0231_0312_2103
Counting sequence:
1, 1, 2, 6, 21, 73, 240, 759, 2365, 7369, 23069, 72495, 228186, 718341, 2260566, 7111650, 22370236, 70367607, 221357774, 696358788, 2190680327, 6891703804, 21680712093, 68205549672, 214568342539, 675012376279, 2123528489810, 6680433701268, 21016061929924, 66114705510348, 207991128637943, 654322059367031, 2058440504389873, 6475675573915492, 20371914868532040, 64088281566059123, 201616190018533209, 634267095718233802, 1995349428362411119, 6277196740910023455, 19747518102298660841, 62123984244977881275, 195436682226028874867, 614826901956171850134, 1934192266948192446629, 6084801614994080300950, 19142259706701367511486, 60219893742090910548924, 189446578303205288811097, 595982553295107195974162, 1874909576191139389766100, 5898303397459620687582891, 18555552443963616928647840, 58374163433234195986040991, 183640070368675946421424368, 577715781462866140096610385, 1817443891638638136825555575, 5717521323189719151508255054, 17986827671291638396880925670, 56585004478192552186579366872, 178011531011007632456139653996, 560008883362374158626286143739, 1761739521387581623833920006565, 5542280191313968226186270841839, 17435534224060117834215227633500, 54850682965255843502104894130950, 172555505503430807130955194690791, 542844698914789715298249667158739, 1707742481354975195341033509963956, 5372410172660168922128922165580361, 16901137834553334632828479130057243, 53169518134750109605250483145662961, 167266706322097584097576884486754259, 526206594028865764409331149787044517, 1655400442131378139509971976483402874, 5207746643437991177951291371652630771, 16383120610576282074022494831940775416, 51539880742642227144653942690391909434, 162140008006224708490369373066929113958, 510078444448315025987264226275154749093, 1604662678201078256332150200416189313190, 5048130025561920776299068585901652103154, 15880980533272226831643113232406712756853, 49960191481022273447145203011560268674212, 157170442189699808861392227423406033739391, 494444620122987410956209256105818408581426, 1555480018777901420881431440635561223714579, 4893405631990642904025452047852782169397513, 15394230970585537403137120832286666068917416, 48428919447523963467243960603597064339603616, 152353192786060703356679089477627093767320346, 479289970061335296425893219528390234806931574, 1507804800152592688169781350609865855079188191, 4743423516816470597952101248117541316886862257, 14922400205656915780884184286437601275513562799, 46944580661698750276767690304467551891713896076, 147683591321140592128194715900590706741461184826, 464599807647327140379548919706671352343793407817, 1461590819501113276516971764191745553418817711553, 4598038329950276725536747781391300560320823017884, 14465030979674832500002525657054726487039201547489
Generating function in Maple syntax:
-(x^2+x-1)*(x^3-2*x^2+3*x-1)*(x-1)^3/(x^9-2*x^8+6*x^7-4*x^6-7*x^5+32*x^4-40*x^3+25*x^2-8*x+1)
Generating function in latex syntax:
-\frac{\left(x^{2}+x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3}}{x^{9}-2 x^{8}+6 x^{7}-4 x^{6}-7 x^{5}+32 x^{4}-40 x^{3}+25 x^{2}-8 x +1}
Generating function in sympy syntax:
(x - 1)**3*(-x**2 - x + 1)*(x**3 - 2*x**2 + 3*x - 1)/(x**9 - 2*x**8 + 6*x**7 - 4*x**6 - 7*x**5 + 32*x**4 - 40*x**3 + 25*x**2 - 8*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^9-2*x^8+6*x^7-4*x^6-7*x^5+32*x^4-40*x^3+25*x^2-8*x+1)*F(x)+(x^2+x-1)*(x^3-2*x^2+3*x-1)*(x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{9}-2 x^{8}+6 x^{7}-4 x^{6}-7 x^{5}+32 x^{4}-40 x^{3}+25 x^{2}-8 x +1\right) F \! \left(x \right)+\left(x^{2}+x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+7)-1564927109193/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+7)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+6)+2319611559304/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+6)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+5)-8158171237737/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+5)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+4)+2082480184784/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+4)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+3)+12235877201842/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+3)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+2)-43703293918168/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+2)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n+1)+40041349058213/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n+1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n-1)+3501868394607/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n-1)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 1)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 2)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 3)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 4)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 5)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 6)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 7)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 8)^(-n)-17558611111888/8887218836975*RootOf(_Z^9-2*_Z^8+6*_Z^7-4*_Z^6-7*_Z^5+32*_Z^4-40*_Z^3+25*_Z^2-8*_Z+1,index = 9)^(-n)
Explicit closed form in latex syntax:
-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +7}}{8887218836975}-\frac{1564927109193 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +7}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +6}}{8887218836975}+\frac{2319611559304 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +6}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{8887218836975}-\frac{8158171237737 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +5}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{8887218836975}+\frac{2082480184784 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +4}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{8887218836975}+\frac{12235877201842 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +3}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{8887218836975}-\frac{43703293918168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +2}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{8887218836975}+\frac{40041349058213 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{8887218836975}+\frac{3501868394607 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{8887218836975}-\frac{17558611111888 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+32 \textit{\_Z}^{4}-40 \textit{\_Z}^{3}+25 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{8887218836975}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 240
