0123_0132_0213_2103
Counting sequence:
1, 1, 2, 6, 20, 66, 218, 719, 2373, 7832, 25849, 85313, 281570, 929304, 3067109, 10122799, 33409657, 110266457, 363927458, 1201119527, 3964218930, 13083653518, 43181769827, 142518696542, 470373931995, 1552439373000, 5123727832065, 16910539215677, 55812163709269, 184204511646942, 607955324718100, 2006518046428242, 6622385736170761, 21856764715724848, 72136867719636036, 238083163362986014, 785778402483875978, 2593411852768185706, 8559391575052262335, 28249729813209247863, 93236444146960369888, 307720979090727371513, 1015613603016658608449, 3351968376287935011154, 11062959340305411379576, 36512596667390959902019, 120507512898331330715745, 397727414383294224677741, 1312674142445197346140519, 4332397873342598328088144, 14298804803132686919025375, 47192299686073268125262250, 155755196348454159964096380, 514060161317052453792873649, 1696623006157166323996576808, 5599596781915208827454515929, 18481114547099660119441099220, 60995748123528115917652551339, 201312603721335553712434656857, 664419499126217724601163648261, 2192874478093831561191929024832, 7237443336625797199349496206828, 23886723373424123499120976546096, 78836617708774639580794773293777, 260195263896026706687792861770570, 858757989897728541919572194957226, 2834276359111118500885317517617416, 9354349623894458247376175251602646, 30873438507421069119514722295879258, 101895828528448890966339547365946643, 336300728828871715311845571531948617, 1109939257025166308359956689766835268, 3663284223545259521890830323314837005, 12090437578037050415785071484459743637, 39903723519148989700126530054398188658, 131699712306955570625198322100288362968, 434666559711186829860409650783731328945, 1434589452183490893898067317761715514535, 4734771632038114252032720773745563035545, 15626813910719796599580444567513944877533, 51575309640678355061073927946232999479486, 170221043120447906212177030084112654953023, 561803772442310886867744608547787233009610, 1854197770995197075921512788409712638467318, 6119662313795864000380250253003179585376019, 20197557898472069280462683102851737449717842, 66660760699571393486707225633612158935050059, 220009618954065801834372182973604101599914996, 726127813789326488102956029945876676501785437, 2396538862551050069067318760022824418466803989, 7909624739128680831304532059761346752316821385, 26105215522038620493700452256204012937967550302, 86158610544544970918919181602739773407284422232, 284361037536719467448623624881449729058220902002, 938515595340914046776687100217143083905445342801, 3097511284696910557709617606772856156356090126416, 10223139824692517039074235388475950206221398900664, 33740825543252423054438623319944502762082319278106, 111359457843905241231471186166706718719061072312750, 367534838037431427281403558195183209190207315314354, 1213025456360858609028905173652039203205777572913011
Generating function in Maple syntax:
(x^6-x^3-2*x^2-2*x+1)/(x^6-x^2-3*x+1)
Generating function in latex syntax:
\frac{x^{6}-x^{3}-2 x^{2}-2 x +1}{x^{6}-x^{2}-3 x +1}
Generating function in sympy syntax:
(x**6 - x**3 - 2*x**2 - 2*x + 1)/(x**6 - x**2 - 3*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^6-x^2-3*x+1)*F(x)-x^6+x^3+2*x^2+2*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{6}-x^{2}-3 x +1\right) F \! \left(x \right)-x^{6}+x^{3}+2 x^{2}+2 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,120207/890653*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^(-n+1)+32751/890653*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^(-n+2)-13836/890653*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^(-n+3)-12756/890653*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^(-n+4)-41114/890653*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^(-n+5)+1/890653*(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^4+79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^(-n+1)+1/890653*(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^(-n+2)+1/890653*(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^(-n+3)+1/890653*(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^(-n+4)+1/890653*((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^3+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3+79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^(-n+1)+1/890653*((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^(-n+2)+1/890653*((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^(-n+3)+1/890653*(((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^2+((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-25512*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^(-n+1)+1/890653*(((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^(-n+2)+1/890653*((((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+(12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)+((12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+(-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)^(-n+1)+111289/890653*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^(-n)+1/890653*(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^5-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12053)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^(-n)+1/890653*((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^4+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^3+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^4+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^4-24809)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^(-n)+1/890653*(((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^3+((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-25512*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^2+((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^3+(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-25512*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3-25512*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^3+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^3-24809)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^(-n)+1/890653*((((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+(12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)^2+(((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+((-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^2+(-41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2+38268*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-27672)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-27672*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+(12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^2+(12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-27672*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)+((12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)^2+((12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^2+(12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-27672*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+(-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)^2+(-13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1))*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)-32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)^2-24809)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)^(-n)+1/890653*(((((41114*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)-12756)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+(-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+((-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+(13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)-79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 3)+(((-12756*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+13836)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+(13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)-79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 2)+((13836*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)+32751)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)+32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)-79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 4)+(32751*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)-79093)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 1)-79093*RootOf(_Z^6-_Z^2-3*_Z+1,index = 5)-24809)*RootOf(_Z^6-_Z^2-3*_Z+1,index = 6)^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{120207 