0231_0321_1032_2031_2103<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 57, 163, 457, 1280, 3602, 10171, 28749, 81241, 229477, 648046, 1830030, 5168055, 14595229, 41219259, 116409685, 328758020, 928458634, 2622095607, 7405162713, 20913216433, 59061860329, 166798989978, 471063762294, 1330350158043, 3757095474817, 10610564702739, 29965723365825, 84627407065992, 238999671095778, 674968603543987, 1906206036057125, 5383393290419593, 15203457953258381, 42936698337493510, 121259260217291070, 342453163793137535, 967135781478154085, 2731327138148930091, 7713651049265121805, 21784432805126503436, 61522294644945467034, 173747591789006264303, 490687576377014213809, 1385770560222409505121, 3913610488690266082385, 11052585108120699464242, 31214051047050751748710, 88152859556089644005283, 248956043424229360724169, 703086795704124941001347, 1985615755674335698754873, 5607657480231400091012624, 15836811490708505197114162, 44725377588840800992971179, 126310741378591176854678781, 356719255324745357536397753, 1007425225524079289426290485, 2845110180829194923214182302, 8034990325805036499490811758, 22691940006683496897608517959, 64085222307387417790810450989, 180985659092067439890776642715, 511128893957415996839807563333, 1443499709030714331106007349012, 4076645704449955886513935624490, 11513019431621279522292360574183, 32514382176553043062161802344329, 91825177105088575592324972690705, 259327183416737852774364087997753, 732376350136455588419988760773322, 2068333566779396597797398719644374, 5841264184280810684461558427513963, 16496549598472459355180335216427793, 46588570567856941083438636516990451, 131572659761358133175751984086567985, 371579651096267294868847932164878488, 1049393068128689178132340085476425218, 2963633256524165071528701320342788003, 8369716120612810949828259906167305941, 23637252613977327957143256604631197161, 66754917739799026641492083426470927197, 188525253557270674105171682970627676214, 532421766548643814588762895058421680926, 1503633768664655072849096569486971377935, 4246472725795497347925828944969929262837, 11992634767001372419612118689507286939659, 33868883174740620852708885065985176367613, 95650477963404907214409290815687170293788, 270130369738649463203247166424712030206778, 762886064020060118850021653252690274142175, 2154497279365879100212052849273779389330785, 6084602597581225499448774877536016416721601, 17183771418541213182590261415031831126583969, 48529381406446417426473991027465663594182754, 137053781869514620802310439405297337688302278, 387059108943048468418464358731247926372288307<br /><br />


Generating function in Maple syntax:<br />
-(x-1)^4/(x^5-3*x^4+9*x^3-9*x^2+5*x-1)<br /><br />



Generating function in latex syntax:<br />
-\frac{\left(x -1\right)^{4}}{x^{5}-3 x^{4}+9 x^{3}-9 x^{2}+5 x -1}<br /><br />



