0123_0213_0231_1302_2103<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 54, 146, 394, 1075, 2949, 8089, 22159, 60668, 166107, 454864, 1245663, 3411269, 9341656, 25581688, 70054347, 191841178, 525350116, 1438651994, 3939694767, 10788706393, 29544468651, 80906423585, 221559219430, 606731646025, 1661511943548, 4549988376721, 12459973169089, 34121170993538, 93439551933114, 255880721874295, 700719796598130, 1918894982577950, 5254822215757906, 14390134306475575, 39406845152148405, 107914173125227189, 295518931199248987, 809267551870171292, 2216148954831021819, 6068841112743305548, 16619294642372820063, 45511317445769762093, 124631042425149020776, 341297453199150836620, 934630323983566805487, 2559450222442506063982, 7008958807628172833656, 19193771825008430052506, 52561427022447296266539, 143937504093718665396745, 394167477147857567233983, 1079412909230006384237213, 2955931922753051228579950, 8094709130524874631199873, 22167058518308406820685832, 60703661543703607858066993, 166234709118894940697981041, 455227540038067174186952450, 1246623610120391956879658526, 3413832179792206920413177179, 9348651876294327926842139934, 25600933877617017166310279354, 70107200918247581495375832538, 191985950359754366820854011771, 525746352054749749478206964565, 1439736742094540179029529268977, 3942665276584060000339563853351, 10796841553524044889448915106012, 29566747201249035654873311185995, 80967432533751948603158246931736, 221726288877348315517372126805391, 607189157922569646562299868559525, 1662764823086269793840396224018072, 4553419343574127117567858996241968, 12469368746899034454232868218989267, 34146900431115802735498690532573650, 93510011029428247288379953375774684, 256073671470217970616685296488411450, 701248181861518764303501190427814279, 1920341945896914961565363915085882985, 5258784670759250351763572157001307379, 14400985341439291379769779157399708473, 39436560305939874400209527398875231766, 107995546963635438306305365161165682921, 295741770415461882133451148521800831140, 809877788738109875631122084877274238113, 2217820065694172428102893805786231051729, 6073417387405683426695865230608046792066, 16631826599556137512620626016370764010290, 45545635742295470622912424071943219694719, 124725021797979991187801798849260202709306, 341554812200378672685720550527629584145126, 935335091992947071381447664937752919031074, 2561380203304554219958686900565477021920319, 7014243988110680734235280854460978812120997, 19208245094294138804171398326445911196442509<br /><br />


Generating function in Maple syntax:<br />
-(x-1)^3/(x^5-x^4-4*x^3+5*x^2-4*x+1)<br /><br />



Generating function in latex syntax:<br />
-\frac{\left(x -1\right)^{3}}{x^{5}-x^{4}-4 x^{3}+5 x^{2}-4 x +1}<br /><br />



