0132_0231_1032_2103
Counting sequence:
1, 1, 2, 6, 20, 65, 202, 612, 1840, 5536, 16697, 50439, 152447, 460745, 1392319, 4207014, 12711427, 38407384, 116048333, 350643474, 1059482024, 3201263753, 9672730801, 29226484458, 88308801874, 266828000536, 806229758189, 2436050328702, 7360608065672, 22240325049752, 67199890696132, 203046731234865, 613512531232483, 1853748758525959, 5601164255228873, 16924106286027723, 51136756670698250, 154511431127875187, 466861488748482232, 1410637698998828037, 4262289278059561174, 12878650487468773216, 38913275837988220097, 117577772447296764033, 355265196156389526722, 1073445745509562403102, 3243452443467945159148, 9800200706039551951353, 29611636227958869666226, 89472555348441993201916, 270344336900285882790992, 816854511525114631496136, 2468153395219977606315593, 7457608541528645146021055, 22533415170382534661759263, 68085472227903663661312425, 205722545537155026520110487, 621597594280061008886924206, 1878178049012015459387632739, 5674978179212901919625192232, 17147137541876655640007756909, 51810653115289310625883153610, 156547631910990780535991790376, 473013937932911366972327897193, 1429227531247579356248629276849, 4318459081782427184320481705866, 13048369439644258584073224851306, 39426087363358342363830038061072, 119127249728265117619459609627301, 359946993903571980047345722032614, 1087591954953671440648352443216960, 3286195691349016327163827322439000, 9929350867900500333280221436716076, 30001867788160664810600062872997441, 90651653139596991329788852527925211, 273907020555056311604473440719159943, 827619280078818632574820587932821673, 2500679505659125118350328750515096163, 7555887278783575065590519756300864530, 22830367682257383167928681157508408595, 68982724235528122336625693680944863656, 208433622672361815365816958270395058373, 629789205076787522262001657599981930350, 1902929276696995397468817303678719231232, 5749764846587105084610903688373619472193, 17373107974055815499212615651719179956865, 52493430380436571019354569531949654452546, 158610666394335749132999346233836531371318, 479247466049218065902904686127579220208644, 1448062346220610867651266981647275396260145, 4375369109049380121330306112270481587816346, 13220325002157758631878177394471629744704980, 39945656882111753143789039310311784929926320, 120697146513642195457804518755536355439098480, 364690489870484114797630610643664551620571865, 1101924587645002909309781445148173105757445751, 3329502223345152559546567630519238878201949695, 10060203011670755965184159294583108639603539977, 30397241943976219000864748618406207162385875311, 91846289456456446754927505129125264515933326774, 277516654388142020468134273911023490223958316995
Generating function in Maple syntax:
(2*x-1)*(x-1)^2/(x^5+6*x^3-8*x^2+5*x-1)
Generating function in latex syntax:
\frac{\left(2 x -1\right) \left(x -1\right)^{2}}{x^{5}+6 x^{3}-8 x^{2}+5 x -1}
Generating function in sympy syntax:
(x - 1)**2*(2*x - 1)/(x**5 + 6*x**3 - 8*x**2 + 5*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^5+6*x^3-8*x^2+5*x-1)*F(x)-(2*x-1)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}+6 x^{3}-8 x^{2}+5 x -1\right) F \! \left(x \right)-\left(2 x -1\right) \left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-4753216/5361607729*((((2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3821/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-3065/7683+3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-11930/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+4421/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(3521/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-69739/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-40237/15366-3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3821/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(3521/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-69739/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(10664/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+14798/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+69833/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-27782/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-3065/7683+3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-40237/15366-3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(69833/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-27782/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-10597/15366-27782/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+1)+(((-3221/15366-2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(201/2561+4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-293/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+201/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1609/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((201/2561+4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-293/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(79147/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+53426/7683-293/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+201/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+53426/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-4477/591)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(201/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-1609/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(201/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+53426/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-4477/591)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-1609/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-10597/15366-4477/591*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n+1)+(((1-2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^4+((RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-100/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1631/197)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((6-12228/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+6*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-600/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((46907/15366+39211/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+46907/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+372262/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(50507/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-9392/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-9392/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+230825/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+1)+(((2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3821/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-3065/7683+3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3821/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-67277/7683+293/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-201/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-6438/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-3065/7683+3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-201/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-6438/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+1609/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+30419/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n+2)+(((1-2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3+((RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-100/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1631/197)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((2462/7683-6749/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+2462/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1609/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(2462/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1609/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+1609/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+30419/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+2)+(((1-2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-3821/15366+4247/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+66674/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3065/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+40237/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n+3)+(((173435/15366-55799/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+173435/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-11792/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(173435/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-11792/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-11792/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1248569/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+1)+(((-43636/7683+66619/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-43636/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+5209/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-43636/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+5209/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+5209/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-351235/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+2)+(((-3221/15366-3436/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3065/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-3221/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3065/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+40237/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+3)+(((-1+2038/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+100/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1631/197)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n+4)+(((3065/7683+RