0132_1032_1203_1302_2031
Counting sequence:
1, 1, 2, 6, 19, 60, 188, 586, 1822, 5660, 17581, 54622, 169757, 527741, 1641077, 5104238, 15878417, 49401645, 153716446, 478336585, 1488583330, 4632685229, 14418091234, 44873964954, 139665789505, 434702800955, 1353006930533, 4211255158387, 13107688229034, 40798382552614, 126987665272140, 395258724495969, 1230275590772809, 3829341732583170, 11919181480901036, 37099596816807281, 115476148498993142, 359431100068772264, 1118765880405890290, 3482273883258265844, 10838938548527483554, 33737327001129381493, 105010966172674490952, 326857676552139711735, 1017378986354543901503, 3166699597437479644211, 9856687624050577246620, 30679984568479692494249, 95494705478724354895791, 297237404562095013537482, 925182980390597166759305, 2879730294882688064124578, 8963466505368803584517307, 27899742056328818547782210, 86840912605266120829077638, 270301572001138728612138667, 841342379834764085451469847, 2618767611029970859085250227, 8151192640108904574391586003, 25371453838736581321238868036, 78971348005300063698772682280, 245806718485475755726873224588, 765099550907808085219765432321, 2381453715779844493603106284373, 7412527946068003306379769814314, 23072281524348889151383791778918, 71814929904254201074518184047875, 223531606642649498686834074037720, 695765897724590667158000663465404, 2165645349918068640937624246754242, 6740801463999059580892031313958882, 20981461429700303189310255836629268, 65307030046320938860301237124509417, 203275076328999880289086101490165774, 632715293105888971618077772620067825, 1969393638254295071898044130920515889, 6129947141653577887763590418357782101, 19080112390942201993004480810491114302, 59388878964455336646923345465309955353, 184854201715951640937242346107821546109, 575378361875918287527588418722023192626, 1790926342182948106015995032364931469421, 5574448703070891665906935470818390551590, 17351064424772610116786473528417977171557, 54007033288740526319556759676517452446162, 168102634700070587994583505723200838333254, 523237328035659899475695729727470092239077, 1628631829230869791886319407201368573178499, 5069289771704998826680805943670535054589633, 15778703527893182572104381819435874347825847, 49112892778566694961927426247481141574283310, 152869101876183978850489089397234321537138426, 475821337052947979311785671049798115502581632, 1481044514661084679190098468695455416400651729, 4609908559363009908084798809312456696371031445, 14348830649802052979015690047763063890683221698, 44662261380117653194139461554630900481083914772, 139016038328779547441569064904232650035779891465, 432702203503573124666891742117212058459286043370, 1346831625816025456097987885228986979920936298536, 4192156669438591408152642471866410737010547462258
Generating function in Maple syntax:
(x^2-3*x+1)*(2*x-1)^2/(x-1)/(x^5-3*x^4+13*x^3-16*x^2+7*x-1)
Generating function in latex syntax:
\frac{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2}}{\left(x -1\right) \left(x^{5}-3 x^{4}+13 x^{3}-16 x^{2}+7 x -1\right)}
Generating function in sympy syntax:
(2*x - 1)**2*(x**2 - 3*x + 1)/((x - 1)*(x**5 - 3*x**4 + 13*x**3 - 16*x**2 + 7*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^5-3*x^4+13*x^3-16*x^2+7*x-1)*F(x)-(x^2-3*x+1)*(2*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{5}-3 x^{4}+13 x^{3}-16 x^{2}+7 x -1\right) F \! \left(x \right)-\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
1+10759/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 1)^(-n+4)+10759/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 2)^(-n+4)+10759/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 3)^(-n+4)+10759/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 4)^(-n+4)+10759/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 5)^(-n+4)-33483/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 1)^(-n+3)-33483/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 2)^(-n+3)-33483/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 3)^(-n+3)-33483/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 4)^(-n+3)-33483/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 5)^(-n+3)+142236/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 5)^(-n+2)+142236/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 1)^(-n+2)+142236/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 2)^(-n+2)+142236/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 3)^(-n+2)+142236/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 4)^(-n+2)-184901/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 1)^(-n+1)-184901/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 2)^(-n+1)-184901/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 3)^(-n+1)-184901/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 4)^(-n+1)-184901/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 5)^(-n+1)-11158/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 1)^(-n-1)-11158/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 2)^(-n-1)-11158/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 3)^(-n-1)-11158/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 4)^(-n-1)-11158/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 5)^(-n-1)+81450/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 1)^(-n)+81450/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 2)^(-n)+81450/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 3)^(-n)+81450/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 4)^(-n)+81450/4903*RootOf(_Z^5-3*_Z^4+13*_Z^3-16*_Z^2+7*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
1+\frac{10759 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{4903}+\frac{10759 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{4903}+\frac{10759 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{4903}+\frac{10759 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{4903}+\frac{10759 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{4903}-\frac{33483 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{4903}-\frac{33483 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{4903}-\frac{33483 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{4903}-\frac{33483 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{4903}-\frac{33483 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{4903}+\frac{142236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{4903}+\frac{142236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{4903}+\frac{142236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{4903}+\frac{142236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{4903}+\frac{142236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{4903}-\frac{184901 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{4903}-\frac{184901 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{4903}-\frac{184901 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{4903}-\frac{184901 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{4903}-\frac{184901 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{4903}-\frac{11158 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{4903}-\frac{11158 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{4903}-\frac{11158 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{4903}-\frac{11158 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{4903}-\frac{11158 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{4903}+\frac{81450 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{4903}+\frac{81450 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{4903}+\frac{81450 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{4903}+\frac{81450 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{4903}+\frac{81450 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+13 \textit{\_Z}^{3}-16 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{4903}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = a(n)-3*a(n+1)+13*a(n+2)-16*a(n+3)+7*a(n+4)-1, 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 +5\right) = a \! \left(n \right)-3 a \! \left(n +1\right)+13 a \! \left(n +2\right)-16 a \! \left(n +3\right)+7 a \! \left(n +4\right)-1, \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19659/
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[21,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[6,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[10,x]
F[19,x] = F[14,x]
F[20,x] = F[12,x]*F[13,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[15,x]+F[23,x]+F[30,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[10,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]+F[23,x]+F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[2,x]+F[27,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[29,x]+F[32,x]
F[32,x] = F[33,x]+F[46,x]
F[33,x] = F[34,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[36,x]
F[39,x] = F[33,x]+F[40,x]
F[40,x] = 2*F[15,x]+F[41,x]+F[45,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[37,x]
F[44,x] = F[40,x]
F[45,x] = F[12,x]*F[39,x]
F[46,x] = 2*F[15,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[27,x]
F[50,x] = F[46,x]
F[51,x] = F[12,x]*F[32,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_{21}\! \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_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \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_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{46}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{15}\! \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_{27}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \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_21(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_6(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_10(x))
Eq(F_19(x), F_14(x))
Eq(F_20(x), F_12(x)*F_13(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_15(x) + F_23(x) + F_30(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_10(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x) + F_23(x) + F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_2(x) + F_27(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_29(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_46(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_36(x))
Eq(F_39(x), F_33(x) + F_40(x))
Eq(F_40(x), 2*F_15(x) + F_41(x) + F_45(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_37(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_12(x)*F_39(x))
Eq(F_46(x), 2*F_15(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_27(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_12(x)*F_32(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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