0132_0231_2013_2103
Counting sequence:
1, 1, 2, 6, 20, 63, 191, 574, 1727, 5205, 15697, 47340, 142761, 430502, 1298189, 3914728, 11805002, 35598424, 107348374, 323712995, 976168484, 2943672080, 8876751793, 26768172678, 80720412775, 243415384251, 734028076018, 2213488757186, 6674857050103, 20128277812497, 60697564705385, 183035746797879, 551951050564653, 1664428766233354, 5019146380880938, 15135421174989680, 45641421221932909, 137633390380980383, 415038568927392290, 1251564124232327293, 3774137813537670841, 11381051885225483971, 34319982049829214782, 103493172667955328057, 312087482252413232306, 941111322300856932183, 2837955930082866267650, 8557960859935106253568, 25806846858979486068278, 77821499268678531294096, 234673603540902356596159, 707666913595916625680736, 2133995698886027776474164, 6435142798642131159030467, 19405410639080841938561516, 58517732061953828804142847, 176462381001014257565097461, 532128823372370268635977168, 1604654108469927661854977836, 4838893694032353187509856571, 14591862544428766737331589291, 44002300107996451442416961849, 132690560159740168651507037113, 400133281948731096710210046765, 1206616681173985419749572780726, 3638597139924666564849303636474, 10972323980956914321971970525136, 33087447967810687456390892933939, 99776420649137823328933810591399, 300879479349353271875837154985974, 907313175844218523121635360016591, 2736036371907831389291966222421801, 8250618670270321967765225807512701, 24880045141631755706586878231004772, 75026694480518582395038345516219661, 226245766542202491180223181923414250, 682252460043538733649791946544214473, 2057357476117171039031155320839372576, 6204037409062768450772709921181879934, 18708503806393524430310632586518892512, 56416183784216739526425379805789582290, 170125084598524704470426910587172613387, 513018472152529604105969176205928174500, 1547026138977732585572217911813572871256, 4665114424902779563706586306778615519697, 14067824743941993464381806488283744699554, 42422044777688578063887961372048407946583, 127925241881847206693250347631600427721707, 385763288787438227496167182414872886070414, 1163283436380332596967037809556013672754274, 3507924140761061091427615357947648174600115, 10578274728662917238394699702183205073541189, 31899177902630269585462701153241869041748825, 96193148406940030890051019060492473282701303, 290073989639608129530504408545108045857187753, 874728822779324264409629276756135545597792390, 2637777052508347549425047229727770623884063646, 7954314065737547798238647738675106319758397108, 23986527669661713819373340885118241893573412321, 72332259562861314862344418683500962212769439543, 218120598592790371831009883686312335781657092602
Generating function in Maple syntax:
-(x-1)*(x^3+2*x-1)/(x^5+3*x^3-4*x^2+4*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(x^{3}+2 x -1\right)}{x^{5}+3 x^{3}-4 x^{2}+4 x -1}
Generating function in sympy syntax:
(1 - x)*(x**3 + 2*x - 1)/(x**5 + 3*x**3 - 4*x**2 + 4*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^5+3*x^3-4*x^2+4*x-1)*F(x)+(x-1)*(x^3+2*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}+3 x^{3}-4 x^{2}+4 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(x^{3}+2 x -1\right) = 0
Explicit closed form in Maple syntax:
129217109/93901387697*((((RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-4021/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-4021/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-3189/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-4021/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-3189/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-3189/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+2258/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+((-4021/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-3189/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-3189/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+2258/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-3189/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+2258/2947)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+2258/2947*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-5048/2947)*((((55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-374027/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+367994/131541+188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(-136354/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-936209/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-185872/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+739972/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-1115888/131541+367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-374027/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(-185872/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+739972/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(158768/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1017068/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+32940/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+173744/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(367994/131541+188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(-1115888/131541+367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(32940/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+173744/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+82912/43847+173744/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+1)+(((-55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-188155/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+281639/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-170810/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-170810/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-512060/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+281639/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-170810/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-583500/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+281639/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+190588/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-170810/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+190588/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+793472/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-170810/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-512060/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-170810/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+190588/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+793472/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-512060/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+82912/43847+793472/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n+1)+(((1-55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^4+((RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+187394/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1328/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((3-167808/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+3*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+562182/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((406967/43847-64929/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+406967/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-198234/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-155215/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-194250/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-194250/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1198800/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+1)+(((55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-374027/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+367994/131541+188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-374027/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(884408/131541-281639/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+170810/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-201276/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(367994/131541+188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(170810/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-201276/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+512060/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-272240/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n+2)+(((1-55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3+((RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+187394/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1328/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((144436/131541-95767/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+144436/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+512060/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(144436/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+512060/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+512060/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-272240/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+2)+(((1-55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((374027/131541+4813/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-371978/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-367994/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1115888/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n+3)+(((20173/43847-2578/269*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+20173/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+555326/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(20173/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+555326/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+555326/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1193488/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+1)+(((-250187/131541+407657/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-250187/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1174486/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-250187/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