0213_0231_0321_2103
Counting sequence:
1, 1, 2, 6, 20, 65, 201, 603, 1793, 5343, 15990, 47976, 144041, 432355, 1297280, 3891703, 11674228, 35021058, 105061817, 315186608, 945565820, 2836707574, 8510129236, 25530375271, 76591080316, 229773170871, 689319473248, 2067958511229, 6203875833277, 18611627916263, 55834883874950, 167504650789675, 502513950136095, 1507541847546482, 4522625541975804, 13567876631704396, 40703629909326485, 122110889743902579, 366332669229034539, 1098998007638011129, 3296994022809264955, 9890982068318696414, 29672946204979789054, 89018838615264756753, 267056515846435783609, 801169547539851304432, 2403508642619034973737, 7210525927854443488470, 21631577783558623395880, 64894733350672111907493, 194684200052019865324878, 584052600156076583854002, 1752157800468257198888122, 5256473401404786457918412, 15769420204214317797279871, 47308260612642817294960190, 141924781837928249793441845, 425774345513784641958692430, 1277323036541354192262544183, 3831969109624063412353582987, 11495907328872191338175481859, 34487721986616574181094352946, 103463165959849719874952693765, 310389497879549152987504232825, 931168493638647450724153788962, 2793505480915942350438499395846, 8380516442747827067727268216664, 25141549328243481242142842438565, 75424647984730443766825880410421, 226273943954191331283039974297479, 678821831862573993695796508196365, 2036465495587721980777033347361631, 6109396486763165942016479566043958, 18328189460289497826118782233346244, 54984568380868493479263136272276333, 164953705142605480439510828442792059, 494861115427816441319805582812705836, 1484583346283449323957446630880650655, 4453750038850347971864132022168294468, 13361250116551043915578457942738810822, 40083750349653131746724430945780247241, 120251251048959395240183054283715827280, 360753753146878185720595625694494533292, 1082261259440634557161858409414687583102, 3246783778321903671485602633984806133256, 9740351334965711014456665109883860005359, 29221054004897133043369578350931047632800, 87663162014691399130108134515030321514855, 262989486044074197390324080213509772542196, 788968458132222592170972962196102965175033, 2366905374396667776512921124070465407806337, 7100716123190003329538766115358324698074447, 21302148369570009988616298031746433854788282, 63906445108710029965848885294346851870624727, 191719335326130089897546635585243369983877703, 575158005978390269692639882036005573422188042, 1725474017935170809077919639880148184335844044, 5176422053805512427233758963267715410370833584, 15529266161416537281701276991383664114466329569, 46587798484249611845103831066856608547117766975, 139763395452748835535311493109828302952263416087
Generating function in Maple syntax:
-(2*x-1)*(x-1)^4/(3*x-1)/(x^5-2*x^4+6*x^3-7*x^2+4*x-1)
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(x -1\right)^{4}}{\left(3 x -1\right) \left(x^{5}-2 x^{4}+6 x^{3}-7 x^{2}+4 x -1\right)}
Generating function in sympy syntax:
(1 - 2*x)*(x - 1)**4/((3*x - 1)*(x**5 - 2*x**4 + 6*x**3 - 7*x**2 + 4*x - 1))
Implicit equation for the generating function in Maple syntax:
(3*x-1)*(x^5-2*x^4+6*x^3-7*x^2+4*x-1)*F(x)+(2*x-1)*(x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x -1\right) \left(x^{5}-2 x^{4}+6 x^{3}-7 x^{2}+4 x -1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x -1\right)^{4} = 0
Explicit closed form in Maple syntax:
-8233119560/51784918969*((((RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-10979/13290)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)-10979/13290*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+895/1329)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+(-10979/13290*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+895/1329)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)+895/1329*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-19753/26580)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)+((-10979/13290*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+895/1329)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)+895/1329*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-19753/26580)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+(895/1329*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-19753/26580)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)-19753/26580*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-25787/26580)*((((1-755879/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(-630800/464623+1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+208215/464623-363813/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^3+((1-755879/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^3+(-1827033/464623+3032961/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(72205/20201-3107773/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)-17145/20201+935841/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^2+((-630800/464623+1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^3+(72205/20201-3107773/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(-5401680/464623+9704718/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+2796872/464623-5041975/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)+(208215/464623-363813/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^3+(-17145/20201+935841/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(2796872/464623-5041975/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+2841062/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)-1680730/464623)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^(-n+1)+(((-1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+755879/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2+363813/464623)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(-1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2+4352989/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-1871481/929246)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+871059/929246-1871481/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+363813/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^2+((-1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2+4352989/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-1871481/929246)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(4352989/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2-2321530/464623+4707215/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+3640561/929246-2321530/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-1871481/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)+(871059/929246-1871481/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+363813/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(3640561/929246-2321530/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-1871481/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+3640561/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-1381285/464623+871059/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)^(-n+1)+(((755879/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-1)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)+266987/464623-RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^4+((-1976381/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+1196233/464623)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)-516659/464623+1196233/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^3+((5464520/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-3321712/464623)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)+1567292/464623-3321712/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^2+((1167797/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)-840745/464623)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)+1695662/464623-840745/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)+(1591772/464623-2442667/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)-1813300/464623+1591772/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^(-n+1)+(((1-755879/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(-630800/464623+1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+208215/464623-363813/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)^2+((-630800/464623+1056580/464623*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)^2+(-4352989/929246*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index 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3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 1)+((-5152952/464623*3^n*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3)+3178168/464623*3^n)*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)-2005640/464623*3^n+3178168/464623*3^n*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 2)+(-2005640/464623*3^n+3178168/464623*3^n*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 4)+1697080/464623*3^n-2005640/464623*3^n*RootOf(_Z^5-2*_Z^4+6*_Z^3-7*_Z^2+4*_Z-1,index = 3))
