02341_02413_02431_03241_03412_03421_04123_04132_04213_04231_04312_04321_20341_20413_20431_24013_24031_24103_40123_40132_40213_40231_40312_40321_41023_41032_41203_42013_42031_42103
Counting sequence:
1, 1, 2, 6, 24, 90, 310, 1088, 3888, 13836, 49032, 173932, 617576, 2192304, 7780680, 27615816, 98021080, 347916944, 1234885920, 4383079872, 15557257152, 55218725104, 195992508032, 695652957216, 2469140810688, 8763933294432, 31106579331040, 110409248185664, 391885010481792, 1390951062969408, 4937021842788864, 17523394845956416, 62197287517104896, 220762164412896000, 783570074804513664, 2781192437471781504, 9871524734170965376, 35037848968604776448, 124362840939066302976, 441411692262141904896, 1566740359054478831616, 5560965864111264559360, 19738012851387178921472, 70057821040737102100992, 248662229877474233591808, 882598168899404679578112, 3132681340983742735404544, 11119094430464731201642496, 39465955038621247193610240, 140079897409898409589386240, 497197588127925989552265216, 1764746021457027469067607040, 6263764335572580041875232768, 22232515713052928155716870144, 78911773887157590458993092608, 280088323714167618068681877504, 994141497733832127701743802368, 3528591639989436689644083679232, 12524332793858402414601314500608, 44453688024887627425820251619328, 157783285667966208694232306171904, 560033741682829997978143265910784, 1987775767854647686693596062203904, 7055382933530262237346428515278848, 25042275463733312518179369078374400, 88884695034931748228459763244720128, 315486067665634266993628897234739200, 1119781744787550088032623849173041152, 3974537339279270644558773336962236416, 14107166092730159951439338450044796928, 50071773939847732123538777508153065472, 177724039612409456140844925883924627456, 630811169064990745692300684197023318016, 2238992158207480123842104818549520990208, 7947046803158466597633749328378897334272, 28207134473464638187203175394856886370304, 100118000423490377736947967128929609547776, 355357401448472430837315551239479604281344, 1261300487725106135756077559404275207241728, 4476841945182535889289016909817216292618240, 15890038890172716614229203940532975685861376, 56399877195330910391229167696060877732118528, 200184918969309861610837857690822167703977984, 710533493609569416182550384391896575699189760, 2521957438853919086651552782360289466021052416, 8951399730757124943717492766418999567437135872, 31771970416840966915097599186541626286758297600, 112770978230377367407063338692435052502571810816, 400267700246105951904278859148700786096647176192, 1420704461151417637675419404598632418232750571520, 5042628132858382404889574582244243594098608963584, 17898232307714776645553691183688698806192451616768, 63527730243185406733392170828891365466812617064448, 225484418822263908635889865502387135870637400129536, 800331177219542703397500162711077797951216676241408, 2840684055134253645401006547123168036229495065673728, 10082683432536588320824944882394200064699054033469440, 35787332638068832720934715302730126680456630912417792, 127023047576292052546107714218203409766688188285321216, 450853791724211284356683510737011492706802301640114176, 1600254012091875093937015439968528627513797754012827648
Generating function in Maple syntax:
(x+1)*(6*x^4+8*x^3+2*x-1)/(6*x^5+14*x^4+8*x^3+2*x^2+2*x-1)
Generating function in latex syntax:
\frac{\left(x +1\right) \left(6 x^{4}+8 x^{3}+2 x -1\right)}{6 x^{5}+14 x^{4}+8 x^{3}+2 x^{2}+2 x -1}
Generating function in sympy syntax:
(x + 1)*(6*x**4 + 8*x**3 + 2*x - 1)/(6*x**5 + 14*x**4 + 8*x**3 + 2*x**2 + 2*x - 1)
Implicit equation for the generating function in Maple syntax:
(6*x^5+14*x^4+8*x^3+2*x^2+2*x-1)*F(x)-(x+1)*(6*x^4+8*x^3+2*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(6 x^{5}+14 x^{4}+8 x^{3}+2 x^{2}+2 x -1\right) F \! \left(x \right)-\left(x +1\right) \left(6 x^{4}+8 x^{3}+2 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,-53/149*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^(-n+1)+830/2831*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^(-n+2)-4398/2831*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^(-n+3)-4680/2831*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^(-n+4)+1/2831*(4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^3+10920*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2+6240*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+553)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^(-n+1)+1/2831*(4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2+10920*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+7070)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^(-n+2)+1/2831*(4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^(-n+3)+1/2831*((-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^2+(-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2-17442*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-15218)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)-6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2-15218*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-8143)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^(-n+1)+1/2831*((-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)-6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^(-n+2)+1/2831*(((4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)+(6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+8148*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+10869)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)^(-n+1)+783/2831*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^(-n)+1/2831*(4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^4+10920*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^3+6240*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2+1560*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+2343)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^(-n)+1/2831*((-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^3+(-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2-17442*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-15218)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^2+(-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^3-17442*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2-21458*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)-8696)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)-6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^3-15218*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2-8696*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+169)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^(-n)+1/2831*(((4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)^2+((4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2+(4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^2+23964*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+23366)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^2+23366*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+19012)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)+(6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)^2+(6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^2+23366*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+19012)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+8148*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)^2+19012*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)+11033)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)^(-n)+1/2831*((((-4680*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-6522)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)-6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+(-6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)-8148*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-10869)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 2)+((-6522*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-8148)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)-8148*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-10869)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 