0123_0132_0231_1320_2103
Counting sequence:
1, 1, 2, 6, 19, 49, 105, 233, 520, 1150, 2521, 5536, 12171, 26740, 58717, 128949, 283216, 622011, 1366037, 3000065, 6588742, 14470151, 31779166, 69793054, 153278834, 336629436, 739302048, 1623647501, 3565837998, 7831256758, 17198925359, 37772102685, 82954703076, 182184264772, 400111206074, 878720110433, 1929836057985, 4238286077979, 9308080239845, 20442309971188, 44895190651400, 98598355394221, 216540692785532, 475564439635983, 1044429725135366, 2293765807176497, 5037544845334667, 11063404114475398, 24297334189205161, 53361555141014771, 117192097902351247, 257376078610537222, 565246693477008913, 1241388967504498124, 2726325667050650014, 5987528355243128898, 13149748116344339142, 28879341401679271374, 63424512197166316499, 139292260564314302886, 305912228269115308478, 671841285549144397647, 1475490912940066532789, 3240457948917550772570, 7116660378327566328994, 15629536238041798668582, 34325426538573810538751, 75385148292963460715841, 165560086391521118351329, 363601356854085162479433, 798537555685296432547300, 1753739956739888024415686, 3851545633600881597691701, 8458724858665139092991636, 18576964429655771199636063, 40798537981427633993805480, 89601328985956216196915625, 196781516036291691466659861, 432169539132735628343086292, 949126291514878425384629927, 2084461387659493719245588317, 4577872634534674691913286057, 10053876738658423838424052986, 22080220562189456873325491771, 48492353024410589678697511770, 106498406355180412023856556022, 233890703354479861656390496370, 513668354183708247496042604252, 1128113149883970159109564239768, 2477550482866589955668655016617, 5441170857536596606763332510042, 11949843406076731484795634315342, 26244123033182126727721012182195, 57637072752815791452158840807261, 126581945653627760925429774166904, 277997965548574596894180874794644, 610536269213457052391887001438018, 1340853467360916672221124959170469, 2944768577385221992629821873505769, 6467270425472404321242693234103131, 14203352710768405412384606905058557
Generating function in Maple syntax:
(3*x^7+2*x^6+10*x^5+5*x^4+x^3-x+1)/(x-1)/(x^5+3*x^4+2*x^3+x^2+x-1)
Generating function in latex syntax:
\frac{3 x^{7}+2 x^{6}+10 x^{5}+5 x^{4}+x^{3}-x +1}{\left(x -1\right) \left(x^{5}+3 x^{4}+2 x^{3}+x^{2}+x -1\right)}
Generating function in sympy syntax:
(3*x**7 + 2*x**6 + 10*x**5 + 5*x**4 + x**3 - x + 1)/((x - 1)*(x**5 + 3*x**4 + 2*x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(x^5+3*x^4+2*x^3+x^2+x-1)*F(x)+3*x^7+2*x^6+10*x^5+5*x^4+x^3-x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(x^{5}+3 x^{4}+2 x^{3}+x^{2}+x -1\right) F \! \left(x \right)+3 x^{7}+2 x^{6}+10 x^{5}+5 x^{4}+x^{3}-x +1 = 0
Explicit closed form in Maple syntax:
1/7367*((14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2+(14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+66069*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+70083)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+70083*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+52091)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^(1-n)+1/7367*(((-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+(-23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-45452*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-84265)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)^(1-n)+1/7367*(-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^3-42708*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2-28472*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+5369)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(1-n)+1/7367*((14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^(-n+2)+1/7367*(-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2-42708*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)-24631)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(-n+2)+1/7367*(-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)-23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(-n+3)+19605/7367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(1-n)+3841/7367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n+2)+19347/7367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n+3)+14236/7367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n+4)+1/7367*(((-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2+((-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+(-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-89430*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-115535)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-115535*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-136356)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+(-23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+(-23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-115535*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-136356)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-45452*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-136356*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-86817)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)^(-n)+1/7367*((((14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+(23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+45452*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+84265)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+((23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+45452)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+45452*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+84265)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+(45452*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+84265)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+84265*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+165978)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 5)^(-n)+1/7367*((14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+23361)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^3+(14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+66069*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+70083)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2+(14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^3+66069*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+98555*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+46722)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+23361*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^3+70083*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+46722*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+4087)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^(-n)+1/7367*(-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^4-42708*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^3-28472*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2-14236*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)-19274)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(-n)+piecewise(n = 0,-4,n = 1,3,0)-5038/7367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n)-3
Explicit closed form in latex syntax:
