0123_0132_0231_2031_2103
Counting sequence:
1, 1, 2, 6, 19, 52, 134, 352, 945, 2543, 6807, 18177, 48570, 129895, 347430, 929085, 2484281, 6642864, 17763350, 47500349, 127018058, 339650598, 908237864, 2428663831, 6494344435, 17366132467, 46437713669, 124176255240, 332052160893, 887920469276, 2374334048659, 6349062029997, 16977639986566, 45398872894370, 121398360594163, 324623961118320, 868057159817754, 2321218773028064, 6207029723494681, 16597840081629643, 44383273102220631, 118682606987239521, 317361929771385122, 848638204242950387, 2269291727020232490, 6068174772916026217, 16226536516303228549, 43390392855872470312, 116027606402360933498, 310262354438206494845, 829653662316511778830, 2218526319899629572298, 5932426090116754492320, 15863539232786902433935, 42419723932071270931255, 113431999761695992637739, 303321600832236480837877, 811093815896021447257872, 2168896565162963669182465, 5799714186180835247752752, 15508662414641188200060191, 41470769450052493799538137, 110894458387061193539871174, 296536116017111432269400142, 792949164290914534589349995, 2120377057590438937212100956, 5669971126555611811215896302, 15161724402219015937611311136, 40543043644825323281514650353, 108413683323886255538850623975, 289902426537531158293214182407, 775210419345947780303380331473, 2072942960291918281623526036010, 5543130496426142335591575059551, 14822547599709428832451047016094, 39636071618249909219249482747669, 105988404675983847192313654073137, 283417136641457112249512055271968, 757868500687447910736513912141230, 2026569991993294645081710232149933, 5419127366716435022183165850898498, 14490958384225483116169142112998654, 38749389095940544632129429529776248, 103617380955500507419162442651034295, 277076926541845808470643222847960731, 740914531075107359896207648176062195, 1981234414607020241437683341021865461, 5297898260852588177487070216136499032, 14166787016927595105525930072202220261, 37882542189605970509329314525603511636, 101299398447405266779281987442048767371, 270878550717266599342907988771401092069, 724339831857769950322521044015875694598, 1936913021080699921013324932533459971242, 5179381122269453671207542789293172570259, 13849867556135088929251085928107345410424, 37035087164706258604773821227966140582290, 99033270588195071862588536226327653796128, 264818836250535697349697724359113137366233, 708135918530873332479190350999871501959811, 1893583123517518614935259054839355615345575
Generating function in Maple syntax:
(x-1)^2/(2*x^6-3*x^4-2*x^3+2*x^2-3*x+1)
Generating function in latex syntax:
\frac{\left(x -1\right)^{2}}{2 x^{6}-3 x^{4}-2 x^{3}+2 x^{2}-3 x +1}
Generating function in sympy syntax:
(x - 1)**2/(2*x**6 - 3*x**4 - 2*x**3 + 2*x**2 - 3*x + 1)
Implicit equation for the generating function in Maple syntax:
(2*x^6-3*x^4-2*x^3+2*x^2-3*x+1)*F(x)-(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{6}-3 x^{4}-2 x^{3}+2 x^{2}-3 x +1\right) F \! \left(x \right)-\left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-446372/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+4)-446372/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+4)-446372/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+4)-446372/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+4)-446372/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+4)-446372/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+4)-546750/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+3)-546750/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+3)-546750/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+3)-546750/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+3)-546750/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+3)-546750/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+3)+179508/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+2)+179508/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+2)+179508/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+2)+179508/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+2)+179508/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+2)+179508/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+2)+827267/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+1)+827267/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+1)+827267/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+1)+827267/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+1)+827267/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+1)+827267/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+1)+658105/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n-1)+658105/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n-1)+658105/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n-1)+658105/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n-1)+658105/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n-1)+658105/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n-1)+1541786/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n)+1541786/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n)+1541786/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n)+1541786/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n)+1541786/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n)+1541786/9900119*RootOf(2*_Z^6-3*_Z^4-2*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n)
Explicit closed form in latex syntax:
-\frac{446372 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{9900119}-\frac{446372 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{9900119}-\frac{446372 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{9900119}-\frac{446372 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{9900119}-\frac{446372 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{9900119}-\frac{446372 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{9900119}-\frac{546750 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{9900119}-\frac{546750 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{9900119}-\frac{546750 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{9900119}-\frac{546750 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{9900119}-\frac{546750 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{9900119}-\frac{546750 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{9900119}+\frac{179508 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{9900119}+\frac{179508 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{9900119}+\frac{179508 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{9900119}+\frac{179508 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{9900119}+\frac{179508 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{9900119}+\frac{179508 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{9900119}+\frac{827267 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{9900119}+\frac{827267 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{9900119}+\frac{827267 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{9900119}+\frac{827267 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{9900119}+\frac{827267 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{9900119}+\frac{827267 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{9900119}+\frac{658105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{9900119}+\frac{658105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{9900119}+\frac{658105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{9900119}+\frac{658105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{9900119}+\frac{658105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{9900119}+\frac{658105 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{9900119}+\frac{1541786 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{9900119}+\frac{1541786 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{9900119}+\frac{1541786 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{9900119}+\frac{1541786 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{9900119}+\frac{1541786 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{9900119}+\frac{1541786 \mathit{RootOf}\! \left(2 \textit{\_Z}^{6}-3 \textit{\_Z}^{4}-2 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{9900119}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 52
a(n) = 3/2*a(n+2)+a(n+3)-a(n+4)+3/2*a(n+5)-1/2*a(n+6), 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) = 52
a \! \left(n \right) = \frac{3 a \! \left(n +2\right)}{2}+a \! \left(n +3\right)-a \! \left(n +4\right)+\frac{3 a \! \left(n +5\right)}{2}-\frac{a \! \left(n +6\right)}{2}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16157/
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[15,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[4,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]+F[18,x]+F[36,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = F[21,x]+F[7,x]
F[21,x] = F[13,x]
F[22,x] = F[23,x]+F[33,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[2,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[2,x]*F[4,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[27,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[27,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[17,x]+F[28,x]+F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[12,x]+F[4,x]
F[43,x] = F[27,x]+F[44,x]
F[44,x] = F[34,x]
F[45,x] = F[16,x]+F[46,x]
F[46,x] = 2*F[17,x]+F[34,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[12,x]
F[50,x] = F[30,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_{15}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{36}\! \left(x \right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \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_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right)+F_{28}\! \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_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{34}\! \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_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \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_15(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_4(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x) + F_18(x) + F_36(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_21(x) + F_7(x))
Eq(F_21(x), F_13(x))
Eq(F_22(x), F_23(x) + F_33(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_2(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_2(x)*F_4(x))
Eq(F_29(x), F_23(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_27(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_27(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_2(x) + F_39(x))
Eq(F_39(x), F_17(x) + F_28(x) + F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_12(x) + F_4(x))
Eq(F_43(x), F_27(x) + F_44(x))
Eq(F_44(x), F_34(x))
Eq(F_45(x), F_16(x) + F_46(x))
Eq(F_46(x), 2*F_17(x) + F_34(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_12(x))
Eq(F_50(x), F_30(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 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{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 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0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": 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