0123_0231_0321_1032_1302
Counting sequence:
1, 1, 2, 6, 19, 54, 155, 451, 1313, 3814, 11078, 32187, 93522, 271723, 789471, 2293765, 6664418, 19363110, 56258467, 163455950, 474912491, 1379832731, 4009029849, 11648020814, 33842698646, 98328142571, 285687135082, 830048621083, 2411661670327, 7006953405341, 20358326637802, 59150024199638, 171857217199955, 499321910740518, 1450752983247995, 4215084844327411, 12246702540015953, 35582136218557046, 103381984966076966, 300370802637537179, 872711228235009794, 2535615583138171275, 7367094838983541263, 21404698222987855349, 62190200619216302770, 180690286439296287174, 524985918817355468163, 1525318379796223495678, 4431730597623148185291, 12876155135908795678155, 37410976915634448734345, 108695583348402359454814, 315809177239420922180342, 917566596141791803862475, 2665940444526576065694746, 7745746721433911699568571, 22504850922601358844006631, 65386635177086266923342605, 189977355303768257783128122, 551968998411801983682234102, 1603716267765543762555128883, 4659511448824249368784738134, 13537960160480404035099996635, 39333815855952315729741487395, 114282288575966981686884602497, 332041049106202599244786793734, 964727427717377352804489273862, 2802963706732854930201991726971, 8143860447557654986518461122226, 23661548963329133370833387776171, 68747359185400427140700601346623, 199741758339285558248898351687397, 580338946793206459473775706936194, 1686143628479348497851626437346150, 4898999716582152310977934134271331, 14233780454822006057997224528334382, 41355484334957198201692971328985515, 120156137718106828747941632750638587, 349107202188630755473401057239178041, 1014312218539357535511688837884658286, 2947029652290968694643247244188390742, 8562436311759002491709410699251537579, 24877698646817170949485880321073439434, 72280816747436543770599611475751864411, 210008029434222718969351645073104303127, 610167045856043020138850000596582679933, 1772807567652078594954464638590717829770, 5150797135422440404534875056155384401174, 14965364326266678290356012953190201307923, 43481061965669349238642239791047029255814, 126331889317526242789317221169659207731771, 367050516639561018924647395403284945296979, 1066445554587917309943195707463169119176369, 3098500259072379389141504383210207454335638, 9002526021294530439642644974561588283644646, 26156355651991555083018834908464862164784475, 75995885974133688859790769433910012347962466, 220801963462895117144893876310672220662375115, 641528241221684544402288165523177547343705199, 1863925835759828387985285704086022131662160597, 5415536367653741432537109798973213576985920338
Generating function in Maple syntax:
-(x^3+2*x-1)/(2*x^5-x^4-2*x^3+x^2-3*x+1)
Generating function in latex syntax:
-\frac{x^{3}+2 x -1}{2 x^{5}-x^{4}-2 x^{3}+x^{2}-3 x +1}
Generating function in sympy syntax:
(-x**3 - 2*x + 1)/(2*x**5 - x**4 - 2*x**3 + x**2 - 3*x + 1)
Implicit equation for the generating function in Maple syntax:
(2*x^5-x^4-2*x^3+x^2-3*x+1)*F(x)+x^3+2*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{5}-x^{4}-2 x^{3}+x^{2}-3 x +1\right) F \! \left(x \right)+x^{3}+2 x -1 = 0
Explicit closed form in Maple syntax:
3657490415/3479215998728*((((RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-15741/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-15741/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1626/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(-15741/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1626/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+1626/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+13029/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+((-15741/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1626/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+1626/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+13029/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(1626/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+13029/12461)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+13029/12461*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-69593/12461)*((((-318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+158209/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-184533/117406-89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(74813/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+232085/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(273351/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+4302731/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-8165601/1174060-280017/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+158209/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(273351/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+4302731/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-1779397/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-4403889/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-696991/587030+815393/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-184533/117406-89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-8165601/1174060-280017/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-696991/587030+815393/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-1187623/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-14773207/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+1)+(((89049/117406-418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(1887/58703-96791/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+1887/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+73317/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((1887/58703-96791/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-2127123/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+9344833/587030-96791/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+1887/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-2895913/587030+9344833/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+1887/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+73317/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(1887/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-2895913/587030+9344833/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-2895913/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+73317/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-3757411/293515)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+1)+(((318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^4+((268623/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-305961/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-305961/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-3774073/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-930329/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+6223/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+6223/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+3432399/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((1248231/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1762671/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+1762671/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1000991/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(1268155/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1556689/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-23861473/1174060-1556689/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+1)+(((-318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+158209/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-184533/117406-89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+158209/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(96791/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+3450683/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-1887/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-2455359/293515)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-184533/117406-89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-1887/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-2455359/293515)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-256437/587030-73317/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+2)+(((318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((268623/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-305961/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-305961/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-3774073/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-79769/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+