0132_0231_1032_1203_2103
Counting sequence:
1, 1, 2, 6, 19, 56, 159, 447, 1259, 3556, 10056, 28441, 80426, 227405, 642969, 1817949, 5140162, 14533610, 41093243, 116189572, 328521463, 928881475, 2626375739, 7425973992, 20996649304, 59367199949, 167858422314, 474613085001, 1341949824617, 3794310331321, 10728263178810, 30333742047262, 85767462193979, 242504124935024, 685670872216551, 1938707414283063, 5481618937735747, 15499061878638380, 43822987669608224, 123907773472247761, 350344354488120706, 990584878431279397, 2800839770375068817, 7919264255010413445, 22391408106964772266, 63310825458998221586, 179008868095838137779, 506140531648980608556, 1431092439737452008047, 4046357568719753628235, 11440916826406703281059, 32348742197336354307232, 91464795840001733148512, 258613111663490027522837, 731218398401789888019474, 2067491252558803534775697, 5845750173614213459686033, 16528628621773897937080817, 46734047128739421080890418, 132138679560750926751232054, 373616917618103757462729763, 1056387135049858224278437672, 2986893062052213159319654127, 8445322617181036856800401327, 23878817428858713359838383707, 67516416796294390086844166900, 190900012138030525018504058808, 539762273585294150497559501193, 1526156592254743995225780686234, 4315147719775854360832082915965, 12200910403287532797891436429641, 34497594134919309669937369185709, 97540590149481899684195596497746, 275792181028610711942194813739450, 779791541141521302734776464525483, 2204829902602594659066442870769364, 6234069803186430526651509859022503, 17626587096413215009217433262258643, 49838481517905685785592271063550923, 140916345655822576306615413211974232, 398435423155037474014198088562250024, 1126560483000818491116923762392407517, 3185305442496250487065077488460998330, 9006325816586327500941066961408985049, 25465031903170416392356860506659130233, 72001375814680024052064824868076551593, 203581057307112691109851233110069257962, 575617429880163816639260616870395912526, 1627535635999809447845831874467951575499, 4601792977326564871699973877597862434400, 13011388591293843561333317503852170570423, 36789189324202302965187136996986302599207, 104019985387079667014013486856667849363507, 294112416138783184923892806700903993355324, 831591285127571340417004395007889527843344, 2351291640723545354320687933571716724542785, 6648184605359715938615480284529230025644402, 18797480406701523565353838732083986862952277, 53149136285334706697601242102113508663948993, 150277091756935513190150153170354577875416277, 424902564468460351997075235925064237061211834
Generating function in Maple syntax:
-(x^2+x-1)*(x-1)^2/(x^5-3*x^4-x^3+4*x^2-4*x+1)
Generating function in latex syntax:
-\frac{\left(x^{2}+x -1\right) \left(x -1\right)^{2}}{x^{5}-3 x^{4}-x^{3}+4 x^{2}-4 x +1}
Generating function in sympy syntax:
(x - 1)**2*(-x**2 - x + 1)/(x**5 - 3*x**4 - x**3 + 4*x**2 - 4*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^5-3*x^4-x^3+4*x^2-4*x+1)*F(x)+(x^2+x-1)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}-3 x^{4}-x^{3}+4 x^{2}-4 x +1\right) F \! \left(x \right)+\left(x^{2}+x -1\right) \left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
1816227/2793775220*((((3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+5938/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+4331/2043+1579/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-9874/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+13268/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(292/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+2289/227)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+1960/227-9880/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+5938/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(292/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+2289/227)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-10986/227-9266/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-9085/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-10745/227)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(4331/2043+1579/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(1960/227-9880/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-9085/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-10745/227)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+23042/2043-534/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n+1)+(((-1579/681-3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-1574/2043-3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-7771/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+2371/2043-1579/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-1574/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-1574/2043-3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-7771/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-48424/2043-43291/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-7771/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-48424/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-1574/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+3814/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(2371/2043-1579/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-1574/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-48424/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-1574/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+3814/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-24157/2043+2371/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2+3814/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)^(-n+1)+(((1-3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1201/2043+RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^4+((-7330/2043+4445/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-26150/2043-7330/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((520/681-2365/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+90460/2043+520/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-8324/2043+373/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+29278/2043-8324/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-475/2043-3175/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-475/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+53675/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n+1)+(((3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 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3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1201/2043+RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((-7330/2043+4445/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-26150/2043-7330/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((1673/227+831/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+99881/2043+1673/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(10622/2043+3818/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+10622/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+76166/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n+2)+(((1-3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1201/2043+RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-5938/2043-3461/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-34084/2043-5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-4331/2043-1579/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-4331/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-10211/681)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n+3)+(((-5899/681+20456/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+481/227-5899/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(481/227-5899/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+481/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+172687/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+1)+(((4499/681+9844/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+9421/2043+4499/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(9421/2043+4499/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+9421/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+5157/227)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+2)+(((464/681-16796/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-7934/2043+464/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-7934/2043+464/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-7934/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-39964/681)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+3)+(((-1+3764/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+1201/2043-RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(1201/2043-RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+1201/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+29753/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n+4)+(((1201/2043-RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+34084/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+10211/681+4331/