Generating function in sympy syntax:<br />
-(x - 1)**4/(x**5 - 3*x**4 + 9*x**3 - 9*x**2 + 5*x - 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5-3*x^4+9*x^3-9*x^2+5*x-1)*F(x)+(x-1)^4 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}-3 x^{4}+9 x^{3}-9 x^{2}+5 x -1\right) F \! \left(x \right)+\left(x -1\right)^{4} = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-2279169/420414016*((((RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-38/471)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-38/471*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-28/157)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+(-38/471*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-28/157)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-28/157*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+73/157)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+((-38/471*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-28/157)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-28/157*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+73/157)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+(-28/157*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+73/157)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+73/157*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+619/471)*((((-1+4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(2921/1613-1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-1570/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^3+((-1+4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^3+(30869/4839-7709/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(-75412/4839+22204/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)-5092/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+3300/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((2921/1613-1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^3+(-75412/4839+22204/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(54560/1613-4832/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+5277/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-29045/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-1570/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^3+(-5092/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+3300/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(5277/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-29045/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+18425/4839-13475/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n+1)+(((-4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2+1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-1174/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(-6334/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2+2617/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)-327/1613+2617/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((-6334/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2+2617/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(-6334/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2+276/1613+19970/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+276/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-15125/4839+2617/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(-327/1613+2617/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(276/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-15125/4839+2617/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+32204/4839-15125/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-327/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^2)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)^(-n+1)+(((-4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-7589/4839+RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^4+((6346/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-22106/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+68750/4839-22106/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^3+((-19038/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+22106/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-68750/1613+22106/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((53686/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-14)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+414502/4839-14*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(655/4839+185/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+655/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-28285/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n+1)+(((-1+4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(2921/1613-1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-1570/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((2921/1613-1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(6334/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-50170/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+2057/1613-2617/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-1570/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^2+(2057/1613-2617/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+327/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+1531/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n+2)+(((-4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-7589/4839+RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^3+((6346/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-22106/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+68750/4839-22106/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((-5290/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+8414/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-47226/1613+8414/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(-1243/1613+825/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-1243/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+6721/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n+2)+(((-4733/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+1)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-7589/4839+RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((1363/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-2921/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+15851/1613-2921/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(1570/4839-1174/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+1570/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-1730/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n+3)+(((-32462/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+14702/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 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4)-45983/1613+7589/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^3+((9*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-22767/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+137949/1613-22767/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^2+((-4877/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)+44677/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)-375967/4839+44677/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)+(4774/4839-4162/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+4774/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-20434/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n)+(((9640/1613*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-23624/4839)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+37880/4839-23624/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)+(37880/4839-23624/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3))*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)+37880/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)-80920/1613)*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^(-n)-82016/4839*RootOf(_Z^5-3*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{2279169 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{38}{471}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{38 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{471}-\frac{28}{157}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{38 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{471}-\frac{28}{157}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{28 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{157}+\frac{73}{157}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{38 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{471}-\frac{28}{157}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{28 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{157}+\frac{73}{157}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{28 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{157}+\frac{73}{157}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{73 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{157}+\frac{619}{471}\right) \left(\left(\left(\left(-1+\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2921}{1613}-\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}-\frac{1570}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{30869}{4839}-\frac{7709 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{75412}{4839}+\frac{22204 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{5092 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}+\frac{3300}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{2921}{1613}-\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{75412}{4839}+\frac{22204 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{54560}{1613}-\frac{4832 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{5277 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}-\frac{29045}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}-\frac{1570}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{5092 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}+\frac{3300}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{5277 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}-\frac{29045}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{18425}{4839}-\frac{13475 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}+\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{1174}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{6334 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}+\frac{2617}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{327}{1613}+\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{6334 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}+\frac{2617}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{6334 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}+\frac{276}{1613}+\frac{19970 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{276 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{15125}{4839}+\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{327}{1613}+\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{276 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{15125}{4839}+\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{32204}{4839}-\frac{15125 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{327 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(-\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{7589}{4839}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\frac{6346 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{22106}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{68750}{4839}-\frac{22106 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{19038 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{22106}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{68750}{1613}+\frac{22106 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{53686 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-14\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{414502}{4839}-14 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{655}{4839}+\frac{185 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{655 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{28285}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2921}{1613}-\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}-\frac{1570}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{2921}{1613}-\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{6334 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}-\frac{50170}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{2057}{1613}-\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}-\frac{1570}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2057}{1613}-\frac{2617 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{327 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}+\frac{1531}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(-\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{7589}{4839}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{6346 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{22106}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{68750}{4839}-\frac{22106 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{5290 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{8414}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{47226}{1613}+\frac{8414 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1243}{1613}+\frac{825 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1243 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{6721}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(-\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{7589}{4839}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1363 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{2921}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{15851}{1613}-\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{1570}{4839}-\frac{1174 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{1730}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{32462 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{14702}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{67646}{4839}+\frac{14702 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{67646}{4839}+\frac{14702 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{67646 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{385562}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{13748 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{13692}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{21524}{1613}-\frac{13692 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{21524}{1613}-\frac{13692 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{21524 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{131228}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{4983 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{13343}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{21197}{4839}+\frac{13343 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{21197}{4839}+\frac{13343 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{21197 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{44253}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(\frac{4733 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{7589}{4839}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{7589}{4839}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{7589 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{45983}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\frac{7589}{4839}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{15851}{1613}+\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}+\frac{1730}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\left(\left(-\frac{7589}{4839}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{15851}{1613}-\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}-\frac{1730}{1613}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-3\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{15851}{1613}+\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{49283}{1613}-\frac{27859 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{398870}{4839}+\frac{22982 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{18292 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}+\frac{51484}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}+\frac{1730}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{1613}-\frac{5190}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{18292 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}+\frac{51484}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{20156}{1613}+\frac{12284 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{1570}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{50170 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}-\frac{2057}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1531}{1613}-\frac{2057 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{50170 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{2921 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}-\frac{2057}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{50170 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}-\frac{4372}{4839}-\frac{31302 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{4372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{26063}{4839}-\frac{2057 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1531}{1613}-\frac{2057 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{1570 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4372 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{26063}{4839}-\frac{2057 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{33932}{1613}+\frac{26063 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{1531 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\frac{7589}{4839}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{7589 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}+\frac{45983}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(-3 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{7589}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{45983}{1613}+\frac{7589 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(9 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{22767}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{137949}{1613}-\frac{22767 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4877 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}+\frac{44677}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{375967}{4839}+\frac{44677 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{4774}{4839}-\frac{4162 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{4774 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{20434}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{9640 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{1613}-\frac{23624}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{37880}{4839}-\frac{23624 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{37880}{4839}-\frac{23624 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{37880 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)}{4839}-\frac{80920}{1613}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{82016 \mathit{RootOf}\left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{4839}\right)}{420414016}<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)-3*a(n+1)+9*a(n+2)-9*a(n+3)+5*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)-3 a \! \left(n +1\right)+9 a \! \left(n +2\right)-9 a \! \left(n +3\right)+5 a \! \left(n +4\right), \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://www.permpal.com/tree/20791/<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[18,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[6,x]<br />
  
