0132_0213_0231_2013_2103
Counting sequence:
1, 1, 2, 6, 19, 58, 173, 513, 1521, 4512, 13388, 39727, 117884, 349801, 1037973, 3080001, 9139358, 27119430, 80472119, 238786802, 708557665, 2102519737, 6238856005, 18512703384, 54933177864, 163004503863, 483687077880, 1435255982281, 4258868654713, 12637440597369, 37499373143450, 111272767244062, 330182285522123, 979757620599938, 2907257709497365, 8626773818055465, 25598427777754153, 75958813632209032, 225394364783088484, 668817971828222167, 1984599215117463140, 5888947681651774465, 17474412230471032349, 51852232233584287273, 153862341814119102118, 456559326547018045102, 1354759171083529375871, 4020008583585289374506, 11928665520067559315001, 35396208274446768946609, 105031996923736195319181, 311663901744858623436656, 924807587171347749369232, 2744203189722785880056239, 8142938326791038966685424, 24162731404965933166506961, 71698638196441445313522289, 212753046543723727357430577, 631307092466958674588524850, 1873292305204089230665122422, 5558664083788217894231666691, 16494353983390108395987843338, 48944082468096594751788979581, 145232920977453468549822947473, 430953044209013691716532857313, 1278777050430928786420450401456, 3794545059335314298109337882748, 11259642329735226248107114529215, 33411000109660873936085747880396, 99141242291486618551538629508825, 294184127707604271694443982620069, 872939444723053322429880879439697, 2590293637156330410908384842453806, 7686238910674095424381894918288214, 22807556542824102368040777588545479, 67677396123053569956625248311570850, 200820720860506879539005063683952017, 595900023304767780420168084179326697, 1768228080514054306450868944245954005, 5246904551838437275151234160595339912, 15569262630474381906479585302563142552, 46199037253641680543784848380113697895, 137087484090975219848644053931921613800, 406782898769432919970175212898571705369, 1207056412396119897486150829864973657321, 3581726732156506270972529366583822093865, 10628141528512510714551180580019300946378, 31537133007933919766651526184370186290446, 93580872600528468043802994900188605705915, 277684712636155338878773038066612732064466, 823980344369953238196256100005371585453029, 2445016153257355592349240886851250345327929, 7255153633865480884971106792867534816277529, 21528387115506734014241261880914828513798936, 63881686754603281394810859950804166972680852, 189557623649095229823038727871314079524485351, 562478771443879870463013391418767851277665204, 1669056417961307153615061078954180294233240561, 4952630157377898274696737335685702671936875565, 14696055335103512147287517333261883152095731129, 43607948816991592310568328563619809031581964086
Generating function in Maple syntax:
-(x-1)*(x^3+2*x-1)/(x^5-x^4+3*x^3-4*x^2+4*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(x^{3}+2 x -1\right)}{x^{5}-x^{4}+3 x^{3}-4 x^{2}+4 x -1}
Generating function in sympy syntax:
(1 - x)*(x**3 + 2*x - 1)/(x**5 - x**4 + 3*x**3 - 4*x**2 + 4*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^5-x^4+3*x^3-4*x^2+4*x-1)*F(x)+(x-1)*(x^3+2*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}-x^{4}+3 x^{3}-4 x^{2}+4 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{3}+2 x -1\right) = 0
Explicit closed form in Maple syntax:
207507/25381444*((((RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-555/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+41/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+41/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+41/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+469/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+((-555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+41/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+41/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+469/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(41/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+469/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+469/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-779/263)*((((370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4/3)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+781/263+555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(-2770/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-2980/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(5885/789+1484/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-7174/789+226/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4/3)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(5885/789+1484/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-8134/789+370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-271/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+7801/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(781/263+555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(-7174/789+226/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-271/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+7801/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-3350/789+990/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+1)+(((-370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-555/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-740/263+871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+325/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-1243/789-740/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-740/263+871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+325/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(3752/789+325/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-8365/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+3752/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+656/263-740/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-1243/789-740/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(3752/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+656/263-740/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-1105/789-1243/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+656/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n+1)+(((-370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2717/789+RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^4+((633/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1928/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-2864/789+1928/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((-1373/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-350/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2766/263-350/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((1993/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1562/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1500/263+1562/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-1353/263-1155/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1353/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+11143/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+1)+(((370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4/3)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+781/263+555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4/3)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-325/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+1570/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-1196/263+740/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(781/263+555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-1196/263+740/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+1243/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2245/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+2)+(((-370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2717/789+RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((633/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1928/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-2864/789+1928/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-603/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1175/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+3733/789-1175/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(3586/789+514/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+3586/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-862/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+2)+(((-370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2717/789+RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((871/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+4/3)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-830/263+4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-781/263-555/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+4831/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+3)+(((-4814/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-103/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+6809/789-103/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(6809/789-103/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+6809/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+10555/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+1)+(((770/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-275/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4565/789-275/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-4565/789-275/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4565/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-715/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+2)+(((-1028/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-292/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+374/789-292/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(374/789-292/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+374/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+4684/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+3)+(((370/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-2717/789-RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-2717/789-RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-2717/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+49/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+4)+(((-2717/789-RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+830/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-4831/789+781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3-((RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2717/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-830/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+4831/789-781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*(RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-1)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+830/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(3395/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-7321/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(5498/789-8129/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+4380/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+1795/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-4831/789+781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(4831/789-781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(4380/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+1795/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-2831/789+338/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n)+(((RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-781/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(1196/263+4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-1570/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-2245/789+1196/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((1196/263+4/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-1570/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(7307/789-1570/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+3757/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+7307/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+861/263+1196/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-2245/789+1196/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-781/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(7307/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+861/263+1196/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-13108/789-2245/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+861/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n)+(((2717/789+RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2717/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-49/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^4+((-2717/789-RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-2717/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+49/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+2717/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-147/263+2717/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-10/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-6803/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+5219/789-6803/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(16288/789+2037/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+16288/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-3706/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n)+(((2/3*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1355/263)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+4631/789+1355/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(4631/789+1355/263*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+4631/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-13247/789)*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n)-5038/789*RootOf(_Z^5-_Z^4+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n))
