0132_1203_1302_2031
Counting sequence:
1, 1, 2, 6, 20, 67, 221, 719, 2320, 7457, 23936, 76817, 246581, 791749, 2542839, 8168137, 26240689, 84306052, 270871307, 870324967, 2796468386, 8985570475, 28872655902, 92775169980, 298112163092, 957921192113, 3078090945354, 9890864993256, 31782492369112, 102127394499132, 328168588880097, 1054513396433020, 3388499594377399, 10888372099071343, 34987958399113398, 112427963812845070, 361268552914915621, 1160876515345917746, 3730284273358910225, 11986651004804884848, 38517120548470208121, 123768400834838424024, 397709309835167181480, 1277973190046613098143, 4106555859069850461072, 13195739411189029770632, 42402330771759271344817, 136252892573248093684301, 437826187118738480379069, 1406882210371167837764761, 4520783854924114535260942, 14526793034648653227793224, 46679452696696502662737016, 149996719899181654760353970, 481989712695065876392968164, 1548794422987235429991305113, 4976795359465131393384412651, 15992110823901211559291174804, 51388009788641173259898854157, 165126891593700049471834698247, 530608023974519098644548020949, 1705021346965603582477546367400, 5478804809580456335744580116832, 17605235380777783228393461024825, 56571519445065425917172957092405, 181783244765960449532607260233126, 584130467102012195070986764566824, 1877006888284486452731962520471214, 6031451973689545608602495499797643, 19381075870412983697894973558284867, 62277889890331829737618839507085669, 200119724783959266698557743562620794, 643051720574012057044094892937958365, 2066340615750323925378411339739447600, 6639844671425775005946941167514280747, 21336045434450754752793948042669772939, 68559862061274393245190195690309656925, 220305805980028516632344153601488285483, 707916362275489076534121910958751778737, 2274772440735940116156347664829785739343, 7309605954720094740722533413873375751378, 23488212823609198734517071209133886624749, 75475496909783879923898099565248483393867, 242528057649976548702929168898485147100228, 779323901872167341033673210797427012351111, 2504228788678223861480018730556191706600456, 8046926073972313091441722052449438301767970, 25857469386475110070419757833717682538966826, 83088712003346812278741891163940237746191467, 266991868352988244326976907289973141377934176, 857934321616980269562244475360218086993110798, 2756830403670810898290094366794081607319707788, 8858619690467198624842237249861058948168220090, 28465712912858611521964291552391354003684051595, 91469872276970140894637801133709729083055878020, 293923344199322659687456582292344850270726685781, 944474176193473473564666998025984598397432652391, 3034911949325857175253033511966113120638074617334, 9752188860560323801155169942849269511063712576462, 31337050023201681937310034635797835896948521572327, 100696440378434414668295286698516461440607633701002
Generating function in Maple syntax:
-(x-1)*(x^2-3*x+1)*(2*x-1)^2/(3*x^6-17*x^5+44*x^4-52*x^3+31*x^2-9*x+1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2}}{3 x^{6}-17 x^{5}+44 x^{4}-52 x^{3}+31 x^{2}-9 x +1}
Generating function in sympy syntax:
(1 - x)*(2*x - 1)**2*(x**2 - 3*x + 1)/(3*x**6 - 17*x**5 + 44*x**4 - 52*x**3 + 31*x**2 - 9*x + 1)
Implicit equation for the generating function in Maple syntax:
(3*x^6-17*x^5+44*x^4-52*x^3+31*x^2-9*x+1)*F(x)+(x-1)*(x^2-3*x+1)*(2*x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x^{6}-17 x^{5}+44 x^{4}-52 x^{3}+31 x^{2}-9 x +1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-132009/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 1)^(-n+4)-132009/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 2)^(-n+4)-132009/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 3)^(-n+4)-132009/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 4)^(-n+4)-132009/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 5)^(-n+4)-132009/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 6)^(-n+4)+671623/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 1)^(-n+3)+671623/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 2)^(-n+3)+671623/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 3)^(-n+3)+671623/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 4)^(-n+3)+671623/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 5)^(-n+3)+671623/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 6)^(-n+3)-1552642/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 1)^(-n+2)-1552642/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 2)^(-n+2)-1552642/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 3)^(-n+2)-1552642/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 4)^(-n+2)-1552642/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 5)^(-n+2)-1552642/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 6)^(-n+2)+1414429/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 1)^(-n+1)+1414429/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 2)^(-n+1)+1414429/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 3)^(-n+1)+1414429/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 4)^(-n+1)+1414429/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 5)^(-n+1)+1414429/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 6)^(-n+1)+88782/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 1)^(-n-1)+88782/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 2)^(-n-1)+88782/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 3)^(-n-1)+88782/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 4)^(-n-1)+88782/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 5)^(-n-1)+88782/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 6)^(-n-1)-575169/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 1)^(-n)-575169/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 2)^(-n)-575169/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 3)^(-n)-575169/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 4)^(-n)-575169/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 5)^(-n)-575169/93253*RootOf(3*_Z^6-17*_Z^5+44*_Z^4-52*_Z^3+31*_Z^2-9*_Z+1,index = 6)^(-n)