Generating function in sympy syntax:<br />
-(x - 1)**3/(x**5 - x**4 - 4*x**3 + 5*x**2 - 4*x + 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5-x^4-4*x^3+5*x^2-4*x+1)*F(x)+(x-1)^3 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}-x^{4}-4 x^{3}+5 x^{2}-4 x +1\right) F \! \left(x \right)+\left(x -1\right)^{3} = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-1445304521/71815952072*((((RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-1586/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1586/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+2894/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(-1586/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+2894/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+2894/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-6595/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+((-1586/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+2894/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+2894/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-6595/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(2894/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-6595/5911)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-6595/5911*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-5171/5911)*((((-1+100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(28223/12869-234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1272/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^3+((-1+100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^3+(1303217/244511-579259/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-101668/12869+784412/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-37936/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+136304/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((28223/12869-234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^3+(-101668/12869+784412/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-319962/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+1086558/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-23345/14383*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+814667/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1272/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^3+(-37936/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+136304/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-23345/14383*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+814667/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+926803/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-2132121/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^(-n+1)+(((-13768/244511-100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(21691/244511+234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-511854/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+21691/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+17671/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((21691/244511+234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-511854/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(1628252/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-511854/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-495350/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-495350/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+21691/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+981007/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(-13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+21691/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+17671/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-495350/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+21691/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+981007/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+17671/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+981007/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-2203996/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)^(-n+1)+(((1-100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^4+((-766980/244511+344852/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-766980/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+1869588/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^3+((-455575/244511+156853/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-455575/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+742757/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((1723915/244511-40201/14383*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+1723915/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-4558345/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(-365961/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+830131/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+830131/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-1683577/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^(-n+1)+(((-1+100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(28223/12869-234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1272/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((28223/12869-234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-1392978/244511+511854/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-21691/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+94465/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1272/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-21691/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+94465/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-17671/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-71875/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^(-n+2)+(((1-100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^3+((-766980/244511+344852/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-766980/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+1869588/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((538714/244511-272558/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+538714/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-1388958/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(855/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-41839/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-41839/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+2119/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^(-n+2)+(((1-100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((-28223/12869+234407/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+72173/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(-13768/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+1272/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-112136/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^(-n+3)+(((-1588516/244511+796332/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1588516/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+3442476/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(-1588516/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+3442476/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+3442476/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-8419172/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^(-n+1)+(((52331/12869-429411/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+52331/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-125395/14383)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(52331/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-125395/14383)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-125395/14383*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+285723/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^(-n+2)+(((230743/244511-110445/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+230743/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-498301/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(230743/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-498301/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-498301/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+1234983/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^(-n+3)+(((-1+100341/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(-RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+522469/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-70901/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^(-n+4)+(((-RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-72173/12869+28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+112136/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^3-((-522469/244511+RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(72173/12869-28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-112136/244511)*(RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-1)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((-72173/12869+28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^3+(1483423/244511-1735/757*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-1629736/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+4472168/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+930470/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-2270018/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(-1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+112136/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^3+(1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-112136/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(930470/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-2270018/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)-1877138/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+4974038/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^(-n)+(((1272/12869+RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-94465/244511-28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+1392978/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-94465/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+71875/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((-94465/244511-28223/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+1392978/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(-3211644/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+1392978/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2+1096810/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+1096810/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-94465/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-1949013/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(1272/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-94465/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+71875/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^2+(1096810/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-94465/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-1949013/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+71875/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)^2-1949013/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+268820/14383)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)^(-n)+(((RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-522469/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+70901/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^4+((-RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+522469/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+522469/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-70901/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^3+((2089876/244511-4*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+2089876/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-283604/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^2+((-900844/244511+491044/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-900844/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+3068756/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)+(833798/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-1821474/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-1821474/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+264486/14383)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)^(-n)+(((90079/12869-731511/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3))*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)+90079/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-3666839/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 2)+(90079/12869*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)-3666839/244511)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 4)-3666839/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 3)+492751/12869)*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 1)^(-n)+757976/244511*RootOf(_Z^5-_Z^4-4*_Z^3+5*_Z^2-4*_Z+1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{1445304521 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{1586}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1586 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}+\frac{2894}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{1586 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}+\frac{2894}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2894 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}-\frac{6595}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\left(-\frac{1586 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}+\frac{2894}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2894 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}-\frac{6595}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{2894 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}-\frac{6595}{5911}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{6595 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{5911}-\frac{5171}{5911}\right) \left(\left(\left(\left(-1+\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{28223}{12869}-\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{1272}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{1303217}{244511}-\frac{579259 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{101668}{12869}+\frac{784412 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{37936 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{136304}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{28223}{12869}-\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{101668}{12869}+\frac{784412 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{319962 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{1086558}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{23345 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{14383}+\frac{814667}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{1272}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-\frac{37936 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{136304}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{23345 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{14383}+\frac{814667}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{926803 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{2132121}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{13768}{244511}-\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{21691}{244511}+\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}-\frac{511854 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{21691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{17671}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{21691}{244511}+\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}-\frac{511854 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1628252 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{511854 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}-\frac{495350}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{495350 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{21691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{981007}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{21691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{17671}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{495350 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{21691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{981007}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{17671 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{981007 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{2203996}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{766980}{244511}+\frac{344852 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{766980 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{1869588}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{455575}{244511}+\frac{156853 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{455575 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{742757}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1723915}{244511}-\frac{40201 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{14383}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1723915 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{4558345}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{365961 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{830131}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{830131 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{1683577}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{28223}{12869}-\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{1272}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{28223}{12869}-\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1392978}{244511}+\frac{511854 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{21691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{94465}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{1272}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{21691 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{94465}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{17671 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{71875}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{766980}{244511}+\frac{344852 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{766980 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{1869588}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{538714}{244511}-\frac{272558 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{538714 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{1388958}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{855 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}-\frac{41839}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{41839 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{2119}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{28223}{12869}+\frac{234407 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}+\frac{72173}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{13768 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{1272}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}-\frac{112136}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{1588516}{244511}+\frac{796332 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1588516 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{3442476}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\frac{1588516 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{3442476}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{3442476 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{8419172}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{52331}{12869}-\frac{429411 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{52331 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}-\frac{125395}{14383}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{52331 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}-\frac{125395}{14383}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{125395 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{14383}+\frac{285723}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{230743}{244511}-\frac{110445 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{230743 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{498301}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{230743 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{498301}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{498301 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{1234983}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{100341 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{522469 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{70901}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{72173}{12869}+\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}+\frac{112136}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-\left(\left(-\frac{522469}{244511}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{72173}{12869}-\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}-\frac{112136}{244511}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{72173}{12869}+\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{1483423}{244511}-\frac{1735 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{757}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{1629736 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{4472168}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{930470 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{2270018}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(-\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}+\frac{112136}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{12869}-\frac{112136}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{930470 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}-\frac{2270018}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)-\frac{1877138 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)}{244511}+\frac{4974038}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\frac{1272}{12869}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}-\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{94465}{244511}-\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{12869}+\frac{1392978 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{12869}-\frac{94465 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{71875}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{94465}{244511}-\frac{28223 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{12869}+\frac{1392978 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-\frac{3211644 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{1392978 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}+\frac{1096810}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{1096810 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{94465 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}-\frac{1949013}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{1272 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{12869}-\frac{94465 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{71875}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\frac{1096810 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{94465 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}-\frac{1949013}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\frac{71875 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)^{2}}{244511}-\frac{1949013 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{268820}{14383}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)-\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{522469 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{70901}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)+\frac{522469}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{522469 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{70901}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{2089876}{244511}-4 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{2089876 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{283604}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{900844}{244511}+\frac{491044 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{900844 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{3068756}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)+\left(\frac{833798 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}-\frac{1821474}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{1821474 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{264486}{14383}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{90079}{12869}-\frac{731511 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)+\frac{90079 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}-\frac{3666839}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\frac{90079 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{12869}-\frac{3666839}{244511}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =4\right)-\frac{3666839 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =3\right)}{244511}+\frac{492751}{12869}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}+\frac{757976 \mathit{RootOf}\left(\textit{\_Z}^{5}-\textit{\_Z}^{4}-4 \textit{\_Z}^{3}+5 \textit{\_Z}^{2}-4 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{244511}\right)}{71815952072}<br /><br />