Explicit closed form in latex syntax:
-\frac{8233119560 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{10979}{13290}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{10979 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{13290}+\frac{895}{1329}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{10979 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{13290}+\frac{895}{1329}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{895 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{1329}-\frac{19753}{26580}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{10979 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{13290}+\frac{895}{1329}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{895 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{1329}-\frac{19753}{26580}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{895 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{1329}-\frac{19753}{26580}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{19753 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{26580}-\frac{25787}{26580}\right) \left(\left(\left(\left(1-\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{630800}{464623}+\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{208215}{464623}-\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(1-\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{1827033}{464623}+\frac{3032961 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{72205}{20201}-\frac{3107773 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{17145}{20201}+\frac{935841 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{630800}{464623}+\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{72205}{20201}-\frac{3107773 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{5401680}{464623}+\frac{9704718 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{2796872}{464623}-\frac{5041975 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{208215}{464623}-\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{17145}{20201}+\frac{935841 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2796872}{464623}-\frac{5041975 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{2841062 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}-\frac{1680730}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}+\frac{363813}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}+\frac{4352989 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}-\frac{1871481}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{871059}{929246}-\frac{1871481 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}+\frac{4352989 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}-\frac{1871481}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{4352989 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}-\frac{2321530}{464623}+\frac{4707215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{3640561}{929246}-\frac{2321530 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\frac{1871481 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{871059}{929246}-\frac{1871481 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{3640561}{929246}-\frac{2321530 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\frac{1871481 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{3640561 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}-\frac{1381285}{464623}+\frac{871059 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{266987}{464623}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{1976381 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{1196233}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{516659}{464623}+\frac{1196233 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{5464520 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\frac{3321712}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1567292}{464623}-\frac{3321712 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1167797 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\frac{840745}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1695662}{464623}-\frac{840745 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{1591772}{464623}-\frac{2442667 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1813300}{464623}+\frac{1591772 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(1-\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{630800}{464623}+\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{208215}{464623}-\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{630800}{464623}+\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{4352989 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}+\frac{2253281}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{826869}{929246}+\frac{1871481 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{208215}{464623}-\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{826869}{929246}+\frac{1871481 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{299445}{929246}-\frac{871059 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{266987}{464623}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{1976381 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{1196233}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{516659}{464623}+\frac{1196233 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1862557 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}-\frac{1068149}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{107459}{929246}-\frac{1068149 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{38199}{929246}-\frac{201 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{387825}{929246}-\frac{38199 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{266987}{464623}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1056580 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{630800}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{8300}{20201}+\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{208215}{464623}+\frac{363813 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{22095}{464623}-\frac{208215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{9246688 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\frac{5695028}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{3460681}{464623}-\frac{5695028 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{3460681}{464623}-\frac{5695028 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1692095}{464623}+\frac{3460681 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{9066483 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{5575275}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3242043}{929246}+\frac{5575275 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{3242043}{929246}+\frac{5575275 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{180045}{929246}-\frac{3242043 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{919801 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\frac{565433}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{325759}{464623}-\frac{565433 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{325759}{464623}-\frac{565433 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{545}{20201}+\frac{325759 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-\frac{755879 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{266987}{464623}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{266987}{464623}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{17315}{464623}-\frac{266987 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\frac{266987}{464623}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{8300}{20201}-\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{22095}{464623}+\frac{208215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-2\right) \left(\left(-\frac{266987}{464623}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{8300}{20201}-\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{22095}{464623}+\frac{208215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{8300}{20201}-\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{359705}{464623}+\frac{63905 