0123_0231_0321_2013_2103
Counting sequence:
1, 1, 2, 6, 19, 51, 126, 329, 882, 2350, 6193, 16305, 43081, 113941, 301110, 795314, 2100901, 5550865, 14666266, 38748237, 102370875, 270462675, 714566062, 1887888735, 4987797890, 13177749271, 34815618299, 91982905166, 243018879398, 642055887954, 1696311754190, 4481656201442, 11840537150019, 31282702400877, 82648907877687, 218358437183801, 576903052381432, 1524178025187569, 4026878762755957, 10639014801187283, 28108280047385541, 74262083666722834, 196200445588634708, 518361631487754068, 1369511573720843595, 3618249956522878928, 9559417385798755366, 25255983376875532086, 66726315065974964182, 176290942857037120045, 465760719780844189842, 1230539950464890368781, 3251086889426993270475, 8589372460935526953406, 22693124417135926355569, 59955240985735017520113, 158401763264607679281414, 418497502350232641010501, 1105670516942510341973133, 2921181811529266401923129, 7717763153897226752999719, 20390332386901756733033093, 53871263805029564664071268, 142327893870692142126523916, 376030334966371121144175254, 993472248970289844131564221, 2624753956518835078730841041, 6934600678984146314142588981, 18321216911602092605913981935, 48404660147085293399141282402, 127885125494643981082751341130, 337872536922783026246040632106, 892659335986799183022092574256, 2358406212537191867797526939123, 6230909865727629964226774415721, 16462065588376521746736377596518, 43492781836985180942462934931113, 114907941641006339546150995186137, 303586813592702995833469584858177, 802076445467198042686127711468091, 2119086190734201560640022530608710, 5598626301941483428310962632908713, 14791572237998953194160867322044097, 39079337943321824110646082925259376, 103247621653433924690114284740057478, 272780244960938809656681375882693351, 720685482622688608782144683703758352, 1904051244390780984820958497327858205, 5030503914235425229342922518108958109, 13290592732568401165620309107217849175, 35113749674886613765851596580243434620, 92770536351566302208069018151591786669, 245099782696023780767318209899500659153, 647553693663902306090206778284185605371, 1710837037737470392192465268083360234149, 4520031926825044098746152631997408014009, 11941925600661931574613435576207782519095, 31550570739423185001736448331086304122017, 83356616618694231882859543585298661261985, 220228204158407637443921753977827054433143, 581842976289421126711631447871187493995626
Generating function in Maple syntax:
-(x^3+x^2-1)/(x^9+5*x^8+7*x^7+x^6-8*x^5-6*x^4-3*x^3-2*x^2-x+1)
Generating function in latex syntax:
-\frac{x^{3}+x^{2}-1}{x^{9}+5 x^{8}+7 x^{7}+x^{6}-8 x^{5}-6 x^{4}-3 x^{3}-2 x^{2}-x +1}
Generating function in sympy syntax:
(-x**3 - x**2 + 1)/(x**9 + 5*x**8 + 7*x**7 + x**6 - 8*x**5 - 6*x**4 - 3*x**3 - 2*x**2 - x + 1)
Implicit equation for the generating function in Maple syntax:
(x^9+5*x^8+7*x^7+x^6-8*x^5-6*x^4-3*x^3-2*x^2-x+1)*F(x)+x^3+x^2-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{9}+5 x^{8}+7 x^{7}+x^{6}-8 x^{5}-6 x^{4}-3 x^{3}-2 x^{2}-x +1\right) F \! \left(x \right)+x^{3}+x^{2}-1 = 0
Explicit closed form in Maple syntax:
-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+7)-70147941540/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+7)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+6)-616666782609/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+6)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+5)-1721658224701/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+5)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+4)-1804960996571/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+4)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+3)-676125178963/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+3)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+2)+955319857718/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+2)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n+1)+1947700070921/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n+1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n-1)+892324086899/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n-1)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 1)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 2)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 3)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 4)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 5)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 6)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 7)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 8)^(-n)+3634472439993/18177039023807*RootOf(_Z^9+5*_Z^8+7*_Z^7+_Z^6-8*_Z^5-6*_Z^4-3*_Z^3-2*_Z^2-_Z+1,index = 9)^(-n)
Explicit closed form in latex syntax:
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\left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{18177039023807}+\frac{1947700070921 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{18177039023807}+\frac{1947700070921 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{18177039023807}+\frac{1947700070921 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{18177039023807}+\frac{1947700070921 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{18177039023807}+\frac{1947700070921 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{18177039023807}+\frac{1947700070921 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n +1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{18177039023807}+\frac{892324086899 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n -1}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{18177039023807}+\frac{3634472439993 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+5 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+\textit{\_Z}^{6}-8 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}-3 \textit{\_Z}^{3}-2 \textit{\_Z}^{2}-\textit{\_Z} +1, \mathit{index} =9\right)^{-n}}{18177039023807}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 126