519727/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+519727/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+2736383/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(272469/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-331167/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-5057007/1174060-331167/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+2)+(((318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((-418249/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-158209/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-3469553/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(89049/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+184533/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+4544133/587030+184533/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+3)+(((1785477/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+1150749/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+1150749/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1309431/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(1150749/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1309431/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-3893851/234812-1309431/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+1)+(((1780889/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+507281/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+507281/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-825683/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(507281/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-825683/234812)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-13841443/1174060-825683/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+2)+(((-343436/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+73876/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+73876/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+30452/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(73876/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+30452/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+1174012/293515+30452/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+3)+(((-318407/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-1)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(-RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+2196109/293515+123629/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+4)+(((-RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+3469553/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-4544133/587030-184533/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3-(-1/2+RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2))*((RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(-158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-3469553/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+4544133/587030+184533/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+3469553/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(-527275/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-12557819/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(9608849/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-8108083/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+1733083/587030-2514697/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-4544133/587030-184533/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^3+(4544133/1174060+184533/234812*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(1733083/587030-2514697/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-6875221/1174060*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-36777217/1174060)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n)+(((184533/117406-158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(2455359/293515-3450683/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+184533/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2455359/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+256437/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((2455359/293515-3450683/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-158209/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(8175601/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-4713619/587030-3450683/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+2455359/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-3565829/587030-4713619/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(184533/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2+2455359/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+256437/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^2+(2455359/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-3565829/587030-4713619/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)-3565829/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+256437/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)^2-1759715/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n)+(((RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-2196109/293515-123629/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^4+((-1/2*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+123629/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+123629/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+2196109/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^3+((-RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)+123629/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)+2196109/293515+123629/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^2+((5134137/587030*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-571311/117406)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-571311/117406*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-6568079/587030)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)+(-1718681/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-281105/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-7254961/293515-281105/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n)+(((2420311/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-223841/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-223841/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-437197/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 2)+(-223841/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3)-437197/58703)*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 4)-10858197/293515-437197/58703*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 3))*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n)-10551536/293515*RootOf(2*_Z^5-_Z^4-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n))
Explicit closed form in latex syntax:
\frac{3657490415 \left(\left(\left(\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{15741}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{15741 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}+\frac{1626}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{15741 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}+\frac{1626}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1626 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}+\frac{13029}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{15741 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}+\frac{1626}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1626 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}+\frac{13029}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{1626 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}+\frac{13029}{12461}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{13029 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{12461}-\frac{69593}{12461}\right) \left(\left(\left(\left(-\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{293515}-1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}+\frac{158209}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{184533}{117406}-\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{293515}-1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{74813 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{293515}+\frac{232085}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{273351 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{1174060}+\frac{4302731}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{8165601}{1174060}-\frac{280017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}+\frac{158209}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{273351 