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^3-((RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1201/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-34084/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-10211/681-4331/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*(RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-3)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+34084/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-13483/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-23873/681)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-163544/2043-7487/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-13832/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-67103/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(10211/681+4331/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^3+(-10211/227-4331/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-13832/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-67103/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-76967/2043+5306/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^(-n)+(((-4331/2043-5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(-28262/2043-5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-3962/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+15733/2043-4331/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-28262/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-28262/2043-5938/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-3962/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(59023/2043-16933/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-3962/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+59023/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-28262/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-41893/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(15733/2043-4331/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-28262/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^2+(59023/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-28262/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-41893/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)-116116/2043+15733/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)^2-41893/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)^(-n)+(((-1201/2043+RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-1201/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-29753/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^4+((1201/681-3*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+29753/681+1201/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^3+((1201/2043-RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+1201/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+29753/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^2+((-37561/2043-48452/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-158243/2043-37561/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+(-36470/2043-37165/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-36470/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-221560/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)^(-n)+(((-10919/681-56624/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-4359/227-10919/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-4359/227-10919/681*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-4359/227*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-341773/2043)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)^(-n)-118190/2043*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 5)^(-n))*((((RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+785/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+785/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-397/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(785/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-397/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-397/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+261/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 1)+((785/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-397/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)-397/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+261/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 2)+(-397/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)+261/889)*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 4)+261/889*RootOf(_Z^5-3*_Z^4-_Z^3+4*_Z^2-4*_Z+1,index = 3)-3625/889)
Explicit closed form in latex syntax:
\frac{1816227 \left(\left(\left(\left(\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{5938}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{4331}{2043}+\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{9874 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{13268}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{292 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{2289}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1960}{227}-\frac{9880 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{5938}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{292 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{2289}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{10986}{227}-\frac{9266 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{9085 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}-\frac{10745}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{4331}{2043}+\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{1960}{227}-\frac{9880 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{9085 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}-\frac{10745}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{23042}{2043}-\frac{534 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{1579}{681}-\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1574}{2043}-\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{7771 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{2371}{2043}-\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{681}-\frac{1574 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1574}{2043}-\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{7771 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{48424}{2043}-\frac{43291 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{7771 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{48424 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{1574 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}+\frac{3814}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{2371}{2043}-\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{681}-\frac{1574 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{48424 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{1574 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}+\frac{3814}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{24157}{2043}+\frac{2371 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}+\frac{3814 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1201}{2043}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{7330}{2043}+\frac{4445 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{26150}{2043}-\frac{7330 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{520}{681}-\frac{2365 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{90460}{2043}+\frac{520 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{8324}{2043}+\frac{373 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{29278}{2043}-\frac{8324 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{475}{2043}-\frac{3175 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{475 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}+\frac{53675}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{5938}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{4331}{2043}+\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{5938}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{3962}{227}+\frac{7771 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{28262}{2043}+\frac{1574 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{4331}{2043}+\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{28262}{2043}+\frac{1574 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{2371 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}-\frac{15733}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1201}{2043}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{7330}{2043}+\frac{4445 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{26150}{2043}-\frac{7330 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1673}{227}+\frac{831 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{99881}{2043}+\frac{1673 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{10622}{2043}+\frac{3818 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{10622 