a(7) = 759
a(8) = 2365
a(n+9) = -a(n)+2*a(n+1)-6*a(n+2)+4*a(n+3)+7*a(n+4)-32*a(n+5)+40*a(n+6)-25*a(n+7)+8*a(n+8), n >= 9
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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 240
a \! \left(7\right) = 759
a \! \left(8\right) = 2365
a \! \left(n +9\right) = -a \! \left(n \right)+2 a \! \left(n +1\right)-6 a \! \left(n +2\right)+4 a \! \left(n +3\right)+7 a \! \left(n +4\right)-32 a \! \left(n +5\right)+40 a \! \left(n +6\right)-25 a \! \left(n +7\right)+8 a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14751/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[17,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[6,x]
F[10,x] = F[11,x]+F[14,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[15,x] = F[16,x]*F[4,x]
F[16,x] = F[7,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[70,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[32,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[26,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[22,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[10,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[11,x]+F[29,x]
F[32,x] = F[33,x]+F[44,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[2,x]+F[33,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[2,x]+F[38,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[33,x]
F[44,x] = 2*F[19,x]+F[45,x]+F[47,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[32,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[69,x]
F[49,x] = F[50,x]+F[66,x]
F[50,x] = F[19,x]+F[51,x]+F[64,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[57,x]
F[53,x] = F[11,x]+F[54,x]
F[54,x] = F[19,x]+F[30,x]+F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[53,x]
F[57,x] = F[38,x]+F[58,x]
F[58,x] = 2*F[19,x]+F[59,x]+F[61,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[57,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[50,x]+F[63,x]
F[63,x] = F[61,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[2,x]+F[50,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[33,x]
F[69,x] = F[63,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[17,x]+F[72,x]
F[72,x] = F[50,x]+F[73,x]
F[73,x] = 2*F[19,x]+F[67,x]+F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[80,x]
F[76,x] = F[14,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[76,x]
F[80,x] = F[41,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[80,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \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_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{7}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{70}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{32}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{10}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{44}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{33}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{32}\! \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_{69}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{66}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right)+F_{51}\! \left(x \right)+F_{64}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{19}\! \left(x \right)+F_{30}\! \left(x \right)+F_{55}\! \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_{38}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{19}\! \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_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{33}\! \left(x \right)
F_{69}\! \left(x \right) = F_{63}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{17}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{50}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{76}\! \left(x \right)
F_{80}\! \left(x \right) = F_{41}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{80}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_17(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_6(x))
Eq(F_10(x), F_11(x) + F_14(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))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_7(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_70(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_32(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_26(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_22(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_10(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_11(x) + F_29(x))
Eq(F_32(x), F_33(x) + F_44(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_2(x) + F_33(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_2(x) + F_38(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_33(x))
Eq(F_44(x), 2*F_19(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_32(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_69(x))
Eq(F_49(x), F_50(x) + F_66(x))
Eq(F_50(x), F_19(x) + F_51(x) + F_64(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_57(x))
Eq(F_53(x), F_11(x) + F_54(x))
Eq(F_54(x), F_19(x) + F_30(x) + F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_53(x))
Eq(F_57(x), F_38(x) + F_58(x))
Eq(F_58(x), 2*F_19(x) + F_59(x) + F_61(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_57(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_50(x) + F_63(x))
Eq(F_63(x), F_61(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_2(x) + F_50(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_33(x))
Eq(F_69(x), F_63(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_17(x) + F_72(x))
Eq(F_72(x), F_50(x) + F_73(x))
Eq(F_73(x), 2*F_19(x) + F_67(x) + F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_80(x))
Eq(F_76(x), F_14(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_76(x))
Eq(F_80(x), F_41(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_80(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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "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, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [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, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 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