01324_01342_03124_03142_03214_03241_03412_03421_10324_10342_13024_13042_13204_30124_30142_30214_30241_30412_30421_31024_31042_31204_32014_32041_32104
Counting sequence:
1, 1, 2, 6, 24, 95, 354, 1246, 4266, 14486, 49291, 168461, 577605, 1983135, 6809821, 23376662, 80221521, 275247238, 944350861, 3240034142, 11116749946, 38142986475, 130874534309, 449051298346, 1540763238108, 5286582349300, 18139011898861, 62237496967608, 213545609962416, 732705163457102, 2514015260052854, 8625943098713065, 29596834939384629, 101550939717641935, 348435677416478873, 1195532220843890107, 4102040580480915070, 14074682923446276313, 48292233029135778384, 165697499928275761029, 568531620280023136276, 1950712614292113011764, 6693171615310464085257, 22965220986621927606409, 78796929954165051976350, 270363441037620309144030, 927655307033898402403764, 3182916911292513531826627, 10921039299211131848970774, 37471634572674922004226870, 128570492155423436799487978, 441143591455017636395772530, 1513626221843247248091657283, 5193466217868659628948323225, 17819519090581955056445994449, 61141297025695258142922620563, 209784460679424603548219460197, 719800234595331802493588495030, 2469736681380026165706980765661, 8474016792705263682947694765190, 29075553335072774924141355709921, 99762346761974690779662917137234, 342298759262170235801528503254774, 1174475585182213488993769472831915, 4029792287773416721090922787493365, 13826788813220569909875823084876446, 47441673226049664764129267948609164, 162779108648513180446446473202346848, 558518205843027614701874311909737457, 1916355168965128956171174741507997700, 6575286347337988597278039086375350152, 22560739913800427757526081607838777606, 77409098033306432786086329523675865610, 265601592909842032729422960444448247401, 911316730830434688967259191054589276945, 3126856939345924847855734682895136475915, 10728689585481755336804071641427683218229, 36811655427287398790115131545557964813011, 126306010114327416081163473208786164701238, 433373832440443168386917618602206522558525, 1486967076816979713134122499525618708461576, 5101994910690627124566827591644539066027721, 17505668063904923054297925711008064530836648, 60064429645253921443130889396122653185689864, 206089575984162365229428381735469462247717897, 707122561226016608914169951400873278645306993, 2426237786200634793985914491947150621080320842, 8324765914668959163230645884584557799419078550, 28563452406928794689479073366502029478949517872, 98005255855332972033301511091490667008506791031, 336269931184485685148978512045914421127927678570, 1153789821086065859364303483635164430721588459902, 3958816497664999051006389397255026005392105763994, 13583260812122829797356075469456353799715919044094, 46606094119032046998588796557676906227397646517275, 159912118236991088701190288720716221308505180597797, 548681155166763747457164298180594347495767994510349, 1882602853080678828968435313622430938081070552063815, 6459477365046928473754300807985640539912269792903069, 22163382872428640836047519746583485426269025807366534, 76045709674267822319615560888497486896135443809388793
Generating function in Maple syntax:
(x+1)*(x-1)^2*(2*x-1)^3/(12*x^8-10*x^7+23*x^6-37*x^5+6*x^4+26*x^3-23*x^2+8*x-1)
Generating function in latex syntax:
\frac{\left(x +1\right) \left(x -1\right)^{2} \left(2 x -1\right)^{3}}{12 x^{8}-10 x^{7}+23 x^{6}-37 x^{5}+6 x^{4}+26 x^{3}-23 x^{2}+8 x -1}
Generating function in sympy syntax:
(x - 1)**2*(x + 1)*(2*x - 1)**3/(12*x**8 - 10*x**7 + 23*x**6 - 37*x**5 + 6*x**4 + 26*x**3 - 23*x**2 + 8*x - 1)
Implicit equation for the generating function in Maple syntax:
(12*x^8-10*x^7+23*x^6-37*x^5+6*x^4+26*x^3-23*x^2+8*x-1)*F(x)-(x+1)*(x-1)^2*(2*x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(12 x^{8}-10 x^{7}+23 x^{6}-37 x^{5}+6 x^{4}+26 x^{3}-23 x^{2}+8 x -1\right) F \! \left(x \right)-\left(x +1\right) \left(x -1\right)^{2} \left(2 x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n)-35875210301/27313805423*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n-1)+623266909448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n-1)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n+6)+4434484175064/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n+6)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n+5)-897714697812/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n+5)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n+4)+594908699570/191196637961*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n+4)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n+3)-8886205318448/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n+3)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n+2)-3844213516999/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n+2)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 