02341_02413_02431_03241_03421_04213_04231_04321_20341_20413_20431_24013_24031_24103_40213_40231_40321_42013_42031_42103

Counting sequence:
1, 1, 2, 6, 24, 100, 400, 1558, 6040, 23492, 91600, 357346, 1393664, 5434052, 21186864, 82607654, 322094760, 1255883604, 4896820752, 19093172882, 74446067440, 290272233588, 1131799021808, 4412992183926, 17206676587832, 67090468635748, 261592117061456, 1019972541269058, 3976969942477536, 15506584042616740, 60461645958239152, 235745707845452230, 919194935625861832, 3584028474613442036, 13974467883991583632, 54487779331291203826, 212453033711224887248, 828374583933904729172, 3229911285898657955184, 12593731286676216325142, 49104156022322336126808, 191461774415950874270724, 746527667553031192987344, 2910782374822350278988962, 11349417311414682098433472, 44252457491433278631430788, 172544540419847836854811184, 672767573065516902117663078, 2623184751410431118616947432, 10228046825559612247006419604, 39880127318364397865506563344, 155496409241550049289954810706, 606295288226960195516903406768, 2364002990932013748472269522484, 9217472491792658168436533247472, 35939801879632125706503658796470, 140132705608541375314335258756472, 546390746586139125751624638141860, 2130429485811352998696545137324624, 8306747181156535175993494078861570, 32388797278297758458469748059354272, 126287000947176163739911828933784420, 492405027306103957011750425741900976, 1919934031989113942644502196076002566, 7486005387387079069624235578354706184, 29188646967171485116416774280536408372, 113809310531573617487742925409336081040, 443753325676243786844245020214358673842, 1730236420280365905612391231363080078736, 6746356358011364603904458551909581053460, 26304685056800172228380095780044656568944, 102564468761832440913979592508909126824790, 399908618167525070451414276407085495930776, 1559281735822467796186514570519496213680452, 6079787784545846854391698024578093239372240, 23705670794390306839221503952763516485974370, 92430664971637203051183768352938310236262272, 360395953407095797066681986777933845339296324, 1405218098042088956533845302694708139206720304, 5479079008510719582734504144765394258997834918, 21363450145803377369490317190843644890725744424, 83298123904272847949438335853808675857464015316, 324787307228771819397962412609056951594685508624, 1266376600007741358905754690343698362513581044754, 4937722803057556440168009986749758133729051357808, 19252650814683033959498191193231723588220435160052, 75067916563196074816374166972554750318532791870192, 292696946066319781271222018678043571082837816818934, 1141253229859222033699784626936250606142542266332600, 4449854882903331967088875273049197687284080393006820, 17350407394983829592312513961432565682903157142121808, 67650888555605339731281772763539923193513530897616322, 263777248463115924147405994315510748074241550270320224, 1028492578476374525818010109002132973825602127692105508, 4010190378981429016812312267182243204118983032346056112, 15636113679593875537944464368221201023392776125892356166, 60966694320203728497732734321123941378154313720718783304, 237714939434343088019264591226625483881136769793221436532, 926873156899161398717480624279897873050309561218634848656, 3613966589666104472381334702791122975069959234759882717810, 14091199441914348566573699442144793811070242974275411903312

Generating function in Maple syntax:
(x^5-x^4+10*x^3-8*x^2+5*x-1)/(2*x^5-5*x^4+16*x^3-12*x^2+6*x-1)

Generating function in latex syntax:
\frac{x^{5}-x^{4}+10 x^{3}-8 x^{2}+5 x -1}{2 x^{5}-5 x^{4}+16 x^{3}-12 x^{2}+6 x -1}

Generating function in sympy syntax:
(x**5 - x**4 + 10*x**3 - 8*x**2 + 5*x - 1)/(2*x**5 - 5*x**4 + 16*x**3 - 12*x**2 + 6*x - 1)

Implicit equation for the generating function in Maple syntax:
(2*x^5-5*x^4+16*x^3-12*x^2+6*x-1)*F(x)-x^5+x^4-10*x^3+8*x^2-5*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(2 x^{5}-5 x^{4}+16 x^{3}-12 x^{2}+6 x -1\right) F \! \left(x \right)-x^{5}+x^{4}-10 x^{3}+8 x^{2}-5 x +1 = 0

Explicit closed form in Maple syntax:
piecewise(n = 0,1,731/69900*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+1)+20599/69900*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+2)-5891/69900*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+3)+1541/34950*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+4)+1/69900*(-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^3+7705*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2-24656*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+19223)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n+1)+1/69900*(-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2+7705*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-4057)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n+2)+1/69900*(-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n+3)+1/69900*((3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^2+(3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2-9519*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+4535)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)-1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2+4535*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+4711)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n+1)+1/69900*((3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)-1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n+2)+1/69900*(((-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)+(1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-478*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+5906)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n+1)+6433/69900*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n)+1/69900*(-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^4+7705*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^3-24656*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2+18492*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-2813)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n)+1/69900*((3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^3+(3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2-9519*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+4535)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^2+(3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^3-9519*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2+29191*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-14512)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)-1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^3+4535*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2-14512*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+8071)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n)+1/69900*(((-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)^2+((-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2+(-3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^2+11333*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-5013)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^2-5013*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+1195)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)+(1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)^2+(1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^2-5013*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+1195)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)-478*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)^2+1195*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+4247)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n)+1/69900*((((3082*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)-1814)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)+478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+(-1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)+478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+478*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)-5906)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 2)+((-1814*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)+478)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)+478*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)-5906)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 1)+(478*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)-5906)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 3)-5906*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 4)+19012)*RootOf(2*_Z^5-5*_Z^4+16*_Z^3-12*_Z^2+6*_Z-1,index = 5)^(-n))