a(7) = 329
a(8) = 882
a(n+9) = -a(n)-5*a(n+1)-7*a(n+2)-a(n+3)+8*a(n+4)+6*a(n+5)+3*a(n+6)+2*a(n+7)+a(n+8), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 51
a \! \left(6\right) = 126
a \! \left(7\right) = 329
a \! \left(8\right) = 882
a \! \left(n +9\right) = -a \! \left(n \right)-5 a \! \left(n +1\right)-7 a \! \left(n +2\right)-a \! \left(n +3\right)+8 a \! \left(n +4\right)+6 a \! \left(n +5\right)+3 a \! \left(n +6\right)+2 a \! \left(n +7\right)+a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17141/
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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[70,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[29,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[15,x]
F[29,x] = F[30,x]+F[45,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[39,x]
F[33,x] = F[2,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[2,x]*F[4,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = F[41,x]
F[41,x] = F[36,x]*F[4,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[34,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[22,x]+F[49,x]+F[59,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[55,x]
F[51,x] = F[15,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[15,x]
F[55,x] = F[40,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[48,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[2,x]+F[61,x]
F[61,x] = F[22,x]+F[38,x]+F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[4,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[15,x]*F[4,x]
F[67,x] = F[37,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[48,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[83,x]
F[72,x] = F[2,x]+F[73,x]
F[73,x] = F[22,x]+F[74,x]+F[82,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = F[11,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[54,x]
F[79,x] = F[34,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[4,x]*F[58,x]
F[82,x] = F[4,x]*F[60,x]
F[83,x] = F[48,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[34,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_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{70}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{45}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{39}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \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_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{22}\! \left(x \right)+F_{49}\! \left(x \right)+F_{59}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)
F_{55}\! \left(x \right) = F_{40}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{48}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{37}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{83}\! \left(x \right)
F_{72}\! \left(x \right) = F_{2}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right)+F_{74}\! \left(x \right)+F_{82}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{11}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{79}\! \left(x \right) = F_{34}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{83}\! \left(x \right) = F_{48}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{34}\! \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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_70(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_29(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_15(x))
Eq(F_29(x), F_30(x) + F_45(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_39(x))
Eq(F_33(x), F_2(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_2(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_36(x)*F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_34(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_22(x) + F_49(x) + F_59(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_55(x))
Eq(F_51(x), F_15(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_15(x))
Eq(F_55(x), F_40(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_48(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_2(x) + F_61(x))
Eq(F_61(x), F_22(x) + F_38(x) + F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_4(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_15(x)*F_4(x))
Eq(F_67(x), F_37(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_48(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_83(x))
Eq(F_72(x), F_2(x) + F_73(x))
Eq(F_73(x), F_22(x) + F_74(x) + F_82(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_11(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_54(x))
Eq(F_79(x), F_34(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_58(x))
Eq(F_82(x), F_4(x)*F_60(x))
Eq(F_83(x), F_48(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_34(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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[[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 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2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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[0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], 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