1)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 2)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 3)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 4)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 5)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 6)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 7)^(-n+1)+7398626152616/2485556293493*RootOf(12*_Z^8-10*_Z^7+23*_Z^6-37*_Z^5+6*_Z^4+26*_Z^3-23*_Z^2+8*_Z-1,index = 8)^(-n+1)
Explicit closed form in latex syntax:
-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{27313805423}-\frac{35875210301 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n}}{27313805423}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{2485556293493}+\frac{623266909448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n -1}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +6}}{2485556293493}+\frac{4434484175064 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +6}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{2485556293493}-\frac{897714697812 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +5}}{2485556293493}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{191196637961}+\frac{594908699570 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +4}}{191196637961}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{2485556293493}-\frac{8886205318448 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{2485556293493}-\frac{3844213516999 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +2}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{2485556293493}+\frac{7398626152616 \mathit{RootOf}\! \left(12 \textit{\_Z}^{8}-10 \textit{\_Z}^{7}+23 \textit{\_Z}^{6}-37 \textit{\_Z}^{5}+6 \textit{\_Z}^{4}+26 \textit{\_Z}^{3}-23 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +1}}{2485556293493}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 95
a(6) = 354
a(7) = 1246
a(n+8) = 12*a(n)-10*a(n+1)+23*a(n+2)-37*a(n+3)+6*a(n+4)+26*a(n+5)-23*a(n+6)+8*a(n+7), n >= 8
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 95
a(6) = 354
a(7) = 1246
a{\left(n + 8 \right)} = 12 a{\left(n \right)} - 10 a{\left(n + 1 \right)} + 23 a{\left(n + 2 \right)} - 37 a{\left(n + 3 \right)} + 6 a{\left(n + 4 \right)} + 26 a{\left(n + 5 \right)} - 23 a{\left(n + 6 \right)} + 8 a{\left(n + 7 \right)}, \quad n \geq 8
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/24516/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[29,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[18,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[16,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = x
F[17,x] = F[10,x]
F[18,x] = F[19,x]+F[6,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[16,x]*F[22,x]
F[22,x] = F[14,x]
F[23,x] = F[16,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[16,x]
F[26,x] = F[27,x]
F[27,x] = F[20,x]+F[23,x]+F[28,x]
F[28,x] = F[14,x]*F[16,x]
F[29,x] = F[141,x]+F[20,x]+F[30,x]
F[30,x] = F[16,x]*F[31,x]
F[31,x] = F[109,x]+F[32,x]
F[32,x] = F[2,x]+F[33,x]
F[33,x] = F[20,x]+F[34,x]+F[92,x]
F[34,x] = F[16,x]*F[35,x]
F[35,x] = F[36,x]+F[84,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[20,x]+F[38,x]+F[44,x]
F[38,x] = F[16,x]*F[39,x]
F[39,x] = F[2,x]+F[40,x]
F[40,x] = F[20,x]+F[38,x]+F[41,x]
F[41,x] = F[16,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[14,x]+F[40,x]
F[44,x] = F[16,x]*F[45,x]
F[45,x] = F[43,x]+F[46,x]
F[46,x] = F[47,x]+F[55,x]
F[47,x] = F[20,x]+F[48,x]+F[50,x]
F[48,x] = F[16,x]*F[49,x]
F[49,x] = F[14,x]
F[50,x] = F[16,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[16,x]
F[53,x] = F[54,x]
F[54,x] = F[20,x]+F[28,x]+F[50,x]
F[55,x] = F[20,x]+F[56,x]+F[58,x]+F[76,x]
F[56,x] = F[16,x]*F[57,x]
F[57,x] = F[37,x]
F[58,x] = F[16,x]*F[59,x]
F[59,x] = F[60,x]+F[66,x]
F[60,x] = F[61,x]
F[61,x] = F[20,x]+F[62,x]+F[63,x]
F[62,x] = F[16,x]*F[2,x]
F[63,x] = F[16,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[16,x]+F[61,x]