    F[10,x] = F[11,x]+F[14,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[13,x]*F[4,x]<br />
  
    F[13,x] = F[1,x]+F[11,x]<br />
  
    F[14,x] = F[15,x]<br />
  
    F[15,x] = F[16,x]*F[4,x]<br />
  
    F[16,x] = F[11,x]+F[17,x]<br />
  
    F[17,x] = F[15,x]<br />
  
    F[18,x] = F[19,x]+F[2,x]<br />
  
    F[19,x] = F[20,x]+F[21,x]+F[34,x]<br />
  
    F[20,x] = 0<br />
  
    F[21,x] = F[22,x]*F[4,x]<br />
  
    F[22,x] = F[23,x]+F[27,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[23,x]<br />
  
    F[27,x] = F[28,x]+F[31,x]<br />
  
    F[28,x] = F[29,x]<br />
  
    F[29,x] = F[30,x]*F[4,x]<br />
  
    F[30,x] = F[2,x]+F[28,x]<br />
  
    F[31,x] = F[32,x]<br />
  
    F[32,x] = F[33,x]*F[4,x]<br />
  
    F[33,x] = F[27,x]<br />
  
    F[34,x] = F[35,x]*F[4,x]<br />
  
    F[35,x] = F[18,x]+F[36,x]<br />
  
    F[36,x] = F[37,x]+F[40,x]<br />
  
    F[37,x] = F[20,x]+F[21,x]+F[38,x]<br />
  
    F[38,x] = F[39,x]*F[4,x]<br />
  
    F[39,x] = F[2,x]+F[37,x]<br />
  
    F[40,x] = 2*F[20,x]+F[41,x]+F[54,x]<br />
  
    F[41,x] = F[4,x]*F[42,x]<br />
  
    F[42,x] = F[43,x]+F[47,x]<br />
  
    F[43,x] = F[17,x]+F[44,x]<br />
  
    F[44,x] = F[45,x]<br />
  
    F[45,x] = F[4,x]*F[46,x]<br />
  
    F[46,x] = F[43,x]<br />
  
    F[47,x] = F[48,x]+F[51,x]<br />
  
    F[48,x] = F[49,x]<br />
  
    F[49,x] = F[4,x]*F[50,x]<br />
  
    F[50,x] = F[28,x]+F[48,x]<br />
  
    F[51,x] = F[52,x]<br />
  
    F[52,x] = F[4,x]*F[53,x]<br />
  
    F[53,x] = F[47,x]<br />
  
    F[54,x] = F[4,x]*F[55,x]<br />
  
    F[55,x] = F[28,x]+F[56,x]<br />
  
    F[56,x] = F[54,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_{18}\! \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_{6}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)<br />
  