Explicit closed form in latex syntax:
\frac{207507 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{555}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{41}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{41}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{41 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{469}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{41}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{41 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{469}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{41 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{469}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{469 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{779}{263}\right) \left(\left(\left(\left(\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}-\frac{4}{3}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{781}{263}+\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{2770 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}-\frac{2980}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{5885}{789}+\frac{1484 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{7174}{789}+\frac{226 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}-\frac{4}{3}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{5885}{789}+\frac{1484 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{8134}{789}+\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{271 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}+\frac{7801}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{781}{263}+\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{7174}{789}+\frac{226 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{271 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}+\frac{7801}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{3350}{789}+\frac{990 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}+\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{555}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{740}{263}+\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{789}+\frac{325 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1243}{789}-\frac{740 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{740}{263}+\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{789}+\frac{325 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{3752}{789}+\frac{325 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{789}-\frac{8365 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{3752 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{656}{263}-\frac{740 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1243}{789}-\frac{740 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{3752 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{656}{263}-\frac{740 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1105}{789}-\frac{1243 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{789}+\frac{656 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(-\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2717}{789}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\frac{633 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{1928}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2864}{789}+\frac{1928 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{1373 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{350}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2766}{263}-\frac{350 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1993 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{1562}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1500}{263}+\frac{1562 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1353}{263}-\frac{1155 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1353 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{11143}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}-\frac{4}{3}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{781}{263}+\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}-\frac{4}{3}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{325 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}+\frac{1570}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1196}{263}+\frac{740 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{781}{263}+\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{1196}{263}+\frac{740 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1243 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}+\frac{2245}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(-\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2717}{789}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{633 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{1928}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2864}{789}+\frac{1928 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{603 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{1175}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3733}{789}-\frac{1175 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{3586}{789}+\frac{514 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3586 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{862}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(-\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2717}{789}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{871 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{4}{3}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{830}{263}+\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{3}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{781}{263}-\frac{555 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}+\frac{4831}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{4814 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{103}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{6809}{789}-\frac{103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{6809}{789}-\frac{103 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{6809 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{10555}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{770 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{275}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{4565}{789}-\frac{275 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{4565}{789}-\frac{275 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{4565 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{715}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{1028 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{292}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{374}{789}-\frac{292 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{374}{789}-\frac{292 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{374 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{4684}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(\frac{370 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2717}{789}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{2717}{789}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2717 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{49}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\frac{2717}{789}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{3}+\frac{830}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{4831}{789}+\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2717}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{3}-\frac{830}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{4831}{789}-\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{3}+\frac{830}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{3395 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}-\frac{7321}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{5498}{789}-\frac{8129 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{4380 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}+\frac{1795}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{4831}{789}+\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{4831}{789}-\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{4380 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{263}+\frac{1795}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{2831}{789}+\frac{338 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{3}-\frac{781}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{1196}{263}+\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{3}-\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{2245}{789}+\frac{1196 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1196}{263}+\frac{4 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{3}-\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{7307}{789}-\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}+\frac{3757 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{7307 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{861}{263}+\frac{1196 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{2245}{789}+\frac{1196 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}-\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{7307 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{861}{263}+\frac{1196 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{13108}{789}-\frac{2245 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{789}+\frac{861 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\frac{2717}{789}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2717 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{49}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{2717}{789}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2717 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}+\frac{49}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{2717}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{147}{263}+\frac{2717 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{10 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{3}-\frac{6803}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{5219}{789}-\frac{6803 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{16288}{789}+\frac{2037 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{16288 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{3706}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{2 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{3}+\frac{1355}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{4631}{789}+\frac{1355 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{4631}{789}+\frac{1355 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{263}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{4631 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{789}-\frac{13247}{789}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{5038 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{789}\right)}{25381444}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = a(n)-a(n+1)+3*a(n+2)-4*a(n+3)+4*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) = a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)-4 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18186/
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[14,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[7,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]+F[17,x]+F[37,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[24,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[20,x]
F[24,x] = F[25,x]+F[32,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[2,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[4,x]
F[31,x] = F[25,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[15,x]
F[36,x] = F[32,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[50,x]
F[39,x] = F[2,x]+F[40,x]
F[40,x] = F[16,x]+F[41,x]+F[49,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[11,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]*F[4,x]
F[46,x] = F[29,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[35,x]*F[4,x]
F[49,x] = F[39,x]*F[4,x]
F[50,x] = F[15,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_{14}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{50}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right)+F_{41}\! \left(x \right)+F_{49}\! \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_{11}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{46}\! \left(x \right) = F_{29}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{15}\! \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_14(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_7(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_37(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_24(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_20(x))
Eq(F_24(x), F_25(x) + F_32(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_2(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_4(x))
Eq(F_31(x), F_25(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_15(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_50(x))
Eq(F_39(x), F_2(x) + F_40(x))
Eq(F_40(x), F_16(x) + F_41(x) + F_49(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_11(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)*F_4(x))
Eq(F_46(x), F_29(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_35(x)*F_4(x))
Eq(F_49(x), F_39(x)*F_4(x))
Eq(F_50(x), F_15(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 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": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 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": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 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