1174486/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-1174486/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-260288/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+2)+(((-188155/131541-126728/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-367994/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-188155/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-367994/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1115888/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+3)+(((-1+55936/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(-RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-187394/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1328/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n+4)+(((RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-367994/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-884408/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+201276/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+201276/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+272240/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-884408/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+201276/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-112891/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-884408/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+2607431/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+201276/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+2607431/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+2313991/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+201276/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+272240/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(201276/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2+2607431/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+2313991/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+272240/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^2-689794/43847+2313991/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)^(-n)+(((-RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+371978/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-1115888/131541+367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^3-RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)*((187394/43847+RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-371978/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+1115888/131541-367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-374027/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+371978/131541)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(-1115888/131541+367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^2+(-515443/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-86647/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+778397/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+439217/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(-1115888/131541+367994/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^3+(778397/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+439217/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)-355885/131541+2313991/131541*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)^(-n)+(((RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+187394/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+187394/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1328/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^4+((3*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+562182/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+562182/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-3984/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^2+((-458625/43847-141416/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)-458625/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+766994/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)+(410403/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+1555105/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+1555105/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1053102/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)^(-n)+(((290951/43847+33972/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+290951/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+761682/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 2)+(290951/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)+761682/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 4)+761682/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 3)-1235184/43847)*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 1)^(-n)-1263457/43847*RootOf(_Z^5+3*_Z^3-4*_Z^2+4*_Z-1,index = 5)^(-n))
Explicit closed form in latex syntax:
\frac{129217109 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{4021}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{4021 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}-\frac{3189}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{4021 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}-\frac{3189}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3189 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}+\frac{2258}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{4021 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}-\frac{3189}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3189 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}+\frac{2258}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{3189 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}+\frac{2258}{2947}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2258 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{2947}-\frac{5048}{2947}\right) \left(\left(\left(\left(\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{374027}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{367994}{131541}+\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{136354 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{936209}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{185872 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}+\frac{739972}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1115888}{131541}+\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{374027}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{185872 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}+\frac{739972}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{158768 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{1017068}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{32940 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}+\frac{173744}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{367994}{131541}+\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{1115888}{131541}+\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{32940 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}+\frac{173744}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{82912}{43847}+\frac{173744 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{43847}+\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{188155}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{281639 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{170810}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}-\frac{170810 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{512060}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{281639 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{170810}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{583500 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{281639 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{190588}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{170810 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{43847}+\frac{190588 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{793472}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}-\frac{170810 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{512060}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{170810 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{43847}+\frac{190588 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{793472}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{512060 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{82912}{43847}+\frac{793472 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{187394 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{1328}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(3-\frac{167808 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{562182}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{406967}{43847}-\frac{64929 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{406967 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{198234}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{155215 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{194250}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{194250 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{1198800}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{374027}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{367994}{131541}+\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{374027}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{884408}{131541}-\frac{281639 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{170810 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}-\frac{201276}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{367994}{131541}+\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{170810 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}-\frac{201276}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{512060 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{272240}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{187394 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{1328}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{144436}{131541}-\frac{95767 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{144436 