0123_0132_0213_0321_2103
Counting sequence:
1, 1, 2, 6, 19, 55, 149, 403, 1116, 3110, 8640, 23929, 66252, 183568, 508812, 1410232, 3908121, 10830078, 30012738, 83173958, 230499085, 638776518, 1770222425, 4905767930, 13595228098, 37676109526, 104410825728, 289350986455, 801870816543, 2222203677567, 6158335144555, 17066433624643, 47295762331092, 131069512407462, 363229521108626, 1006608498427444, 2789587877938313, 7730712128329493, 21423920888558734, 59371553181247742, 164534836810665774, 455971101878664664, 1263620822052307154, 3501839426536274829, 9704556268184480256, 26893983672922938595, 74530595507059441346, 206544695430455047021, 572391927371796142557, 1586254819266085596847, 4395946608119439964631, 12182372180516287521745, 33760690284658624238836, 93560120443499034314273, 259280721560950017869795, 718537901132407048690239, 1991265344586745478121225, 5518341713503435813820601, 15292836461888941022714553, 42380638820860914670316976, 117448358997387087560603634, 325481574015096572899366287, 901998596895692955515053523, 2499685185755130043249929106, 6927312358786547474910232977, 19197480062554455783403903686, 53201475790927565055726141033, 147435862264728581948888078888, 408585159689327259105023391556, 1132301396376686928243360899397, 3137917327226129461831597786472, 8696028446149063830408691018405, 24099076824016080989455927280824, 66785143053092739587811743170283, 185079925060746183615775677330008, 512907169087887952233123689979042, 1421406260108470850511862123686368, 3939106095686780941689408140213129, 10916341983672317661452223227192400, 30252173820596282998056669554928792, 83837060275359272783894523609696437, 232335458512702877890114261201170609, 643865196429999190192005740204559968, 1784326825649711820239648161174527652, 4944858393319479842527347967529757012, 13703557094188024992064136129793559029, 37976310360549951063073285796896922605, 105242758408507075563975066461966798956, 291656511448180347873298324100020399660, 808260083225323603039540719555773794093, 2239910087697385075455568397166801330703, 6207404404962842354679254658735688974537, 17202417926677870904511923144317864347865, 47672612128750065010148562238423022848628, 132113866600911440891616246724007445564482, 366123712732689614419441365635789803430718, 1014629095900250131950919346672683894595407, 2811815150030957899349353937599529289400754, 7792309987846928621778455179386373360866974, 21594625431202501574348486647015522784697902, 59844622228996766377008765029927115716319614
Generating function in Maple syntax:
-(x^4+3*x^3+x^2-1)/(4*x^10+16*x^9+17*x^8+6*x^7-7*x^6-9*x^5-5*x^4-5*x^3-2*x^2-x+1)
Generating function in latex syntax:
-\frac{x^{4}+3 x^{3}+x^{2}-1}{4 x^{10}+16 x^{9}+17 x^{8}+6 x^{7}-7 x^{6}-9 x^{5}-5 x^{4}-5 x^{3}-2 x^{2}-x +1}
Generating function in sympy syntax:
(-x**4 - 3*x**3 - x**2 + 1)/(4*x**10 + 16*x**9 + 17*x**8 + 6*x**7 - 7*x**6 - 9*x**5 - 5*x**4 - 5*x**3 - 2*x**2 - x + 1)
Implicit equation for the generating function in Maple syntax:
(4*x^10+16*x^9+17*x^8+6*x^7-7*x^6-9*x^5-5*x^4-5*x^3-2*x^2-x+1)*F(x)+x^4+3*x^3+x^2-1 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{10}+16 x^{9}+17 x^{8}+6 x^{7}-7 x^{6}-9 x^{5}-5 x^{4}-5 x^{3}-2 x^{2}-x +1\right) F \! \left(x \right)+x^{4}+3 x^{3}+x^{2}-1 = 0
Explicit closed form in Maple syntax:
-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+8)-32207991978230324/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+8)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+7)-22167685197394040/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+7)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+6)-64948856793633577/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+6)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+5)+10908512902856352/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+5)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+4)+26233201813983284/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+4)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+3)+14175593626436033/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+3)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+2)+12740678177383828/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+2)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+1)+38838788152470408/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n+1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n-1)+4551243551595971/155258632311136045*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n-1)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 10)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n)+4182254103515372/31051726462227209*RootOf(4*_Z^10+16*_Z^9+17*_Z^8+6*_Z^7-7*_Z^6-9*_Z^5-5*_Z^4-5*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +8}}{155258632311136045}-\frac{32207991978230324 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n +8}}{155258632311136045}-\frac{22167685197394040 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +7}}{31051726462227209}-\frac{22167685197394040 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +7}}{31051726462227209}-\frac{22167685197394040 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +7}}{31051726462227209}-\frac{22167685197394040 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{31051726462227209}-\frac{22167685197394040 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +7}}{31051726462227209}-\frac{22167685197394040 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +7}}{31051726462227209}-\frac{22167685197394040 \mathit{RootOf}\! 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\left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{155258632311136045}-\frac{64948856793633577 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{155258632311136045}-\frac{64948856793633577 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{155258632311136045}-\frac{64948856793633577 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{155258632311136045}-\frac{64948856793633577 \mathit{RootOf}\! 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\left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +2}}{155258632311136045}+\frac{12740678177383828 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n +2}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{155258632311136045}+\frac{38838788152470408 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n +1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{155258632311136045}+\frac{4551243551595971 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n -1}}{155258632311136045}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =10\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{31051726462227209}+\frac{4182254103515372 \mathit{RootOf}\! \left(4 \textit{\_Z}^{10}+16 \textit{\_Z}^{9}+17 \textit{\_Z}^{8}+6 \textit{\_Z}^{7}-7 \textit{\_Z}^{6}-9 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{31051726462227209}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 149
