0132_0321_2103
Counting sequence:
1, 1, 2, 6, 21, 73, 241, 766, 2399, 7514, 23648, 74706, 236352, 747770, 2364773, 7475960, 23631523, 74699975, 236139689, 746503680, 2359936092, 7460507061, 23584937695, 74558966315, 235702724400, 745125438325, 2355561039070, 7446624613760, 23540983585802, 74420013414420, 235263670168398, 743738016212083, 2351175734727394, 7432761571257625, 23497156752904593, 74281459400073597, 234825654577544258, 742353320561718006, 2346798323046521873, 7418923328500054505, 23453410039737452793, 74143163117890199970, 234388458992189496715, 740971215681955720898, 2342429080483282000468, 7405110861205347643682, 23409744748929540231852, 74005124228466853917514, 233952077257011605178793, 739591684001660835471348, 2338067972970744256328195, 7391324110967597044790087, 23366160755351839368336453, 73867342339214984844562008, 233516507970138017435861540, 738214720710449268055599185, 2333714984909308302712100847, 7377563028747086991939453659, 23322657905995847779237676684, 73729816970806498643590393193, 233081749621303060239491105870, 736840321033737967072658919948, 2329370101190793524185979174170, 7363827566750607340392874720040, 23279236049743836706672893365318, 73592547645547888556126393351199, 232647800700566033250523439459142, 735468480198547410080006450557041, 2325033306726828128510519239034033, 7350117677279306401152292572059865, 23235895035804379120510145331780978, 73455533886740244569279975036371414, 232214659700938684192905927900015213, 734099193440846154308052006293767577, 2320704586456918046393213735820623361, 7336433312722544562270733498193638534, 23192634713666203783814267988469348455, 73318775218572933716831022431908248346, 231782325118242821100613908916207442664, 732732456005482012669187763527226587154, 2316383925348621225231507990573451272312, 7322774425558328600967544627480078480234, 23149454933098241943224783477565259132829, 73182271166121135062585921869852282208656, 231350795451100676930204725699139554126147, 731368263146155981502366908960853909819607, 2312071308397483264879959829313105242122113, 7309140968353142083589587556638642168461472, 23106355544149124454399648434840419629165532, 73046021255344237755207861021926381904975757, 230920069200929731113250968391655178190081039, 730006610125405658540732094257674487002340523, 2307766720626984884108594524196900669146141384, 7295532893761779763094308936773427283935478669, 23063336397146659948892182761541824951880920654, 72910025013084194383316086967834402244185671608, 230490144871937506886679680900518596368746919818, 728647492214588794584107446720273370843769922780, 2303470147088489912938938425758452079756469568750, 7281950154527183150802960840099900621385950369019, 23020397342697315022747946316395198950149725332394
Generating function in Maple syntax:
-(x^3-2*x^2+3*x-1)*(x-1)^4/(x^8-4*x^7+18*x^6-35*x^5+51*x^4-47*x^3+26*x^2-8*x+1)
Generating function in latex syntax:
-\frac{\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{4}}{x^{8}-4 x^{7}+18 x^{6}-35 x^{5}+51 x^{4}-47 x^{3}+26 x^{2}-8 x +1}
Generating function in sympy syntax:
(x - 1)**4*(-x**3 + 2*x**2 - 3*x + 1)/(x**8 - 4*x**7 + 18*x**6 - 35*x**5 + 51*x**4 - 47*x**3 + 26*x**2 - 8*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^8-4*x^7+18*x^6-35*x^5+51*x^4-47*x^3+26*x^2-8*x+1)*F(x)+(x^3-2*x^2+3*x-1)*(x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{8}-4 x^{7}+18 x^{6}-35 x^{5}+51 x^{4}-47 x^{3}+26 x^{2}-8 x +1\right) F \! \left(x \right)+\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{4} = 0
Explicit closed form in Maple syntax:
-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n+6)-9949964691/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n+6)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n+5)+34366338489/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n+5)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n+4)-159892967682/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n+4)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n+3)+259435485695/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n+3)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n+2)-359740963329/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n+2)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n+1)+261480651042/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n+1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n-1)+20425731213/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n-1)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 1)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 2)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 3)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 4)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 5)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 6)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 7)^(-n)-100130251439/75243945211*RootOf(_Z^8-4*_Z^7+18*_Z^6-35*_Z^5+51*_Z^4-47*_Z^3+26*_Z^2-8*_Z+1,index = 8)^(-n)