F[66,x] = F[67,x]
F[67,x] = F[20,x]+F[68,x]+F[69,x]+F[73,x]
F[68,x] = F[16,x]*F[40,x]
F[69,x] = F[16,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[61,x]
F[72,x] = F[67,x]
F[73,x] = F[16,x]*F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[54,x]+F[67,x]
F[76,x] = F[16,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[47,x]+F[79,x]
F[79,x] = F[20,x]+F[69,x]+F[80,x]+F[82,x]
F[80,x] = F[16,x]*F[81,x]
F[81,x] = F[40,x]
F[82,x] = F[16,x]*F[83,x]
F[83,x] = F[78,x]
F[84,x] = F[85,x]
F[85,x] = F[20,x]+F[86,x]+F[89,x]
F[86,x] = F[16,x]*F[87,x]
F[87,x] = F[39,x]+F[88,x]
F[88,x] = F[85,x]
F[89,x] = F[16,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[10,x]+F[85,x]
F[92,x] = F[16,x]*F[93,x]
F[93,x] = F[91,x]+F[94,x]
F[94,x] = F[95,x]+F[98,x]
F[95,x] = F[20,x]+F[50,x]+F[96,x]
F[96,x] = F[16,x]*F[97,x]
F[97,x] = F[49,x]
F[98,x] = F[101,x]+F[20,x]+F[58,x]+F[99,x]
F[99,x] = F[100,x]*F[16,x]
F[100,x] = F[57,x]
F[101,x] = F[102,x]*F[16,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]+F[95,x]
F[104,x] = F[105,x]+F[107,x]+F[20,x]+F[69,x]
F[105,x] = F[106,x]*F[16,x]
F[106,x] = F[81,x]
F[107,x] = F[108,x]*F[16,x]
F[108,x] = F[103,x]
F[109,x] = F[110,x]+F[132,x]
F[110,x] = F[111,x]+F[129,x]+F[20,x]
F[111,x] = F[112,x]*F[16,x]
F[112,x] = F[113,x]+F[114,x]
F[113,x] = F[2,x]+F[85,x]
F[114,x] = F[110,x]+F[115,x]
F[115,x] = F[116,x]+F[118,x]+F[126,x]+F[20,x]
F[116,x] = F[117,x]*F[16,x]
F[117,x] = F[40,x]
F[118,x] = F[119,x]*F[16,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[61,x]
F[121,x] = F[122,x]
F[122,x] = F[118,x]+F[123,x]+F[20,x]+F[68,x]
F[123,x] = F[124,x]*F[16,x]
F[124,x] = F[125,x]
F[125,x] = F[122,x]+F[27,x]
F[126,x] = F[127,x]*F[16,x]
F[127,x] = F[128,x]
F[128,x] = F[115,x]+F[19,x]
F[129,x] = F[130,x]*F[16,x]
F[130,x] = F[131,x]
F[131,x] = F[110,x]+F[6,x]
F[132,x] = F[133,x]+F[135,x]+F[139,x]+F[20,x]
F[133,x] = F[134,x]*F[16,x]
F[134,x] = F[37,x]
F[135,x] = F[136,x]*F[16,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = F[61,x]
F[138,x] = F[122,x]
F[139,x] = F[140,x]*F[16,x]
F[140,x] = F[128,x]
F[141,x] = F[142,x]*F[16,x]
F[142,x] = F[131,x]+F[143,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[20,x]+F[21,x]+F[50,x]
F[145,x] = F[133,x]+F[146,x]+F[20,x]+F[58,x]
F[146,x] = F[147,x]*F[16,x]
F[147,x] = F[148,x]
F[148,x] = F[144,x]+F[149,x]
F[149,x] = F[116,x]+F[150,x]+F[20,x]+F[69,x]
F[150,x] = F[151,x]*F[16,x]
F[151,x] = F[148,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_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{18}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{10}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right)
F_{29}\! \left(x \right) = F_{141}\! \left(x \right)+F_{20}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{109}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{92}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{84}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{16}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{44}\! \left(x \right) = F_{16}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{16}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right)
F_{50}\! \left(x \right) = F_{16}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)+F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)+F_{76}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{37}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{66}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{20}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right)
F_{63}\! \left(x \right) = F_{16}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{16}\! \left(x \right)+F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{69}\! \left(x \right) = F_{16}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{61}\! \left(x \right)
F_{72}\! \left(x \right) = F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{16}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{54}\! \left(x \right)+F_{67}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{47}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{20}\! \left(x \right)+F_{69}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{16}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{40}\! \left(x \right)
