0123_0213_0231_1032_2013
Counting sequence:
1, 1, 2, 6, 19, 58, 175, 529, 1603, 4860, 14732, 44651, 135330, 410169, 1243181, 3767957, 11420290, 34613714, 104910579, 317973106, 963743583, 2921007069, 8853270127, 26833345508, 81329093208, 246500064667, 747116185418, 2264431838009, 6863258552065, 20801826383937, 63048182962266, 191092517622102, 579181644505211, 1755439624251106, 5320555828428215, 16126054084883905, 48876401025459187, 148139313227331668, 448994927266318748, 1360857157488781571, 4124617207512421578, 12501287894095388753, 37890109832837200493, 114841001607726974517, 348071190831868902362, 1054967757081662280034, 3197498091761096245979, 9691285802988232344890, 29373284305377673163591, 89027384851090845390413, 269832789926496819907903, 817835260928984053659644, 2478774037065610911996904, 7512907574871711065299571, 22770845339086758748707090, 69016075639059510703372529, 209180582700642767872897729, 634004697801399405077524737, 1921602625084420128612033138, 5824178687533983949711392230, 17652482850264036756799535779, 53502848641274228251393300618, 162161597153925738551043744447, 491495018663847715290099741745, 1489670536126240644517492034595, 4515037227102359124057294169580, 13684610568408668574329158209004, 41476638395113881711378988258779, 125711398505590322849598595000690, 381018238838107888755405703729641, 1154826849856718218207637263731565, 3500160667417917499494771855059541, 10608624746869597232552975083242738, 32153643707709391152761531812656434, 97454366456631538508770774042835331, 295374099053858580402983028761771778, 895248325591488020768191817541898287, 2713405024481252170907356033978425725, 8224049815469554489121615194261603983, 24926243873324900377055824348477344340, 75548865531402769504824113507578365112, 228980792777609904128577166435625422475, 694017085395791541944393943917903440730, 2103493961124790205665673659606062908713, 6375472502906902236398618651218615160129, 19323397350562029883388714851131966385217, 58567217566613062842773222555953871644746, 177511175248653837210455166488631625986486, 538018001321631299151626865275719468774027, 1630676881839404163939996559016126337309490, 4942412868033104003744228782132344257360839, 14979941906421734031039491432224707840869217, 45402653625145710062942211976204921188749523, 137610744359512989003631938216058293032139204, 417083924642928017695681611479203828816217724, 1264138211047485874984320591631289270286071027, 3831472090415494372197354455800496858323711130, 11612795382135185320879870017354295210442603265, 35197180980304636448375073694372206755117860141, 106679012950328845483861517055625222195142014197, 323333047905870400601798417361244154979462066122
Generating function in Maple syntax:
-(x^2-x+1)*(x^2+2*x-1)/(x^5-x^4-3*x^3+4*x^2-4*x+1)
Generating function in latex syntax:
-\frac{\left(x^{2}-x +1\right) \left(x^{2}+2 x -1\right)}{x^{5}-x^{4}-3 x^{3}+4 x^{2}-4 x +1}
Generating function in sympy syntax:
(-x**2 + x - 1)*(x**2 + 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^2-x+1)*(x^2+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^{2}-x +1\right) \left(x^{2}+2 x -1\right) = 0
Explicit closed form in Maple syntax:
776251/1096337138*((((-1069/1211*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+(3646/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+5916/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+2561/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((-1069/1211*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+(3504/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+12184/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(447/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+507/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+1702/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+14852/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((3646/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+5916/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(447/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+507/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-21593/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+4643/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-25304/1211-838/173*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)+(859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+2561/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(1702/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+14852/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-25304/1211-838/173*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)-7891/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-60455/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n+1)+(((-859/1211+1069/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-3646/1211*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+(-695/1211-3646/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+4539/1211*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)-859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-695/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+6708/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-695/1211-3646/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+4539/1211*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+(-35121/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+4539/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-9168/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-695/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+27043/1211-9168/1211*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)+(-859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-695/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+6708/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-695/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+27043/1211-9168/1211*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)+27043/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-102097/1211+6708/1211*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 = 4)^(-n+1)+(((1+1069/1211*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)+RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^4+((-6268/1211+142/1211*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)-6268/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+102/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((1424/1211-4418/1211*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)+1424/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+19514/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((14443/1211-6441/1211*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)+14443/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+12821/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-104/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-208/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-8216/1211-208/1211*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)^(-n+1)+(((-1069/1211*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+(3646/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+5916/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+2561/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((3646/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+5916/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(7599/1211-4539/1211*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)+695/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+10705/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+2561/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(695/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+10705/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-41642/1211-6708/1211*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+2)+(((1+1069/1211*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)+RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((-6268/1211+142/1211*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)-6268/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+102/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((4050/1211-7668/1211*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)+4050/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+28/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-1007/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-4147/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-24229/1211-4147/1211*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)^(-n+2)+(((1+1069/1211*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)+RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-5916/1211-3646/1211*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)-5916/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-6904/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-859/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-2