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{20201}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{3447199}{929246}-\frac{9982511 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{1609085}{929246}+\frac{5275951 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{22095}{464623}+\frac{208215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{44190}{464623}-\frac{416430 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{1609085}{929246}+\frac{5275951 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{3062645 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{929246}+\frac{1443115}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-\frac{208215}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}-\frac{2253281 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{826869}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{299445}{929246}+\frac{826869 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}-\frac{208215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{630800 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}-\frac{2253281 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{826869}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{2253281 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}+\frac{1661384}{464623}-\frac{3822211 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{2463755}{929246}+\frac{1661384 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{826869 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{299445}{929246}+\frac{826869 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}-\frac{208215 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{2463755}{929246}+\frac{1661384 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{826869 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{2463755 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{2287417}{929246}-\frac{299445 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\frac{266987}{464623}-\mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{17315}{464623}+\frac{266987 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(2 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{533974}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{34630}{464623}-\frac{533974 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(-6 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{1601922}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{103890}{464623}+\frac{1601922 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1580051 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{1244779}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3323285}{929246}+\frac{1244779 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{1874225}{929246}+\frac{2777371 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2690539}{929246}-\frac{1874225 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{8084773 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}+\frac{4982597}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3080875}{929246}+\frac{4982597 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{3080875}{929246}+\frac{4982597 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{2018045}{929246}-\frac{3080875 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{929246}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}+\frac{682689 \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{929246}+\left(\left(\left(-\frac{5152952 \,3^{n}}{464623}+\frac{8361976 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{5152952 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{3178168 \,3^{n}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{5152952 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{3178168 \,3^{n}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2005640 \,3^{n}}{464623}+\frac{3178168 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{5152952 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}+\frac{3178168 \,3^{n}}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{2005640 \,3^{n}}{464623}+\frac{3178168 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{2005640 \,3^{n}}{464623}+\frac{3178168 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1697080 \,3^{n}}{464623}-\frac{2005640 \,3^{n} \mathit{RootOf}\left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+6 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{464623}\right)}{51784918969}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(n+6) = -3*a(n)+7*a(n+1)-20*a(n+2)+27*a(n+3)-19*a(n+4)+7*a(n+5), n >= 6
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 65
a \! \left(n +6\right) = -3 a \! \left(n \right)+7 a \! \left(n +1\right)-20 a \! \left(n +2\right)+27 a \! \left(n +3\right)-19 a \! \left(n +4\right)+7 a \! \left(n +5\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15692/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[14,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]+F[17,x]+F[65,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[29,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[16,x]+F[21,x]+F[23,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[19,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[11,x]+F[26,x]
F[29,x] = F[30,x]+F[38,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[2,x]+F[30,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[2,x]+F[35,x]
F[38,x] = 2*F[16,x]+F[39,x]+F[41,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[29,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[61,x]
F[43,x] = F[44,x]
F[44,x] = F[16,x]+F[45,x]+F[59,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[53,x]
F[47,x] = F[11,x]+F[48,x]
F[48,x] = F[16,x]+F[49,x]+F[51,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[47,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[11,x]
F[53,x] = F[35,x]+F[54,x]
F[54,x] = 2*F[16,x]+F[55,x]+F[57,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[53,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[44,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[2,x]+F[44,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[35,x]+F[62,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[14,x]+F[67,x]
F[67,x] = F[44,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{65}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{29}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{38}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{29}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{61}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{16}\! \left(x \right)+F_{45}\! \left(x \right)+F_{59}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{16}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right)
F_{53}\! \left(x \right) = F_{35}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{53}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{44}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{35}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{44}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_14(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_65(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_29(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_16(x) + F_21(x) + F_23(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_19(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_11(x) + F_26(x))
Eq(F_29(x), F_30(x) + F_38(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_2(x) + F_30(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_2(x) + F_35(x))
Eq(F_38(x), 2*F_16(x) + F_39(x) + F_41(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_29(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_61(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_16(x) + F_45(x) + F_59(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_53(x))
Eq(F_47(x), F_11(x) + F_48(x))
Eq(F_48(x), F_16(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_11(x))
Eq(F_53(x), F_35(x) + F_54(x))
Eq(F_54(x), 2*F_16(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_53(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_44(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_2(x) + F_44(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_35(x) + F_62(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_14(x) + F_67(x))
Eq(F_67(x), F_44(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": 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