F_{82}\! \left(x \right) = F_{16}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{78}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{20}\! \left(x \right)+F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{39}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{16}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{10}\! \left(x \right)+F_{85}\! \left(x \right)
F_{92}\! \left(x \right) = F_{16}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{98}\! \left(x \right)
F_{95}\! \left(x \right) = F_{20}\! \left(x \right)+F_{50}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{16}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{49}\! \left(x \right)
F_{98}\! \left(x \right) = F_{101}\! \left(x \right)+F_{20}\! \left(x \right)+F_{58}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{16}\! \left(x \right)
F_{100}\! \left(x \right) = F_{57}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{16}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{95}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)+F_{20}\! \left(x \right)+F_{69}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{16}\! \left(x \right)
F_{106}\! \left(x \right) = F_{81}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{16}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{132}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{129}\! \left(x \right)+F_{20}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{16}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{114}\! \left(x \right)
F_{113}\! \left(x \right) = F_{2}\! \left(x \right)+F_{85}\! \left(x \right)
F_{114}\! \left(x \right) = F_{110}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{126}\! \left(x \right)+F_{20}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{16}\! \left(x \right)
F_{117}\! \left(x \right) = F_{40}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{16}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{61}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)+F_{123}\! \left(x \right)+F_{20}\! \left(x \right)+F_{68}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{16}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{122}\! \left(x \right)+F_{27}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{16}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{115}\! \left(x \right)+F_{19}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{16}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{110}\! \left(x \right)+F_{6}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{135}\! \left(x \right)+F_{139}\! \left(x \right)+F_{20}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{16}\! \left(x \right)
F_{134}\! \left(x \right) = F_{37}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{16}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{61}\! \left(x \right)
F_{138}\! \left(x \right) = F_{122}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{16}\! \left(x \right)
F_{140}\! \left(x \right) = F_{128}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{16}\! \left(x \right)
F_{142}\! \left(x \right) = F_{131}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{50}\! \left(x \right)
F_{145}\! \left(x \right) = F_{133}\! \left(x \right)+F_{146}\! \left(x \right)+F_{20}\! \left(x \right)+F_{58}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{16}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{144}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{116}\! \left(x \right)+F_{150}\! \left(x \right)+F_{20}\! \left(x \right)+F_{69}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{16}\! \left(x \right)
F_{151}\! \left(x \right) = F_{148}\! \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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_29(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_18(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_16(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x), F_10(x))
Eq(F_18(x), F_19(x) + F_6(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_14(x))
Eq(F_23(x), F_16(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_16(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_20(x) + F_23(x) + F_28(x))
Eq(F_28(x), F_14(x)*F_16(x))
Eq(F_29(x), F_141(x) + F_20(x) + F_30(x))
Eq(F_30(x), F_16(x)*F_31(x))
Eq(F_31(x), F_109(x) + F_32(x))
Eq(F_32(x), F_2(x) + F_33(x))
Eq(F_33(x), F_20(x) + F_34(x) + F_92(x))