Explicit closed form in latex syntax:
-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{75243945211}-\frac{9949964691 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +6}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{75243945211}+\frac{34366338489 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{75243945211}-\frac{159892967682 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{75243945211}+\frac{259435485695 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{75243945211}-\frac{359740963329 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{75243945211}+\frac{261480651042 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{75243945211}+\frac{20425731213 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{75243945211}-\frac{100130251439 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-4 \textit{\_Z}^{7}+18 \textit{\_Z}^{6}-35 \textit{\_Z}^{5}+51 \textit{\_Z}^{4}-47 \textit{\_Z}^{3}+26 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{75243945211}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 241
a(7) = 766
a(n+8) = -a(n)+4*a(n+1)-18*a(n+2)+35*a(n+3)-51*a(n+4)+47*a(n+5)-26*a(n+6)+8*a(n+7), n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 241
a \! \left(7\right) = 766
a \! \left(n +8\right) = -a \! \left(n \right)+4 a \! \left(n +1\right)-18 a \! \left(n +2\right)+35 a \! \left(n +3\right)-51 a \! \left(n +4\right)+47 a \! \left(n +5\right)-26 a \! \left(n +6\right)+8 a \! \left(n +7\right), \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14701/
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[20,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[11,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[19,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[16,x]
F[19,x] = F[13,x]*F[4,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[15,x]+F[22,x]+F[87,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[42,x]
F[24,x] = F[25,x]+F[7,x]
F[25,x] = F[15,x]+F[26,x]+F[34,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[17,x]+F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[11,x]+F[29,x]
F[32,x] = F[33,x]
F[33,x] = F[28,x]*F[4,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[13,x]+F[36,x]
F[36,x] = F[18,x]+F[37,x]
F[37,x] = 2*F[15,x]+F[38,x]+F[41,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[18,x]+F[40,x]
F[40,x] = F[38,x]
F[41,x] = F[36,x]*F[4,x]
F[42,x] = F[43,x]+F[55,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[2,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[46,x]
F[49,x] = F[47,x]+F[50,x]
F[50,x] = 2*F[15,x]+F[51,x]+F[54,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[47,x]+F[53,x]
F[53,x] = F[51,x]
F[54,x] = F[4,x]*F[49,x]
F[55,x] = 2*F[15,x]+F[56,x]+F[79,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[47,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[58,x]
F[61,x] = F[62,x]+F[77,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[62,x]+F[65,x]
F[65,x] = F[15,x]+F[66,x]+F[75,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[70,x]
F[68,x] = F[11,x]+F[69,x]
F[69,x] = F[15,x]+F[19,x]+F[26,x]
F[70,x] = F[47,x]+F[71,x]
F[71,x] = 2*F[15,x]+F[56,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[65,x]+F[74,x]
F[74,x] = 2*F[15,x]+F[60,x]+F[72,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[2,x]+F[65,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[61,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[73,x]+F[81,x]
F[81,x] = F[59,x]+F[82,x]
F[82,x] = 3*F[15,x]+F[83,x]+F[86,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[53,x]+F[85,x]
F[85,x] = F[83,x]
F[86,x] = F[4,x]*F[81,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[76,x]+F[89,x]
F[89,x] = F[65,x]+F[90,x]
F[90,x] = F[116,x]+F[15,x]+F[60,x]+F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[103,x]+F[93,x]
F[93,x] = F[14,x]+F[94,x]
F[94,x] = F[15,x]+F[33,x]+F[41,x]+F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[39,x]+F[97,x]
F[97,x] = F[101,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[29,x]+F[98,x]
F[101,x] = F[102,x]
F[102,x] = F[4,x]*F[97,x]
F[103,x] = F[104,x]+F[50,x]
F[104,x] = 2*F[15,x]+F[105,x]+F[113,x]+F[86,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[84,x]
F[107,x] = F[108,x]+F[111,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[108,x]+F[62,x]
F[111,x] = F[112,x]
F[112,x] = F[107,x]*F[4,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[62,x]
F[115,x] = F[113,x]