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}+\frac{76166}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1201}{2043}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{5938}{2043}-\frac{3461 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{34084}{2043}-\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{4331}{2043}-\frac{1579 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{10211}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{5899}{681}+\frac{20456 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{481}{227}-\frac{5899 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{481}{227}-\frac{5899 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{481 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}+\frac{172687}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{4499}{681}+\frac{9844 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{9421}{2043}+\frac{4499 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{9421}{2043}+\frac{4499 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{9421 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}+\frac{5157}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{464}{681}-\frac{16796 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{7934}{2043}+\frac{464 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{7934}{2043}+\frac{464 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{7934 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{39964}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{3764 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1201}{2043}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{1201}{2043}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1201 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}+\frac{29753}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\frac{1201}{2043}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{34084}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{10211}{681}+\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1201}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}-\frac{34084}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{10211}{681}-\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-3\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}+\frac{34084}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{13483 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}-\frac{23873}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{163544}{2043}-\frac{7487 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{13832 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}-\frac{67103}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{10211}{681}+\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{10211}{227}-\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{13832 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{681}-\frac{67103}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{76967}{2043}+\frac{5306 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{4331}{2043}-\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{28262}{2043}-\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{3962 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{15733}{2043}-\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{28262 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{28262}{2043}-\frac{5938 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{3962 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{59023}{2043}-\frac{16933 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{3962 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{227}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{59023 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{28262 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{41893}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{15733}{2043}-\frac{4331 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{28262 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{59023 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{28262 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{41893}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{116116}{2043}+\frac{15733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{2043}-\frac{41893 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\frac{1201}{2043}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1201 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{29753}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(\frac{1201}{681}-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{29753}{681}+\frac{1201 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{1201}{2043}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1201 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}+\frac{29753}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{37561}{2043}-\frac{48452 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{158243}{2043}-\frac{37561 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{36470}{2043}-\frac{37165 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{36470 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}-\frac{221560}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{10919}{681}-\frac{56624 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4359}{227}-\frac{10919 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{4359}{227}-\frac{10919 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{681}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{4359 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{227}-\frac{341773}{2043}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}-\frac{118190 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{2043}\right) \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{785}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{785 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}-\frac{397}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{785 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}-\frac{397}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{397 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}+\frac{261}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(\frac{785 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}-\frac{397}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{397 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}+\frac{261}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{397 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}+\frac{261}{889}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{261 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{889}-\frac{3625}{889}\right)}{2793775220}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = -a(n)+3*a(n+1)+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)+3 a \! \left(n +1\right)+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/18852/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[20,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[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[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[41,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[29,x]
F[25,x] = F[11,x]+F[26,x]
F[26,x] = F[15,x]+F[22,x]+F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[7,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[2,x]+F[30,x]
F[33,x] = 2*F[22,x]+F[34,x]+F[39,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[36,x]*F[4,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[21,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[32,x]+F[43,x]
F[43,x] = F[21,x]+F[44,x]
F[44,x] = F[34,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{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_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{41}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{7}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \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_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{21}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{21}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_20(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_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_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_41(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_29(x))
Eq(F_25(x), F_11(x) + F_26(x))
Eq(F_26(x), F_15(x) + F_22(x) + F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_7(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_2(x) + F_30(x))
Eq(F_33(x), 2*F_22(x) + F_34(x) + F_39(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_36(x)*F_4(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_21(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_32(x) + F_43(x))
Eq(F_43(x), F_21(x) + F_44(x))
Eq(F_44(x), F_34(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:
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