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(6438/2561-3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+67277/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+6438/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-30419/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((6438/2561-3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2+67277/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(116177/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-62890/7683+67277/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+6438/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-62890/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+311/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(6438/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-30419/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(6438/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-62890/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+311/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-30419/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^2-320303/7683+311/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)^(-n)+(((-RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-66674/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-40237/15366-3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^3-((-100/2561+RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(-3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+66674/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+40237/15366+3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((3821/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-66674/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-40237/15366-3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^2+(38921/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-444026/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-32471/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-266863/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-40237/15366-3065/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^3+(-32471/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-266863/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)-244835/15366+311/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)^(-n)+(((RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-100/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-100/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+1631/197)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^4+((6*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-600/2561)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-600/2561*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+9786/197)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^2+((-43982/7683+15995/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-43982/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1055551/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+(-14081/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1957/1182)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1957/1182*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-297080/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)^(-n)+(((-46382/7683+138923/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-46382/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-37807/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-46382/7683*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-37807/15366)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-37807/15366*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-614825/7683)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)^(-n)-219669/5122*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 5)^(-n))*((((RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+141/464)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+141/464*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1321/2784)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(141/464*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1321/2784)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1321/2784*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3/116)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 1)+((141/464*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)-1321/2784)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)-1321/2784*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3/116)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 2)+(-1321/2784*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+3/116)*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 4)+3/116*RootOf(_Z^5+6*_Z^3-8*_Z^2+5*_Z-1,index = 3)+13909/2784)
Explicit closed form in latex syntax:
-\frac{4753216 \left(\left(\left(\left(\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{2561}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}+\frac{3821}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{3065}{7683}+\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{2561}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{11930 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}+\frac{4421}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{3521 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}-\frac{69739}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{40237}{15366}-\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}+\frac{3821}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{3521 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}-\frac{69739}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{10664 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}+\frac{14798}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{69833 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}-\frac{27782}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{3065}{7683}+\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{40237}{15366}-\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{69833 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}-\frac{27782}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{10597}{15366}-\frac{27782 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{3221}{15366}-\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{2561}+\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{201}{2561}+\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{7683}-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}-\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{15366}-\frac{1609}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{201}{2561}+\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{7683}-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{79147 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{53426}{7683}-\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{2561}+\frac{53426 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}-\frac{4477}{591}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}-\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{15366}-\frac{1609}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{2561}+\frac{53426 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}-\frac{4477}{591}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1609 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{15366}-\frac{10597}{15366}-\frac{4477 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{591}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{100 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}+\frac{1631}{197}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(6-\frac{12228 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+6 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{600}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{46907}{15366}+\frac{39211 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{46907 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}+\frac{372262}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{50507 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}-\frac{9392}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{9392 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{230825}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{2561}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}+\frac{3821}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{3065}{7683}+\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}+\frac{3821}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{67277}{7683}+\frac{293 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{2561}-\frac{6438}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{3065}{7683}+\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{2561}-\frac{6438}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1609 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}+\frac{30419}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{100 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}+\frac{1631}{197}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{2462}{7683}-\frac{6749 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2462 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{1609}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{2462 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{1609}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1609 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}+\frac{30419}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{3821}{15366}+\frac{4247 