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{1174060}+\frac{4302731}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1779397 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{1174060}-\frac{4403889}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{696991}{587030}+\frac{815393 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{184533}{117406}-\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{8165601}{1174060}-\frac{280017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{696991}{587030}+\frac{815393 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1187623 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{234812}-\frac{14773207}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(\frac{89049}{117406}-\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}+\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{293515}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1887}{58703}-\frac{96791 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}+\frac{1887 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}+\frac{73317}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1887}{58703}-\frac{96791 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{2127123 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+\frac{9344833}{587030}-\frac{96791 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1887 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{58703}-\frac{2895913}{587030}+\frac{9344833 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}+\frac{1887 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}+\frac{73317}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1887 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{58703}-\frac{2895913}{587030}+\frac{9344833 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{2895913 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}+\frac{73317 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}-\frac{3757411}{293515}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(\frac{268623 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{305961}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{305961 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}-\frac{3774073}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{930329 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}+\frac{6223}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{6223 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}+\frac{3432399}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1248231 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{1174060}+\frac{1762671}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1762671 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}+\frac{1000991}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{1268155 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}-\frac{1556689}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{23861473}{1174060}-\frac{1556689 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{293515}-1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}+\frac{158209}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{184533}{117406}-\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}+\frac{158209}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{96791 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}+\frac{3450683}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1887 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{58703}-\frac{2455359}{293515}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{184533}{117406}-\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1887 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{58703}-\frac{2455359}{293515}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{256437}{587030}-\frac{73317 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{268623 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{305961}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{305961 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}-\frac{3774073}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{79769 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{1174060}+\frac{519727}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{519727 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}+\frac{2736383}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{272469 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}-\frac{331167}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{5057007}{1174060}-\frac{331167 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{418249 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{158209}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}-\frac{3469553}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{89049 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}+\frac{184533}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{4544133}{587030}+\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{1785477 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{1174060}+\frac{1150749}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1150749 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}-\frac{1309431}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{1150749 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}-\frac{1309431}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{3893851}{234812}-\frac{1309431 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{1780889 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{1174060}+\frac{507281}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{507281 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}-\frac{825683}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{507281 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}-\frac{825683}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{13841443}{1174060}-\frac{825683 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{343436 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+\frac{73876}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{73876 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}+\frac{30452}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{73876 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}+\frac{30452}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1174012}{293515}+\frac{30452 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-\frac{318407 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}-1\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2196109}{293515}+\frac{123629 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}+\frac{3469553}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{4544133}{587030}-\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(-\frac{1}{2}+\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)\right) \left(\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}-\frac{3469553}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{4544133}{587030}+\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}+\frac{3469553}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{527275 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{234812}-\frac{12557819}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{9608849 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{1174060}-\frac{8108083}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1733083}{587030}-\frac{2514697 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{4544133}{587030}-\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{4544133}{1174060}+\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{234812}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1733083}{587030}-\frac{2514697 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{6875221 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)}{1174060}-\frac{36777217}{1174060}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\frac{184533}{117406}-\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}+\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{2455359}{293515}-\frac{3450683 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}+\frac{2455359 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+\frac{256437}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{2455359}{293515}-\frac{3450683 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{158209 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{8175601 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}-\frac{4713619}{587030}-\frac{3450683 