F[116,x] = F[4,x]*F[89,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_{20}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)+F_{87}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{42}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)+F_{34}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{17}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{55}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{56}\! \left(x \right)+F_{79}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{47}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{77}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{75}\! \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_{11}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{70}\! \left(x \right) = F_{47}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{56}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{65}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)+F_{65}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{73}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{59}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{53}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{76}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{65}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{116}\! \left(x \right)+F_{15}\! \left(x \right)+F_{60}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{103}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{41}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{39}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{29}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{50}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{105}\! \left(x \right)+F_{113}\! \left(x \right)+F_{86}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{84}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{111}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{108}\! \left(x \right)+F_{62}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{62}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)
F_{116}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \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_20(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_11(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_16(x))
Eq(F_19(x), F_13(x)*F_4(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_15(x) + F_22(x) + F_87(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_42(x))
Eq(F_24(x), F_25(x) + F_7(x))
Eq(F_25(x), F_15(x) + F_26(x) + F_34(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_17(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_11(x) + F_29(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_28(x)*F_4(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_13(x) + F_36(x))
Eq(F_36(x), F_18(x) + F_37(x))
Eq(F_37(x), 2*F_15(x) + F_38(x) + F_41(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_18(x) + F_40(x))
Eq(F_40(x), F_38(x))
Eq(F_41(x), F_36(x)*F_4(x))
Eq(F_42(x), F_43(x) + F_55(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_2(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_46(x))
Eq(F_49(x), F_47(x) + F_50(x))
Eq(F_50(x), 2*F_15(x) + F_51(x) + F_54(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_47(x) + F_53(x))
Eq(F_53(x), F_51(x))
Eq(F_54(x), F_4(x)*F_49(x))
Eq(F_55(x), 2*F_15(x) + F_56(x) + F_79(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_47(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_58(x))
Eq(F_61(x), F_62(x) + F_77(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_62(x) + F_65(x))
Eq(F_65(x), F_15(x) + F_66(x) + F_75(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_11(x) + F_69(x))
Eq(F_69(x), F_15(x) + F_19(x) + F_26(x))
Eq(F_70(x), F_47(x) + F_71(x))
Eq(F_71(x), 2*F_15(x) + F_56(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_65(x) + F_74(x))
Eq(F_74(x), 2*F_15(x) + F_60(x) + F_72(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_2(x) + F_65(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_61(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_73(x) + F_81(x))
Eq(F_81(x), F_59(x) + F_82(x))
Eq(F_82(x), 3*F_15(x) + F_83(x) + F_86(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_53(x) + F_85(x))
Eq(F_85(x), F_83(x))
Eq(F_86(x), F_4(x)*F_81(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_76(x) + F_89(x))
Eq(F_89(x), F_65(x) + F_90(x))
Eq(F_90(x), F_116(x) + F_15(x) + F_60(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_103(x) + F_93(x))
Eq(F_93(x), F_14(x) + F_94(x))
Eq(F_94(x), F_15(x) + F_33(x) + F_41(x) + F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_39(x) + F_97(x))
Eq(F_97(x), F_101(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_29(x) + F_98(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_4(x)*F_97(x))
Eq(F_103(x), F_104(x) + F_50(x))
Eq(F_104(x), F_105(x) + F_113(x) + 2*F_15(x) + F_86(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_84(x))
Eq(F_107(x), F_108(x) + F_111(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_108(x) + F_62(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_107(x)*F_4(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_62(x))
Eq(F_115(x), F_113(x))
Eq(F_116(x), F_4(x)*F_89(x))
Pack JSON:
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Specification JSON:
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