Eq(F_34(x), F_16(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_84(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_20(x) + F_38(x) + F_44(x))
Eq(F_38(x), F_16(x)*F_39(x))
Eq(F_39(x), F_2(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_38(x) + F_41(x))
Eq(F_41(x), F_16(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_14(x) + F_40(x))
Eq(F_44(x), F_16(x)*F_45(x))
Eq(F_45(x), F_43(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_55(x))
Eq(F_47(x), F_20(x) + F_48(x) + F_50(x))
Eq(F_48(x), F_16(x)*F_49(x))
Eq(F_49(x), F_14(x))
Eq(F_50(x), F_16(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_16(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_20(x) + F_28(x) + F_50(x))
Eq(F_55(x), F_20(x) + F_56(x) + F_58(x) + F_76(x))
Eq(F_56(x), F_16(x)*F_57(x))
Eq(F_57(x), F_37(x))
Eq(F_58(x), F_16(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_66(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_20(x) + F_62(x) + F_63(x))
Eq(F_62(x), F_16(x)*F_2(x))
Eq(F_63(x), F_16(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_16(x) + F_61(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_20(x) + F_68(x) + F_69(x) + F_73(x))
Eq(F_68(x), F_16(x)*F_40(x))
Eq(F_69(x), F_16(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_61(x))
Eq(F_72(x), F_67(x))
Eq(F_73(x), F_16(x)*F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_54(x) + F_67(x))
Eq(F_76(x), F_16(x)*F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_47(x) + F_79(x))
Eq(F_79(x), F_20(x) + F_69(x) + F_80(x) + F_82(x))
Eq(F_80(x), F_16(x)*F_81(x))
Eq(F_81(x), F_40(x))
Eq(F_82(x), F_16(x)*F_83(x))
Eq(F_83(x), F_78(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_20(x) + F_86(x) + F_89(x))
Eq(F_86(x), F_16(x)*F_87(x))
Eq(F_87(x), F_39(x) + F_88(x))
Eq(F_88(x), F_85(x))
Eq(F_89(x), F_16(x)*F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_10(x) + F_85(x))
Eq(F_92(x), F_16(x)*F_93(x))
Eq(F_93(x), F_91(x) + F_94(x))
Eq(F_94(x), F_95(x) + F_98(x))
Eq(F_95(x), F_20(x) + F_50(x) + F_96(x))
Eq(F_96(x), F_16(x)*F_97(x))
Eq(F_97(x), F_49(x))
Eq(F_98(x), F_101(x) + F_20(x) + F_58(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_16(x))
Eq(F_100(x), F_57(x))
Eq(F_101(x), F_102(x)*F_16(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) + F_95(x))
Eq(F_104(x), F_105(x) + F_107(x) + F_20(x) + F_69(x))
Eq(F_105(x), F_106(x)*F_16(x))
Eq(F_106(x), F_81(x))
Eq(F_107(x), F_108(x)*F_16(x))
Eq(F_108(x), F_103(x))
Eq(F_109(x), F_110(x) + F_132(x))
Eq(F_110(x), F_111(x) + F_129(x) + F_20(x))
Eq(F_111(x), F_112(x)*F_16(x))
Eq(F_112(x), F_113(x) + F_114(x))
Eq(F_113(x), F_2(x) + F_85(x))
Eq(F_114(x), F_110(x) + F_115(x))
Eq(F_115(x), F_116(x) + F_118(x) + F_126(x) + F_20(x))
Eq(F_116(x), F_117(x)*F_16(x))
Eq(F_117(x), F_40(x))
Eq(F_118(x), F_119(x)*F_16(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_61(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_118(x) + F_123(x) + F_20(x) + F_68(x))
Eq(F_123(x), F_124(x)*F_16(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_122(x) + F_27(x))
Eq(F_126(x), F_127(x)*F_16(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_115(x) + F_19(x))
Eq(F_129(x), F_130(x)*F_16(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_110(x) + F_6(x))
Eq(F_132(x), F_133(x) + F_135(x) + F_139(x) + F_20(x))
Eq(F_133(x), F_134(x)*F_16(x))
Eq(F_134(x), F_37(x))
Eq(F_135(x), F_136(x)*F_16(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_61(x))
Eq(F_138(x), F_122(x))
Eq(F_139(x), F_140(x)*F_16(x))
Eq(F_140(x), F_128(x))
Eq(F_141(x), F_142(x)*F_16(x))
Eq(F_142(x), F_131(x) + F_143(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_20(x) + F_21(x) + F_50(x))
Eq(F_145(x), F_133(x) + F_146(x) + F_20(x) + F_58(x))
Eq(F_146(x), F_147(x)*F_16(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_144(x) + F_149(x))
Eq(F_149(x), F_116(x) + F_150(x) + F_20(x) + F_69(x))
Eq(F_150(x), F_151(x)*F_16(x))
Eq(F_151(x), F_148(x))
Pack JSON:
{"name": "regular_insertion_encoding_left", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}], "inferral_strats": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 1, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 1, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"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, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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