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{731 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{69900}\\+\\\frac{20599 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{69900}\\-\\\frac{5891 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{69900}\\+\\\frac{1541 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{34950}\\+\\\frac{\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+7705 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-24656 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+19223\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{69900}\\+\\\frac{\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+7705 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-4057\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{69900}\\+\\\frac{\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{69900}\\+\\\frac{\left(\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-9519 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+4535\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)-1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+4535 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+4711\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{69900}\\+\\\frac{\left(\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)-1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{69900}\\+\\\frac{\left(\left(\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)+\left(1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-478 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+5906\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{69900}\\+\\\frac{6433 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{69900}\\+\\\frac{\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+7705 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-24656 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+18492 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-2813\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{69900}\\+\\\frac{\left(\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-9519 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+4535\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-9519 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+29191 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-14512\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)-1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+4535 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}-14512 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+8071\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{69900}\\+\\\frac{\left(\left(\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(-3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+11333 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-5013\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-5013 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+1195\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)+\left(1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{2}-5013 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+1195\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)-478 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{2}+1195 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+4247\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{69900}\\+\\\frac{\left(\left(\left(\left(3082 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)-1814\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)+478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)+478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+478 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)-5906\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\left(-1814 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)+478\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+478 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)-5906\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)+\left(478 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)-5906\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)-5906 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)+19012\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-5 \textit{\_Z}^{4}+16 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{69900} & \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) = 100
a(n+5) = 2*a(n)-5*a(n+1)+16*a(n+2)-12*a(n+3)+6*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) = 100
a{\left(n + 5 \right)} = 2 a{\left(n \right)} - 5 a{\left(n + 1 \right)} + 16 a{\left(n + 2 \right)} - 12 a{\left(n + 3 \right)} + 6 a{\left(n + 4 \right)}, \quad n \geq 6

Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/24957/
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[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[16,x]*F[9,x]
F[9,x] = F[10,x]+F[40,x]
F[10,x] = F[11,x]+F[2,x]
F[11,x] = F[12,x]+F[17,x]+F[7,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]
F[15,x] = F[11,x]
F[16,x] = x
F[17,x] = F[16,x]*F[18,x]
F[18,x] = F[19,x]+F[32,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[21,x]+F[24,x]+F[7,x]
F[21,x] = F[16,x]*F[22,x]
F[22,x] = F[14,x]+F[23,x]
F[23,x] = F[20,x]
F[24,x] = F[16,x]*F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[2,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[16,x]*F[30,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[28,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[37,x]+F[7,x]
F[34,x] = F[16,x]*F[35,x]
F[35,x] = F[14,x]+F[36,x]
F[36,x] = F[33,x]
F[37,x] = F[16,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[2,x]+F[28,x]
F[40,x] = F[6,x]
F[41,x] = F[16,x]*F[42,x]
F[42,x] = F[43,x]+F[57,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[45,x]+F[49,x]+F[7,x]
F[45,x] = F[16,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[2,x]+F[20,x]
F[48,x] = F[44,x]
F[49,x] = F[16,x]*F[50,x]
F[50,x] = F[26,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[16,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[2,x]+F[28,x]
F[56,x] = F[52,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]+F[63,x]+F[7,x]
F[59,x] = F[16,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[2,x]+F[33,x]
F[62,x] = F[58,x]
F[63,x] = F[16,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[2,x]+F[52,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_{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_{16}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \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_{17}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \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_{11}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{32}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
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_{23}\! \left(x \right) = F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{40}\! \left(x \right) = F_{6}\! \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_{57}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{49}\! \left(x \right)+F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{26}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{16}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{63}\! \left(x \right)+F_{7}\! \left(x \right)
F_{59}\! \left(x \right) = F_{16}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right)+F_{33}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \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_{2}\! \left(x \right)+F_{52}\! \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_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_16(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_40(x))
Eq(F_10(x), F_11(x) + F_2(x))
Eq(F_11(x), F_12(x) + F_17(x) + F_7(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), F_11(x))
Eq(F_16(x), x)
Eq(F_17(x), F_16(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_32(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_24(x) + F_7(x))
Eq(F_21(x), F_16(x)*F_22(x))
Eq(F_22(x), F_14(x) + F_23(x))
Eq(F_23(x), F_20(x))
Eq(F_24(x), F_16(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_16(x)*F_30(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_28(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_37(x) + F_7(x))
Eq(F_34(x), F_16(x)*F_35(x))
Eq(F_35(x), F_14(x) + F_36(x))
Eq(F_36(x), F_33(x))
Eq(F_37(x), F_16(x)*F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_2(x) + F_28(x))
Eq(F_40(x), F_6(x))
Eq(F_41(x), F_16(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_57(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_45(x) + F_49(x) + F_7(x))
Eq(F_45(x), F_16(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_2(x) + F_20(x))
Eq(F_48(x), F_44(x))
Eq(F_49(x), F_16(x)*F_50(x))
Eq(F_50(x), F_26(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_16(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_2(x) + F_28(x))
Eq(F_56(x), F_52(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x) + F_63(x) + F_7(x))
Eq(F_59(x), F_16(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_2(x) + F_33(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_16(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_2(x) + F_52(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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 1, 0, 3], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 1, 0, 3], "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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 1, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 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