\frac{\left(\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+66069 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+70083\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+70083 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+52091\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{1-n}}{7367}+\frac{\left(\left(\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+\left(-23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-45452 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-84265\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{1-n}}{7367}+\frac{\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{3}-42708 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}-28472 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+5369\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{1-n}}{7367}+\frac{\left(\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{7367}+\frac{\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}-42708 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)-24631\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{7367}+\frac{\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)-23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{7367}+\frac{19605 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{1-n}}{7367}+\frac{3841 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{7367}+\frac{19347 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{7367}+\frac{14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{7367}+\frac{\left(\left(\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-89430 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-115535\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-115535 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-136356\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+\left(-23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-115535 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-136356\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-45452 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-136356 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-86817\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{7367}+\frac{\left(\left(\left(\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+\left(23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+45452 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+84265\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+45452\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+45452 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+84265\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+\left(45452 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+84265\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+84265 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+165978\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{7367}+\frac{\left(\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+23361\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+66069 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+70083\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{3}+66069 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+98555 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+46722\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+23361 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{3}+70083 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+46722 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+4087\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{7367}+\frac{\left(-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{4}-42708 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{3}-28472 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}-14236 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)-19274\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{7367}+\left(\left\{\begin{array}{cc}-4 & n =0 \\ 3 & n =1 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)-\frac{5038 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{7367}-3
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 49
a(6) = 105
a(7) = 233
a(n+5) = a(n)+3*a(n+1)+2*a(n+2)+a(n+3)+a(4+n)+21, n >= 8
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) = 49
a \! \left(6\right) = 105
a \! \left(7\right) = 233
a \! \left(n +5\right) = a \! \left(n \right)+3 a \! \left(n +1\right)+2 a \! \left(n +2\right)+a \! \left(n +3\right)+a \! \left(4+n \right)+21, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16138/
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[42,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]+F[26,x]
F[20,x] = F[21,x]+F[7,x]
F[21,x] = F[13,x]+F[17,x]+F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[11,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[13,x]
F[26,x] = F[27,x]+F[33,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[2,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[2,x]*F[4,x]
F[33,x] = 2*F[17,x]+F[34,x]+F[36,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[25,x]+F[7,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[54,x]
F[44,x] = F[2,x]+F[45,x]
F[45,x] = F[17,x]+F[32,x]+F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[4,x]+F[49,x]
F[49,x] = F[13,x]+F[17,x]+F[50,x]
F[50,x] = F[4,x]*F[7,x]
F[51,x] = F[31,x]+F[52,x]
F[52,x] = 2*F[17,x]+F[34,x]+F[53,x]
F[53,x] = F[38,x]*F[4,x]
F[54,x] = F[38,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[12,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_{42}\! \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_{26}\! \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_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \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_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{7}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{54}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{51}\! \left(x \right) = F_{31}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{34}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{38}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \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_42(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_26(x))
Eq(F_20(x), F_21(x) + F_7(x))
Eq(F_21(x), F_13(x) + F_17(x) + F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_11(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x))
Eq(F_26(x), F_27(x) + F_33(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_2(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_2(x)*F_4(x))
Eq(F_33(x), 2*F_17(x) + F_34(x) + F_36(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_25(x) + F_7(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_54(x))
Eq(F_44(x), F_2(x) + F_45(x))
Eq(F_45(x), F_17(x) + F_32(x) + F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_4(x) + F_49(x))
Eq(F_49(x), F_13(x) + F_17(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_7(x))
Eq(F_51(x), F_31(x) + F_52(x))
Eq(F_52(x), 2*F_17(x) + F_34(x) + F_53(x))
Eq(F_53(x), F_38(x)*F_4(x))
Eq(F_54(x), F_38(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_12(x))
Pack JSON:
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Specification JSON:
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