Explicit closed form in latex syntax:
-\frac{132009 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{93253}-\frac{132009 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{93253}-\frac{132009 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{93253}-\frac{132009 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{93253}-\frac{132009 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{93253}-\frac{132009 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{93253}+\frac{671623 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{93253}+\frac{671623 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{93253}+\frac{671623 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{93253}+\frac{671623 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{93253}+\frac{671623 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{93253}+\frac{671623 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{93253}-\frac{1552642 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{93253}-\frac{1552642 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{93253}-\frac{1552642 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{93253}-\frac{1552642 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{93253}-\frac{1552642 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{93253}-\frac{1552642 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{93253}+\frac{1414429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{93253}+\frac{1414429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{93253}+\frac{1414429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{93253}+\frac{1414429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{93253}+\frac{1414429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{93253}+\frac{1414429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{93253}+\frac{88782 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{93253}+\frac{88782 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{93253}+\frac{88782 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{93253}+\frac{88782 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{93253}+\frac{88782 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{93253}+\frac{88782 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{93253}-\frac{575169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{93253}-\frac{575169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{93253}-\frac{575169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{93253}-\frac{575169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{93253}-\frac{575169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{93253}-\frac{575169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{6}-17 \textit{\_Z}^{5}+44 \textit{\_Z}^{4}-52 \textit{\_Z}^{3}+31 \textit{\_Z}^{2}-9 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{93253}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 67
a(n+6) = -3*a(n)+17*a(n+1)-44*a(n+2)+52*a(n+3)-31*a(n+4)+9*a(n+5), 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) = 20
a \! \left(5\right) = 67
a \! \left(n +6\right) = -3 a \! \left(n \right)+17 a \! \left(n +1\right)-44 a \! \left(n +2\right)+52 a \! \left(n +3\right)-31 a \! \left(n +4\right)+9 a \! \left(n +5\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15551/
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[27,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[6,x]
F[26,x] = F[22,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[36,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[15,x]+F[31,x]+F[35,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[10,x]
F[34,x] = F[30,x]
F[35,x] = F[12,x]*F[29,x]
F[36,x] = F[37,x]+F[50,x]
F[37,x] = F[38,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[40,x]
F[43,x] = F[37,x]+F[44,x]
F[44,x] = 2*F[15,x]+F[45,x]+F[49,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[41,x]
F[48,x] = F[44,x]
F[49,x] = F[12,x]*F[43,x]
F[50,x] = 2*F[15,x]+F[51,x]+F[55,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[30,x]
F[54,x] = F[50,x]
F[55,x] = F[12,x]*F[36,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_{27}\! \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_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{50}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{45}\! \left(x \right)+F_{49}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{30}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \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_27(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_6(x))
Eq(F_26(x), F_22(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_36(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_15(x) + F_31(x) + F_35(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_10(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_12(x)*F_29(x))
Eq(F_36(x), F_37(x) + F_50(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_40(x))
Eq(F_43(x), F_37(x) + F_44(x))
Eq(F_44(x), 2*F_15(x) + F_45(x) + F_49(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_41(x))
Eq(F_48(x), F_44(x))
Eq(F_49(x), F_12(x)*F_43(x))
Eq(F_50(x), 2*F_15(x) + F_51(x) + F_55(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_30(x))
Eq(F_54(x), F_50(x))
Eq(F_55(x), F_12(x)*F_36(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": 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