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{2455359 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{293515}-\frac{3565829}{587030}-\frac{4713619 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{184533 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{117406}+\frac{2455359 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}+\frac{256437}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{2455359 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{293515}-\frac{3565829}{587030}-\frac{4713619 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{3565829 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}+\frac{256437 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{587030}-\frac{1759715}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{2196109}{293515}-\frac{123629 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{\mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{2}+\frac{123629}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{123629 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}+\frac{2196109}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{123629}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2196109}{293515}+\frac{123629 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{5134137 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{587030}-\frac{571311}{117406}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{571311 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{117406}-\frac{6568079}{587030}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{1718681 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}-\frac{281105}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{7254961}{293515}-\frac{281105 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{2420311 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{293515}-\frac{223841}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{223841 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}-\frac{437197}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{223841 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}-\frac{437197}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{10858197}{293515}-\frac{437197 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)}{58703}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}-\frac{10551536 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{293515}\right)}{3479215998728}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = -2*a(n)+a(n+1)+2*a(n+2)-a(n+3)+3*a(n+4), 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) = -2 a \! \left(n \right)+a \! \left(n +1\right)+2 a \! \left(n +2\right)-a \! \left(n +3\right)+3 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17073/
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[20,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[4,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[87,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[36,x]
F[25,x] = F[15,x]+F[26,x]
F[26,x] = F[22,x]+F[27,x]+F[34,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]+F[4,x]
F[30,x] = F[31,x]
F[31,x] = x^2
F[32,x] = F[33,x]
F[33,x] = F[18,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[15,x]+F[33,x]
F[36,x] = F[37,x]+F[76,x]
F[37,x] = F[22,x]+F[23,x]+F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[2,x]+F[40,x]
F[40,x] = F[22,x]+F[41,x]+F[70,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[4,x]+F[44,x]
F[44,x] = F[22,x]+F[27,x]+F[45,x]
F[45,x] = F[15,x]*F[4,x]
F[46,x] = F[40,x]+F[47,x]
F[47,x] = F[22,x]+F[48,x]+F[64,x]+F[72,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[54,x]
F[50,x] = F[33,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[33,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = 2*F[22,x]+F[48,x]+F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[40,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[40,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[40,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[2,x]*F[4,x]
F[71,x] = F[61,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[2,x]+F[69,x]
F[76,x] = F[22,x]+F[64,x]+F[77,x]+F[85,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[18,x]
F[81,x] = F[52,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = 2*F[22,x]+F[56,x]+F[77,x]
F[84,x] = F[59,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[61,x]+F[73,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[92,x]
F[89,x] = F[2,x]+F[90,x]
F[90,x] = F[22,x]+F[41,x]+F[91,x]
F[91,x] = F[4,x]*F[75,x]
F[92,x] = F[73,x]+F[93,x]
F[93,x] = F[62,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_{20}\! \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_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{87}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{36}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = x^{2}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{76}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right)+F_{41}\! \left(x \right)+F_{70}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)+F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{33}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{33}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{48}\! \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_{40}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{40}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{40}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{71}\! \left(x \right) = F_{61}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{2}\! \left(x \right)+F_{69}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right)+F_{64}\! \left(x \right)+F_{77}\! \left(x \right)+F_{85}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right)
F_{81}\! \left(x \right) = F_{52}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{56}\! \left(x \right)+F_{77}\! \left(x \right)
F_{84}\! \left(x \right) = F_{59}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{61}\! \left(x \right)+F_{73}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{22}\! \left(x \right)+F_{41}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{92}\! \left(x \right) = F_{73}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{62}\! \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_20(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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_4(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_87(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_36(x))
Eq(F_25(x), F_15(x) + F_26(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_34(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x) + F_4(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), x**2)
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_15(x) + F_33(x))
Eq(F_36(x), F_37(x) + F_76(x))
Eq(F_37(x), F_22(x) + F_23(x) + F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_2(x) + F_40(x))
Eq(F_40(x), F_22(x) + F_41(x) + F_70(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_4(x) + F_44(x))
Eq(F_44(x), F_22(x) + F_27(x) + F_45(x))
Eq(F_45(x), F_15(x)*F_4(x))
Eq(F_46(x), F_40(x) + F_47(x))
Eq(F_47(x), F_22(x) + F_48(x) + F_64(x) + F_72(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_54(x))
Eq(F_50(x), F_33(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_33(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), 2*F_22(x) + F_48(x) + F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_40(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_40(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_40(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_2(x)*F_4(x))
Eq(F_71(x), F_61(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_2(x) + F_69(x))
Eq(F_76(x), F_22(x) + F_64(x) + F_77(x) + F_85(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_18(x))
Eq(F_81(x), F_52(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), 2*F_22(x) + F_56(x) + F_77(x))
Eq(F_84(x), F_59(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_61(x) + F_73(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_92(x))
Eq(F_89(x), F_2(x) + F_90(x))
Eq(F_90(x), F_22(x) + F_41(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_75(x))
Eq(F_92(x), F_73(x) + F_93(x))
Eq(F_93(x), F_62(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "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, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 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, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", 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