a(7) = 403
a(8) = 1116
a(9) = 3110
a(n+10) = -4*a(n)-16*a(n+1)-17*a(n+2)-6*a(n+3)+7*a(n+4)+9*a(n+5)+5*a(n+6)+5*a(n+7)+2*a(n+8)+a(n+9), n >= 10
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) = 19
a \! \left(5\right) = 55
a \! \left(6\right) = 149
a \! \left(7\right) = 403
a \! \left(8\right) = 1116
a \! \left(9\right) = 3110
a \! \left(n +10\right) = -4 a \! \left(n \right)-16 a \! \left(n +1\right)-17 a \! \left(n +2\right)-6 a \! \left(n +3\right)+7 a \! \left(n +4\right)+9 a \! \left(n +5\right)+5 a \! \left(n +6\right)+5 a \! \left(n +7\right)+2 a \! \left(n +8\right)+a \! \left(n +9\right), \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15964/
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[16,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[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[18,x]+F[19,x]+F[79,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[34,x]
F[21,x] = F[22,x]+F[7,x]
F[22,x] = F[18,x]+F[23,x]+F[27,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[4,x]
F[26,x] = F[14,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[11,x]+F[29,x]
F[29,x] = F[30,x]+F[32,x]
F[30,x] = F[31,x]
F[31,x] = F[25,x]*F[4,x]
F[32,x] = F[33,x]
F[33,x] = F[30,x]*F[4,x]
F[34,x] = F[35,x]+F[46,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[2,x]*F[4,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[43,x]
F[43,x] = F[38,x]*F[4,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[42,x]
F[46,x] = 2*F[18,x]+F[47,x]+F[72,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[39,x]
F[50,x] = F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[18,x]+F[54,x]+F[63,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[59,x]
F[56,x] = F[12,x]+F[57,x]
F[57,x] = F[18,x]+F[23,x]+F[58,x]
F[58,x] = F[11,x]*F[4,x]
F[59,x] = F[42,x]+F[60,x]
F[60,x] = 2*F[18,x]+F[47,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[51,x]+F[53,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[2,x]+F[65,x]
F[65,x] = F[18,x]+F[40,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[70,x]
F[68,x] = F[4,x]+F[69,x]
F[69,x] = F[15,x]+F[18,x]+F[23,x]
F[70,x] = F[39,x]+F[71,x]
F[71,x] = 2*F[18,x]+F[47,x]+F[52,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[62,x]+F[74,x]
F[74,x] = F[75,x]+F[77,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[49,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[75,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[64,x]+F[81,x]
F[81,x] = F[53,x]+F[82,x]
F[82,x] = 2*F[18,x]+F[52,x]+F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = F[14,x]+F[86,x]
F[86,x] = F[33,x]
F[87,x] = F[44,x]+F[88,x]
F[88,x] = F[78,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_{16}\! \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_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{79}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{27}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{32}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{46}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{72}\! \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_{39}\! \left(x \right)
F_{50}\! \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_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right)+F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{59}\! \left(x \right) = F_{42}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{2}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right)+F_{40}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{70}\! \left(x \right) = F_{39}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{62}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{64}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{53}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{52}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = F_{14}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{33}\! \left(x \right)
F_{87}\! \left(x \right) = F_{44}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{78}\! \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_16(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_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_79(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_34(x))
Eq(F_21(x), F_22(x) + F_7(x))
Eq(F_22(x), F_18(x) + F_23(x) + F_27(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_4(x))
Eq(F_26(x), F_14(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_11(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_32(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_25(x)*F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_30(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_46(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_2(x)*F_4(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_38(x)*F_4(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_42(x))
Eq(F_46(x), 2*F_18(x) + F_47(x) + F_72(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_39(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_18(x) + F_54(x) + F_63(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_59(x))
Eq(F_56(x), F_12(x) + F_57(x))
Eq(F_57(x), F_18(x) + F_23(x) + F_58(x))
Eq(F_58(x), F_11(x)*F_4(x))
Eq(F_59(x), F_42(x) + F_60(x))
Eq(F_60(x), 2*F_18(x) + F_47(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_51(x) + F_53(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_2(x) + F_65(x))
Eq(F_65(x), F_18(x) + F_40(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_70(x))
Eq(F_68(x), F_4(x) + F_69(x))
Eq(F_69(x), F_15(x) + F_18(x) + F_23(x))
Eq(F_70(x), F_39(x) + F_71(x))
Eq(F_71(x), 2*F_18(x) + F_47(x) + F_52(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_62(x) + F_74(x))
Eq(F_74(x), F_75(x) + F_77(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_49(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_75(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_64(x) + F_81(x))
Eq(F_81(x), F_53(x) + F_82(x))
Eq(F_82(x), 2*F_18(x) + F_52(x) + F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_87(x))
Eq(F_85(x), F_14(x) + F_86(x))
Eq(F_86(x), F_33(x))
Eq(F_87(x), F_44(x) + F_88(x))
Eq(F_88(x), F_78(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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, 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