  
    Recurrence in maple format:<br />
    
      a(0) = 1<br />
    
      a(1) = 1<br />
    
      a(2) = 2<br />
    
      a(3) = 6<br />
    
      a(4) = 19<br />
    
    a(n+5) = -a(n)+a(n+1)+4*a(n+2)-5*a(n+3)+4*a(n+4), n >= 5<br /><br />

    Recurrence in latex format:<br />
    
      a \! \left(0\right) = 1<br />
    
      a \! \left(1\right) = 1<br />
    
      a \! \left(2\right) = 2<br />
    
      a \! \left(3\right) = 6<br />
    
      a \! \left(4\right) = 19<br />
    
    a \! \left(n +5\right) = -a \! \left(n \right)+a \! \left(n +1\right)+4 a \! \left(n +2\right)-5 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://permpal.com/tree/16740/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[4,x]*F[5,x]<br />
  
    F[4,x] = x<br />
  
    F[5,x] = F[14,x]+F[6,x]<br />
  
    F[6,x] = F[1,x]+F[7,x]<br />
  
    F[7,x] = F[8,x]<br />
  
    F[8,x] = F[4,x]*F[9,x]<br />
  
    F[9,x] = F[10,x]+F[13,x]<br />
  
    F[10,x] = F[1,x]+F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[10,x]*F[4,x]<br />
  