    F_{17}\! \left(x \right) = F_{15}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = 0<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)+F_{27}\! \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_{23}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{29}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \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_{27}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{18}\! \left(x \right)+F_{36}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{41}\! \left(x \right)+F_{54}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{17}\! \left(x \right)+F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{45}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{43}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{49}\! \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_{28}\! \left(x \right)+F_{48}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{47}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{28}\! \left(x \right)+F_{56}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{54}\! \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_18(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_6(x))<br />
  
    Eq(F_10(x), F_11(x) + F_14(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_13(x)*F_4(x))<br />
  
    Eq(F_13(x), F_1(x) + F_11(x))<br />
  
    Eq(F_14(x), F_15(x))<br />
  
    Eq(F_15(x), F_16(x)*F_4(x))<br />
  
    Eq(F_16(x), F_11(x) + F_17(x))<br />
  
    Eq(F_17(x), F_15(x))<br />
  
    Eq(F_18(x), F_19(x) + F_2(x))<br />
  
    Eq(F_19(x), F_20(x) + F_21(x) + F_34(x))<br />
  
    Eq(F_20(x), 0)<br />
  
    Eq(F_21(x), F_22(x)*F_4(x))<br />
  
    Eq(F_22(x), F_23(x) + F_27(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_23(x))<br />
  
    Eq(F_27(x), F_28(x) + F_31(x))<br />
  
    Eq(F_28(x), F_29(x))<br />
  
    Eq(F_29(x), F_30(x)*F_4(x))<br />
  
    Eq(F_30(x), F_2(x) + F_28(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_27(x))<br />
  
    Eq(F_34(x), F_35(x)*F_4(x))<br />
  
    Eq(F_35(x), F_18(x) + F_36(x))<br />
  
    Eq(F_36(x), F_37(x) + F_40(x))<br />
  
    Eq(F_37(x), F_20(x) + F_21(x) + F_38(x))<br />
  
    Eq(F_38(x), F_39(x)*F_4(x))<br />
  
    Eq(F_39(x), F_2(x) + F_37(x))<br />
  
    Eq(F_40(x), 2*F_20(x) + F_41(x) + F_54(x))<br />
  
    Eq(F_41(x), F_4(x)*F_42(x))<br />
  
    Eq(F_42(x), F_43(x) + F_47(x))<br />
  
    Eq(F_43(x), F_17(x) + F_44(x))<br />
  
    Eq(F_44(x), F_45(x))<br />
  
    Eq(F_45(x), F_4(x)*F_46(x))<br />
  
    Eq(F_46(x), F_43(x))<br />
  
    Eq(F_47(x), F_48(x) + F_51(x))<br />
  
    Eq(F_48(x), F_49(x))<br />
  
    Eq(F_49(x), F_4(x)*F_50(x))<br />
  
    Eq(F_50(x), F_28(x) + F_48(x))<br />
  
    Eq(F_51(x), F_52(x))<br />
  
    Eq(F_52(x), F_4(x)*F_53(x))<br />
  
    Eq(F_53(x), F_47(x))<br />
  
    Eq(F_54(x), F_4(x)*F_55(x))<br />
  
    Eq(F_55(x), F_28(x) + F_56(x))<br />
  
    Eq(F_56(x), F_54(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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#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, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 2], [1, 2], [1, 0], [1, 2]]}], &#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;: [1, 2, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#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, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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{&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 3], [1, 3], [1, 0], [1, 3]]}], &#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;: 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&#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;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 1], &#34;pos&#34;: [[0, 0], [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, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 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{&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0, 3, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 0, 3, 1], &#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;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 1], [0, 1], [0, 0], [0, 1]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#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], 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{&#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;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, 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