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{512060}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{144436 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{512060}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{512060 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{272240}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{374027}{131541}+\frac{4813 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{371978}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{367994}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{1115888}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{20173}{43847}-\frac{2578 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{269}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{20173 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{555326}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{20173 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{555326}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{555326 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{1193488}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{250187}{131541}+\frac{407657 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{250187 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{1174486}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{250187 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{1174486}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1174486 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{260288}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{188155}{131541}-\frac{126728 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{367994}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{188155 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{367994}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{1115888}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{55936 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{187394 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{1328}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}-\frac{367994}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}-\frac{884408 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{201276}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{201276 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{272240}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}-\frac{884408 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{201276}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{112891 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{884408 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{2607431}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{201276 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{43847}+\frac{2607431 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{2313991}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}+\frac{201276 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{272240}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{201276 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{43847}+\frac{2607431 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}+\frac{2313991}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{272240 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{131541}-\frac{689794}{43847}+\frac{2313991 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}+\frac{371978}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1115888}{131541}+\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right) \left(\left(\frac{187394}{43847}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \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}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}-\frac{371978}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1115888}{131541}-\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{374027 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}+\frac{371978}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{1115888}{131541}+\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{515443 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}-\frac{86647}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{778397 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}+\frac{439217}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1115888}{131541}+\frac{367994 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{778397 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{43847}+\frac{439217}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{355885}{131541}+\frac{2313991 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{131541}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{187394}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{187394 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{1328}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{562182}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{562182 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{3984}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{458625}{43847}-\frac{141416 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{458625 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{766994}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{410403 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{1555105}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1555105 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{1053102}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{290951}{43847}+\frac{33972 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{290951 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{761682}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{290951 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}+\frac{761682}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{761682 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{43847}-\frac{1235184}{43847}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{1263457 \mathit{RootOf}\left(\textit{\_Z}^{5}+3 \textit{\_Z}^{3}-4 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{43847}\right)}{93901387697}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n) = -3*a(n+2)+4*a(n+3)-4*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) = -3 a \! \left(n +2\right)+4 a \! \left(n +3\right)-4 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/15371/
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[17,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[11,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[44,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[28,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[7,x]
F[27,x] = F[23,x]
F[28,x] = F[29,x]+F[39,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[2,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[32,x]*F[4,x]
F[35,x] = F[29,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[33,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[18,x]
F[43,x] = F[39,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[57,x]
F[46,x] = F[2,x]+F[47,x]
F[47,x] = F[19,x]+F[48,x]+F[56,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[11,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[26,x]*F[4,x]
F[53,x] = F[33,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[42,x]
F[56,x] = F[4,x]*F[46,x]
F[57,x] = F[18,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[33,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_{17}\! \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_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{44}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{28}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{39}\! \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_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \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_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{57}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{19}\! \left(x \right)+F_{48}\! \left(x \right)+F_{56}\! \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_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = F_{33}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right)+F_{58}\! \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_{33}\! \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_17(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_11(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_44(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_28(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_7(x))
Eq(F_27(x), F_23(x))
Eq(F_28(x), F_29(x) + F_39(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_2(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_32(x)*F_4(x))
Eq(F_35(x), F_29(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_33(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_18(x))
Eq(F_43(x), F_39(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_57(x))
Eq(F_46(x), F_2(x) + F_47(x))
Eq(F_47(x), F_19(x) + F_48(x) + F_56(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_11(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_26(x)*F_4(x))
Eq(F_53(x), F_33(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_42(x))
Eq(F_56(x), F_4(x)*F_46(x))
Eq(F_57(x), F_18(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_33(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": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"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": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1, 2], "pos": [[1, 0], [1, 0], [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, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"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, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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, 1, 2], "pos": [[0, 0], [0, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"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": 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