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}+\frac{66674}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}+\frac{3065}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{40237}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{173435}{15366}-\frac{55799 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{173435 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}-\frac{11792}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{173435 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}-\frac{11792}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{11792 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{1248569}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{43636}{7683}+\frac{66619 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{43636 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{5209}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{43636 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{5209}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{5209 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}-\frac{351235}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{3221}{15366}-\frac{3436 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}+\frac{3065}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{3221 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}+\frac{3065}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{40237}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{2038 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{100 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}-\frac{1631}{197}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\frac{3065}{7683}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{6438}{2561}-\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{15366}+\frac{67277 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{6438 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}+\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{7683}-\frac{30419}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{6438}{2561}-\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{15366}+\frac{67277 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{116177 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}-\frac{62890}{7683}+\frac{67277 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{6438 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{2561}-\frac{62890 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{311}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{6438 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}+\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{7683}-\frac{30419}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{6438 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{2561}-\frac{62890 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}+\frac{311}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{30419 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{7683}-\frac{320303}{7683}+\frac{311 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}-\frac{66674}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{40237}{15366}-\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\left(\left(-\frac{100}{2561}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}+\frac{66674}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{40237}{15366}+\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{3821 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}-\frac{66674}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{40237}{15366}-\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{38921 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{15366}-\frac{444026}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{32471 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}-\frac{266863}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{40237}{15366}-\frac{3065 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{32471 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}-\frac{266863}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{244835}{15366}+\frac{311 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{100}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{100 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}+\frac{1631}{197}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(6 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{600}{2561}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{600 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2561}+\frac{9786}{197}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{43982}{7683}+\frac{15995 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{43982 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}-\frac{1055551}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{14081 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}-\frac{1957}{1182}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1957 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1182}-\frac{297080}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{46382}{7683}+\frac{138923 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{46382 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}-\frac{37807}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{46382 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{7683}-\frac{37807}{15366}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{37807 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{15366}-\frac{614825}{7683}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{219669 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{5122}\right) \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{141}{464}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{141 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{464}-\frac{1321}{2784}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{141 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{464}-\frac{1321}{2784}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1321 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2784}+\frac{3}{116}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(\frac{141 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{464}-\frac{1321}{2784}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1321 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2784}+\frac{3}{116}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{1321 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{2784}+\frac{3}{116}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3 \mathit{RootOf}\left(\textit{\_Z}^{5}+6 \textit{\_Z}^{3}-8 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{116}+\frac{13909}{2784}\right)}{5361607729}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n) = -6*a(n+2)+8*a(n+3)-5*a(n+4)+a(n+5), 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) = 20
a \! \left(n \right) = -6 a \! \left(n +2\right)+8 a \! \left(n +3\right)-5 a \! \left(n +4\right)+a \! \left(n +5\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15334/
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[28,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[13,x]*F[4,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[2,x]+F[29,x]
F[32,x] = 2*F[22,x]+F[33,x]+F[38,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[29,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[35,x]*F[4,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[21,x]+F[40,x]
F[40,x] = F[33,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[22,x]+F[23,x]+F[45,x]
F[45,x] = F[4,x]*F[43,x]
F[46,x] = F[21,x]+F[47,x]
F[47,x] = 2*F[22,x]+F[33,x]+F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[57,x]
F[50,x] = F[18,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[18,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[54,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[29,x]+F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[58,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[64,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_{28}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{33}\! \left(x \right)+F_{38}\! \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_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{21}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{33}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{21}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{33}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{18}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{29}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \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_28(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_13(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_2(x) + F_29(x))
Eq(F_32(x), 2*F_22(x) + F_33(x) + F_38(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_29(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_35(x)*F_4(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_21(x) + F_40(x))
Eq(F_40(x), F_33(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_22(x) + F_23(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_43(x))
Eq(F_46(x), F_21(x) + F_47(x))
Eq(F_47(x), 2*F_22(x) + F_33(x) + F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_57(x))
Eq(F_50(x), F_18(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_18(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_54(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_29(x) + F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_58(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_64(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], 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