    F[13,x] = F[7,x]<br />
  
    F[14,x] = F[15,x]+F[2,x]<br />
  
    F[15,x] = F[16,x]+F[17,x]+F[49,x]<br />
  
    F[16,x] = 0<br />
  
    F[17,x] = F[18,x]*F[4,x]<br />
  
    F[18,x] = F[19,x]+F[30,x]<br />
  
    F[19,x] = F[20,x]+F[7,x]<br />
  
    F[20,x] = F[16,x]+F[21,x]+F[27,x]<br />
  
    F[21,x] = F[22,x]*F[4,x]<br />
  
    F[22,x] = F[23,x]<br />
  
    F[23,x] = F[11,x]+F[24,x]<br />
  
    F[24,x] = F[25,x]<br />
  
    F[25,x] = F[26,x]*F[4,x]<br />
  
    F[26,x] = F[11,x]+F[24,x]<br />
  
    F[27,x] = F[28,x]*F[4,x]<br />
  
    F[28,x] = F[13,x]+F[29,x]<br />
  
    F[29,x] = F[27,x]<br />
  
    F[30,x] = F[31,x]+F[38,x]<br />
  
    F[31,x] = F[32,x]<br />
  
    F[32,x] = F[33,x]*F[4,x]<br />
  
    F[33,x] = F[34,x]+F[37,x]<br />
  
    F[34,x] = F[2,x]+F[35,x]<br />
  
    F[35,x] = F[36,x]<br />
  
    F[36,x] = F[34,x]*F[4,x]<br />
  
    F[37,x] = F[31,x]<br />
  
    F[38,x] = 2*F[16,x]+F[39,x]+F[46,x]<br />
  
    F[39,x] = F[4,x]*F[40,x]<br />
  
    F[40,x] = F[41,x]<br />
  
    F[41,x] = F[35,x]+F[42,x]<br />
  
    F[42,x] = F[43,x]<br />
  
    F[43,x] = F[4,x]*F[44,x]<br />
  
    F[44,x] = F[35,x]+F[45,x]<br />
  
    F[45,x] = F[43,x]<br />
  
    F[46,x] = F[4,x]*F[47,x]<br />
  
    F[47,x] = F[37,x]+F[48,x]<br />
  
    F[48,x] = F[46,x]<br />
  
    F[49,x] = F[4,x]*F[50,x]<br />
  
    F[50,x] = F[51,x]+F[65,x]<br />
  
    F[51,x] = F[2,x]+F[52,x]<br />
  
    F[52,x] = F[16,x]+F[36,x]+F[53,x]<br />
  
    F[53,x] = F[4,x]*F[54,x]<br />
  
    F[54,x] = F[55,x]+F[60,x]<br />
  
    F[55,x] = F[11,x]+F[56,x]<br />
  
    F[56,x] = F[16,x]+F[21,x]+F[57,x]<br />
  
    F[57,x] = F[4,x]*F[58,x]<br />
  
    F[58,x] = F[59,x]+F[7,x]<br />
  
    F[59,x] = F[57,x]<br />
  
    F[60,x] = F[35,x]+F[61,x]<br />
  
    F[61,x] = 2*F[16,x]+F[39,x]+F[62,x]<br />
  
    F[62,x] = F[4,x]*F[63,x]<br />
  
    F[63,x] = F[31,x]+F[64,x]<br />
  
    F[64,x] = F[62,x]<br />
  
    F[65,x] = F[31,x]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = x<br />
  
    F_{5}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{7}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{49}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = 0<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{30}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{27}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{23}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{25}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{29}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{27}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{36}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{31}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{39}\! \left(x \right)+F_{46}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{43}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{35}\! \left(x \right)+F_{45}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{43}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{37}\! \left(x \right)+F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{46}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{65}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{2}\! \left(x \right)+F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{16}\! \left(x \right)+F_{36}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{60}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{11}\! \left(x \right)+F_{56}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{57}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = F_{57}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{35}\! \left(x \right)+F_{61}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{39}\! \left(x \right)+F_{62}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{31}\! \left(x \right)+F_{64}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = F_{62}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{31}\! \left(x \right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_4(x)*F_5(x))<br />
  
    Eq(F_4(x), x)<br />
  
    Eq(F_5(x), F_14(x) + F_6(x))<br />
  
    Eq(F_6(x), F_1(x) + F_7(x))<br />
  
    Eq(F_7(x), F_8(x))<br />
  
    Eq(F_8(x), F_4(x)*F_9(x))<br />
  
    Eq(F_9(x), F_10(x) + F_13(x))<br />
  
    Eq(F_10(x), F_1(x) + F_11(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_10(x)*F_4(x))<br />
  