561/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-17413/1211-2561/1211*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)^(-n+3)+(((-796/173-1012/173*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)-796/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+2860/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-796/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+2860/173)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+1308/173+2860/173*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)^(-n+1)+(((2626/1211-3250/1211*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)+2626/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-19318/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(2626/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-19318/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-37258/1211-19318/1211*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)^(-n+2)+(((352/1211-3788/1211*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)+352/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-7618/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(352/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-7618/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-3108/173-7618/1211*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)^(-n+3)+(((-1-1069/1211*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)-RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+4343/1211+5057/1211*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)^(-n+4)+(((-RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(5916/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+6904/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+2561/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+17413/1211)*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)-5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-5916/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-6904/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-2561/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-17413/1211)*(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+((5916/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+6904/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-3355/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+10509/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-23116/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-53266/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-72677/1211-8509/1211*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)+(2561/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+17413/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-2561/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-17413/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-72677/1211-8509/1211*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)-1901/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+24233/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n)+(((-2561/1211+RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-5916/1211*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+(-10705/1211-5916/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-7599/1211*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)-2561/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-10705/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+41642/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-10705/1211-5916/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-7599/1211*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+(-36927/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-7599/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+43838/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)-10705/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-43543/1211+43838/1211*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)+(-2561/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-10705/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+41642/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-10705/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-43543/1211+43838/1211*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)-43543/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-146303/1211+41642/1211*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 = 4)^(-n)+(((RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-4343/1211-5057/1211*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+((-RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+5057/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+4343/1211+5057/1211*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+((15171/1211-3*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 = 4)+15171/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+13029/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-2163/173-401/173*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)-2163/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-56827/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-118/173*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-20438/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-56522/1211-20438/1211*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)^(-n)+(((5087/1211-1093/173*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)+5087/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-39455/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(5087/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-39455/1211)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-78951/1211-39455/1211*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)^(-n)-46826/1211*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 5)^(-n))*((((RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+570/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+570/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-1429/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(570/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-1429/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-1429/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+3295/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 1)+((570/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-1429/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)-1429/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+3295/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-1429/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)+3295/641)*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 4)+3295/641*RootOf(_Z^5-_Z^4-3*_Z^3+4*_Z^2-4*_Z+1,index = 3)-8466/641)
Explicit closed form in latex syntax:
\frac{776251 \left(\left(\left(\left(-\frac{1069 \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)}{1211}-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{3646 \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)}{1211}+\frac{5916}{1211}\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{859 \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)}{1211}+\frac{2561}{1211}\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{1069 \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)}{1211}-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{3504 \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)}{1211}+\frac{12184}{1211}\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{447 \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)}{173}+\frac{507}{173}\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{1702 \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)}{1211}+\frac{14852}{1211}\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{3646 \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)}{1211}+\frac{5916}{1211}\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{447 \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)}{173}+\frac{507}{173}\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{21593 \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)}{1211}+\frac{4643}{1211}\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{25304}{1211}-\frac{838 \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)}{173}\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{859 \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)}{1211}+\frac{2561}{1211}\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{1702 \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)}{1211}+\frac{14852}{1211}\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{25304}{1211}-\frac{838 \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)}{173}\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{7891 \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)}{1211}-\frac{60455}{1211}\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{859}{1211}+\frac{1069 \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}}{1211}-\frac{3646 \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)}{1211}\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{695}{1211}-\frac{3646 \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}}{1211}+\frac{4539 \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)}{1211}\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{859 \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}}{1211}-\frac{695 \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)}{1211}+\frac{6708}{1211}\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{695}{1211}-\frac{3646 \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}}{1211}+\frac{4539 \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)}{1211}\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{35121 \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)}{1211}+\frac{4539 \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}}{1211}-\frac{9168}{1211}\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{695 \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}}{1211}+\frac{27043}{1211}-\frac{9168 \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)}{1211}\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{859 \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}}{1211}-\frac{695 \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)}{1211}+\frac{6708}{1211}\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{695 \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}}{1211}+\frac{27043}{1211}-\frac{9168 \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)}{1211}\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{27043 \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)}{1211}-\frac{102097}{1211}+\frac{6708 \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}}{1211}\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(1+\frac{1069 \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)}{1211}\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)+\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{5057}{1211}\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{6268}{1211}+\frac{142 \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)}{1211}\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{6268 \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)}{1211}+\frac{102}{173}\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{1424}{1211}-\frac{4418 \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)}{1211}\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{1424 \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)}{1211}+\frac{19514}{1211}\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{14443}{1211}-\frac{6441 \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)}{1211}\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{14443 \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)}{1211}+\frac{12821}{1211}\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{104 \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)}{173}-\frac{208}{1211}\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{8216}{1211}-\frac{208 \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)}{1211}\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{1069 \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)}{1211}-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{3646 \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)}{1211}+\frac{5916}{1211}\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{859 \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)}{1211}+\frac{2561}{1211}\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{3646 \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)}{1211}+\frac{5916}{1211}\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{7599}{1211}-\frac{4539 \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)}{1211}\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{695 \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)}{1211}+\frac{10705}{1211}\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{859 \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)}{1211}+\frac{2561}{1211}\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{695 \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)}{1211}+\frac{10705}{1211}\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{41642}{1211}-\frac{6708 \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)}{1211}\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(1+\frac{1069 \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)}{1211}\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)+\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{5057}{1211}\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{6268}{1211}+\frac{142 \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)}{1211}\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{6268 \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)}{1211}+\frac{102}{173}\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{4050}{1211}-\frac{7668 \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)}{1211}\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{4050 \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)}{1211}+\frac{28}{173}\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{1007 \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)}{1211}-\frac{4147}{1211}\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{24229}{1211}-\frac{4147 \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)}{1211}\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(1+\frac{1069 \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)}{1211}\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)+\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{5057}{1211}\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{5916}{1211}-\frac{3646 \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)}{1211}\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{5916 \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)}{1211}-\frac{6904}{1211}\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{859 \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)}{1211}-\frac{2561}{1211}\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{17413}{1211}-\frac{2561 \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)}{1211}\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{796}{173}-\frac{1012 \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)}{173}\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{796 \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)}{173}+\frac{2860}{173}\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{796 \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)}{173}+\frac{2860}{173}\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{1308}{173}+\frac{2860 \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)}{173}\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{2626}{1211}-\frac{3250 \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)}{1211}\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{2626 \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)}{1211}-\frac{19318}{1211}\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{2626 \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)}{1211}-\frac{19318}{1211}\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{37258}{1211}-\frac{19318 \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)}{1211}\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{352}{1211}-\frac{3788 \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)}{1211}\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{352 \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)}{1211}-\frac{7618}{1211}\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{352 \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)}{1211}-\frac{7618}{1211}\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{3108}{173}-\frac{7618 \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)}{1211}\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(-1-\frac{1069 \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)}{1211}\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)-\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{5057}{1211}\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(-\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{5057}{1211}\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{4343}{1211}+\frac{5057 \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)}{1211}\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(-\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{5057}{1211}\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{5916 \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)}{1211}+\frac{6904}{1211}\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{2561 \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)}{1211}+\frac{17413}{1211}\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{5057}{1211}\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{5916 \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)}{1211}-\frac{6904}{1211}\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{2561 \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)}{1211}-\frac{17413}{1211}\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{5916 \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)}{1211}+\frac{6904}{1211}\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{3355 \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)}{1211}+\frac{10509}{1211}\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{23116 \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)}{1211}-\frac{53266}{1211}\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{72677}{1211}-\frac{8509 \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)}{1211}\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{2561 \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)}{1211}+\frac{17413}{1211}\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{2561 \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)}{1211}-\frac{17413}{1211}\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{72677}{1211}-\frac{8509 \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)}{1211}\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{1901 \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)}{1211}+\frac{24233}{1211}\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(-\frac{2561}{1211}+\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{5916 \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)}{1211}\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{10705}{1211}-\frac{5916 \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}}{1211}-\frac{7599 \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)}{1211}\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{2561 \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}}{1211}-\frac{10705 \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)}{1211}+\frac{41642}{1211}\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{10705}{1211}-\frac{5916 \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}}{1211}-\frac{7599 \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)}{1211}\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{36927 \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)}{1211}-\frac{7599 \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}}{1211}+\frac{43838}{1211}\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{10705 \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}}{1211}-\frac{43543}{1211}+\frac{43838 \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)}{1211}\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{2561 \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}}{1211}-\frac{10705 \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)}{1211}+\frac{41642}{1211}\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{10705 \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}}{1211}-\frac{43543}{1211}+\frac{43838 \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)}{1211}\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{43543 \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)}{1211}-\frac{146303}{1211}+\frac{41642 \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}}{1211}\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(\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{5057}{1211}\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{4343}{1211}-\frac{5057 \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)}{1211}\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(-\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{5057}{1211}\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{4343}{1211}+\frac{5057 \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)}{1211}\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{15171}{1211}-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)\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{15171 \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)}{1211}+\frac{13029}{1211}\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{2163}{173}-\frac{401 \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)}{173}\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{2163 \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)}{173}-\frac{56827}{1211}\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{118 \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)}{173}-\frac{20438}{1211}\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{56522}{1211}-\frac{20438 \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)}{1211}\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{5087}{1211}-\frac{1093 \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)}{173}\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{5087 \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)}{1211}-\frac{39455}{1211}\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{5087 \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)}{1211}-\frac{39455}{1211}\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{78951}{1211}-\frac{39455 \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)}{1211}\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{46826 \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}}{1211}\right) \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{570}{641}\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{570 \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)}{641}-\frac{1429}{641}\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{570 \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)}{641}-\frac{1429}{641}\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{1429 \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)}{641}+\frac{3295}{641}\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{570 \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)}{641}-\frac{1429}{641}\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{1429 \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)}{641}+\frac{3295}{641}\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{1429 \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)}{641}+\frac{3295}{641}\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{3295 \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)}{641}-\frac{8466}{641}\right)}{1096337138}
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/16707/
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[43,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[26,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[1,x]+F[4,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[7,x]
F[26,x] = F[27,x]+F[40,x]
F[27,x] = F[16,x]+F[17,x]+F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[16,x]+F[31,x]+F[39,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[34,x]+F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[4,x]*F[7,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[4,x]
F[39,x] = F[2,x]*F[4,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[15,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[2,x]+F[46,x]
F[46,x] = F[16,x]+F[31,x]+F[47,x]
F[47,x] = F[4,x]*F[45,x]
F[48,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_{43}\! \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_{26}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \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_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{40}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \left(x \right)+F_{39}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \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_{35}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{48}\! \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_43(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_26(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_1(x) + F_4(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_7(x))
Eq(F_26(x), F_27(x) + F_40(x))
Eq(F_27(x), F_16(x) + F_17(x) + F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_16(x) + F_31(x) + F_39(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_34(x) + F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_4(x)*F_7(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_4(x))
Eq(F_39(x), F_2(x)*F_4(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_15(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_2(x) + F_46(x))
Eq(F_46(x), F_16(x) + F_31(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_45(x))
Eq(F_48(x), F_15(x))
Pack JSON:
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Specification JSON:
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