1)+(-8148*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-10869)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 3)-10869*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 4)-14328)*RootOf(6*_Z^5+14*_Z^4+8*_Z^3+2*_Z^2+2*_Z-1,index = 5)^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ -\frac{53 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{149}\\+\\\frac{830 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{2831}\\-\\\frac{4398 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{2831}\\-\\\frac{4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{2831}\\+\\\frac{\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+10920 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+6240 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+553\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{2831}\\+\\\frac{\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+10920 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+7070\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{2831}\\+\\\frac{\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{2831}\\+\\\frac{\left(\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-17442 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-15218\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)-6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-15218 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-8143\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{2831}\\+\\\frac{\left(\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)-6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{2831}\\+\\\frac{\left(\left(\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)+\left(6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+8148 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+10869\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{2831}\\+\\\frac{783 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{2831}\\+\\\frac{\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+10920 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+6240 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+1560 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+2343\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{2831}\\+\\\frac{\left(\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-17442 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-15218\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-17442 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-21458 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)-8696\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)-6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-15218 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-8696 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+169\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{2831}\\+\\\frac{\left(\left(\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+23964 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+23366\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+23366 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+19012\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)+\left(6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+23366 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+19012\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+8148 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+19012 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)+11033\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{2831}\\+\\\frac{\left(\left(\left(\left(-4680 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-6522\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)-6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)-8148 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-10869\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\left(-6522 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-8148\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)-8148 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-10869\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-8148 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-10869\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)-10869 \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)-14328\right) \mathit{RootOf}\left(6 \textit{\_Z}^{5}+14 \textit{\_Z}^{4}+8 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{2831} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 90
a(n+5) = 6*a(n)+14*a(n+1)+8*a(n+2)+2*a(n+3)+2*a(4+n), n >= 6
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 90
a{\left(n + 5 \right)} = 6 a{\left(n \right)} + 14 a{\left(n + 1 \right)} + 8 a{\left(n + 2 \right)} + 2 a{\left(n + 3 \right)} + 2 a{\left(n + 4 \right)}, \quad n \geq 6
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/24449/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[41,x]+F[7,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[20,x]*F[9,x]
F[9,x] = F[10,x]+F[36,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]+F[21,x]+F[7,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[20,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[20,x]*F[22,x]
F[22,x] = F[23,x]+F[31,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = F[25,x]+F[27,x]+F[7,x]
F[25,x] = F[20,x]*F[26,x]
F[26,x] = F[14,x]
F[27,x] = F[20,x]*F[28,x]
F[28,x] = F[19,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[25,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]+F[33,x]+F[7,x]
F[33,x] = F[20,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[2,x]+F[30,x]
F[36,x] = F[37,x]
F[37,x] = F[27,x]+F[38,x]+F[7,x]
F[38,x] = F[20,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[16,x]+F[2,x]
F[41,x] = F[20,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[2,x]+F[37,x]
F[44,x] = F[45,x]
F[45,x] = F[33,x]+F[46,x]+F[7,x]
F[46,x] = F[20,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[2,x]+F[32,x]
F[49,x] = F[50,x]
F[50,x] = F[17,x]+F[38,x]+F[7,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_{20}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{41}\! \left(x \right)+F_{7}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{36}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{25}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right)+F_{33}\! \left(x \right)+F_{7}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{27}\! \left(x \right)+F_{38}\! \left(x \right)+F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{33}\! \left(x \right)+F_{46}\! \left(x \right)+F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right)+F_{38}\! \left(x \right)+F_{7}\! \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_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_41(x) + F_7(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_20(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_36(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x) + F_21(x) + F_7(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_20(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_20(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_31(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_27(x) + F_7(x))
Eq(F_25(x), F_20(x)*F_26(x))
Eq(F_26(x), F_14(x))
Eq(F_27(x), F_20(x)*F_28(x))
Eq(F_28(x), F_19(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_25(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x) + F_33(x) + F_7(x))
Eq(F_33(x), F_20(x)*F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_2(x) + F_30(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_27(x) + F_38(x) + F_7(x))
Eq(F_38(x), F_20(x)*F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_16(x) + F_2(x))
Eq(F_41(x), F_20(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_2(x) + F_37(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_33(x) + F_46(x) + F_7(x))
Eq(F_46(x), F_20(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_2(x) + F_32(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_17(x) + F_38(x) + F_7(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:
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