    Eq(F_13(x), F_7(x))<br />
  
    Eq(F_14(x), F_15(x) + F_2(x))<br />
  
    Eq(F_15(x), F_16(x) + F_17(x) + F_49(x))<br />
  
    Eq(F_16(x), 0)<br />
  
    Eq(F_17(x), F_18(x)*F_4(x))<br />
  
    Eq(F_18(x), F_19(x) + F_30(x))<br />
  
    Eq(F_19(x), F_20(x) + F_7(x))<br />
  
    Eq(F_20(x), F_16(x) + F_21(x) + F_27(x))<br />
  
    Eq(F_21(x), F_22(x)*F_4(x))<br />
  
    Eq(F_22(x), F_23(x))<br />
  
    Eq(F_23(x), F_11(x) + F_24(x))<br />
  
    Eq(F_24(x), F_25(x))<br />
  
    Eq(F_25(x), F_26(x)*F_4(x))<br />
  
    Eq(F_26(x), F_11(x) + F_24(x))<br />
  
    Eq(F_27(x), F_28(x)*F_4(x))<br />
  
    Eq(F_28(x), F_13(x) + F_29(x))<br />
  
    Eq(F_29(x), F_27(x))<br />
  
    Eq(F_30(x), F_31(x) + F_38(x))<br />
  
    Eq(F_31(x), F_32(x))<br />
  
    Eq(F_32(x), F_33(x)*F_4(x))<br />
  
    Eq(F_33(x), F_34(x) + F_37(x))<br />
  
    Eq(F_34(x), F_2(x) + F_35(x))<br />
  
    Eq(F_35(x), F_36(x))<br />
  
    Eq(F_36(x), F_34(x)*F_4(x))<br />
  
    Eq(F_37(x), F_31(x))<br />
  
    Eq(F_38(x), 2*F_16(x) + F_39(x) + F_46(x))<br />
  
    Eq(F_39(x), F_4(x)*F_40(x))<br />
  
    Eq(F_40(x), F_41(x))<br />
  
    Eq(F_41(x), F_35(x) + F_42(x))<br />
  
    Eq(F_42(x), F_43(x))<br />
  
    Eq(F_43(x), F_4(x)*F_44(x))<br />
  
    Eq(F_44(x), F_35(x) + F_45(x))<br />
  
    Eq(F_45(x), F_43(x))<br />
  
    Eq(F_46(x), F_4(x)*F_47(x))<br />
  
    Eq(F_47(x), F_37(x) + F_48(x))<br />
  
    Eq(F_48(x), F_46(x))<br />
  
    Eq(F_49(x), F_4(x)*F_50(x))<br />
  
    Eq(F_50(x), F_51(x) + F_65(x))<br />
  
    Eq(F_51(x), F_2(x) + F_52(x))<br />
  
    Eq(F_52(x), F_16(x) + F_36(x) + F_53(x))<br />
  
    Eq(F_53(x), F_4(x)*F_54(x))<br />
  
    Eq(F_54(x), F_55(x) + F_60(x))<br />
  
    Eq(F_55(x), F_11(x) + F_56(x))<br />
  
    Eq(F_56(x), F_16(x) + F_21(x) + F_57(x))<br />
  
    Eq(F_57(x), F_4(x)*F_58(x))<br />
  
    Eq(F_58(x), F_59(x) + F_7(x))<br />
  
    Eq(F_59(x), F_57(x))<br />
  
    Eq(F_60(x), F_35(x) + F_61(x))<br />
  
    Eq(F_61(x), 2*F_16(x) + F_39(x) + F_62(x))<br />
  
    Eq(F_62(x), F_4(x)*F_63(x))<br />
  
    Eq(F_63(x), F_31(x) + F_64(x))<br />
  
    Eq(F_64(x), F_62(x))<br />
  
    Eq(F_65(x), F_31(x))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_placements&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], 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{&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 2], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 1]], [[1, 0], [1, 2], [1, 3]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 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&#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 2], [0, 0], [0, 2]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[0, 3], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 2], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 2], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: 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[1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 3], [1, 0], [1, 3]]}, {&#34;patt&#34;: [2, 0, 1], &#34;pos&#34;: [[1, 4], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 3], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 3], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 1], [1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 3]], [[1, 0], [1, 1], [1, 2], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1, 2, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 3, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: 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&#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, &#34;rule_class&#34;: &#34;VerificationRule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}}, {&#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], 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