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{890653}+\\\frac{32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{890653}-\\\frac{13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{890653}-\\\frac{12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{890653}-\\\frac{41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{890653}+\\\frac{\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{890653}\\+\\\frac{\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{890653}\\+\\\frac{\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{890653}\\+\\\frac{\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{890653}\\+\\\frac{\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{890653}\\+\\\frac{\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{890653}\\+\\\frac{\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{890653}\\+\\\frac{\left(\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}+\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-25512 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{890653}\\+\\\frac{\left(\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{890653}\\+\\\frac{\left(\left(\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{890653}\\+\frac{111289 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{890653}\\+\\\frac{\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{5}-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12053\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{890653}\\+\\\frac{\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{4}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}-24809\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{890653}\\+\\\frac{\left(\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{3}+\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-25512 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}+\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-25512 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-25512 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-24809\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{890653}\\+\\\frac{\left(\left(\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}+\left(\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{2}+\left(-41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+38268 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-27672\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-27672 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{2}+\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-27672 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{2}+\left(12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-27672 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{2}+\left(-13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-24809\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{890653}\\+\\\frac{\left(\left(\left(\left(\left(41114 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)-12756\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\left(13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)-79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(\left(\left(-12756 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+13836\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\left(13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)-79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\left(13836 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)+32751\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)-79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+\left(32751 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)-79093\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-79093 \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)-24809\right) \mathit{RootOf}\left(\textit{\_Z}^{6}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{890653} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 66
a(6) = 218
a(n) = a(n+4)+3*a(5+n)-a(n+6), n >= 7
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) = 66
a \! \left(6\right) = 218
a \! \left(n \right) = a \! \left(n +4\right)+3 a \! \left(5+n \right)-a \! \left(n +6\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14788/
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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[4,x]*F[7,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]+F[17,x]+F[53,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[30,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[16,x]+F[21,x]+F[25,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[4,x]
F[24,x] = F[12,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[20,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[20,x]*F[4,x]
F[30,x] = F[31,x]+F[40,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[2,x]*F[4,x]
F[37,x] = F[31,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[31,x]*F[4,x]
F[40,x] = 2*F[16,x]+F[41,x]+F[47,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[35,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[15,x]*F[4,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[15,x]+F[45,x]
F[50,x] = F[40,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[40,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[63,x]
F[55,x] = F[2,x]+F[56,x]
F[56,x] = F[16,x]+F[36,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[4,x]+F[60,x]
F[60,x] = F[13,x]+F[16,x]+F[21,x]
F[61,x] = F[35,x]+F[62,x]
F[62,x] = 2*F[16,x]+F[41,x]+F[46,x]
F[63,x] = F[15,x]+F[64,x]
F[64,x] = 2*F[16,x]+F[46,x]+F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[12,x]+F[68,x]
F[68,x] = F[29,x]
F[69,x] = F[38,x]+F[70,x]
F[70,x] = F[52,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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \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_{53}\! \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_{30}\! \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_{25}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{40}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{41}\! \left(x \right)+F_{47}\! \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_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{35}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = F_{40}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{63}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right)+F_{36}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)+F_{21}\! \left(x \right)
F_{61}\! \left(x \right) = F_{35}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{41}\! \left(x \right)+F_{46}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{46}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{29}\! \left(x \right)
F_{69}\! \left(x \right) = F_{38}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{52}\! \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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_4(x)*F_7(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_53(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_30(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_16(x) + F_21(x) + F_25(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_12(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_20(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_20(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_40(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_2(x)*F_4(x))
Eq(F_37(x), F_31(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_31(x)*F_4(x))
Eq(F_40(x), 2*F_16(x) + F_41(x) + F_47(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_35(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_15(x)*F_4(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_15(x) + F_45(x))
Eq(F_50(x), F_40(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_40(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_63(x))
Eq(F_55(x), F_2(x) + F_56(x))
Eq(F_56(x), F_16(x) + F_36(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_4(x) + F_60(x))
Eq(F_60(x), F_13(x) + F_16(x) + F_21(x))
Eq(F_61(x), F_35(x) + F_62(x))
Eq(F_62(x), 2*F_16(x) + F_41(x) + F_46(x))
Eq(F_63(x), F_15(x) + F_64(x))
Eq(F_64(x), 2*F_16(x) + F_46(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_12(x) + F_68(x))
Eq(F_68(x), F_29(x))
Eq(F_69(x), F_38(x) + F_70(x))
Eq(F_70(x), F_52(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:
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