19(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), x)
Eq(F_17(x), F_12(x) + F_13(x) + F_18(x))
Eq(F_18(x), F_16(x)*F_6(x))
Eq(F_19(x), F_17(x))
Eq(F_20(x), F_16(x)*F_21(x))
Eq(F_21(x), F_6(x))
Eq(F_22(x), F_12(x) + F_23(x) + F_63(x))
Eq(F_23(x), F_16(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_44(x))
Eq(F_25(x), F_26(x) + F_33(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_26(x))
Eq(F_30(x), F_16(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_26(x))
Eq(F_33(x), F_12(x) + F_23(x) + F_34(x))
Eq(F_34(x), F_16(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_33(x) + F_6(x))
Eq(F_37(x), F_17(x) + F_38(x))
Eq(F_38(x), 2*F_12(x) + F_39(x) + F_43(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_31(x) + F_38(x))
Eq(F_42(x), F_38(x))
Eq(F_43(x), F_16(x)*F_33(x))
Eq(F_44(x), F_33(x) + F_45(x))
Eq(F_45(x), F_12(x) + F_46(x) + F_56(x) + F_58(x))
Eq(F_46(x), F_16(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_55(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_12(x) + F_32(x) + F_50(x))
Eq(F_50(x), F_16(x)*F_51(x))
Eq(F_51(x), F_30(x))
Eq(F_52(x), F_12(x) + F_43(x) + F_46(x) + F_53(x))
Eq(F_53(x), F_16(x)*F_54(x))
Eq(F_54(x), F_37(x))
Eq(F_55(x), F_52(x))
Eq(F_56(x), F_16(x)*F_57(x))
Eq(F_57(x), F_33(x))
Eq(F_58(x), F_16(x)*F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_11(x) + F_61(x))
Eq(F_61(x), F_12(x) + F_39(x) + F_56(x) + F_62(x))
Eq(F_62(x), 0)
Eq(F_63(x), F_16(x)*F_64(x))
Eq(F_64(x), F_5(x) + F_65(x))
Eq(F_65(x), F_11(x) + F_66(x))
Eq(F_66(x), F_12(x) + F_39(x) + F_56(x) + F_67(x))
Eq(F_67(x), 0)
Pack JSON:
{"name": "regular_insertion_encoding_left", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}], "inferral_strats": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 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[[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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[0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 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