0123_0132_0231_1032_2103
Counting sequence:
1, 1, 2, 6, 19, 54, 148, 412, 1155, 3237, 9059, 25345, 70924, 198487, 555476, 1554499, 4350255, 12174194, 34069530, 95343689, 266819558, 746695212, 2089628532, 5847831049, 16365170795, 45797974013, 128165752151, 358672198648, 1003745103005, 2808983343384, 7860947365561, 21998882132913, 61563930223114, 172286822649430, 482145131914635, 1349284435420350, 3775976085122276, 10567079128111804, 29571999075878779, 82757318152118869, 231596575197968003, 648123632339514673, 1813775710793206836, 5075856156005857295, 14204796967534211388, 39752162135273141771, 111246531579490374047, 311323714829719505034, 871240244880095873706, 2438168145057314060017, 6823220045798453551262, 19094799465642042547196, 53436847146326612901908, 149543159019704405254705, 418496928689586811339547, 1171164769225852742032989, 3277507725016607072262247, 9172114095136333563706416, 25668185716868853333523813, 71832486072653573035396144, 201023403535176045974614641, 562564530037202193559579041, 1574338335190903139856255698, 4405790022857927844328079590, 12329615109804652072661605315, 34504460713566172987966382662, 96560825178337169737498034036, 270225726363996309560838667228, 756227414731449874586077188531, 2116304433653682873389873076293, 5922483592442518268663893925667, 16574086102628619597784825408481, 46382624088293461763454038462492, 129801897009255977905948540979271, 363250954390351260197082072243876, 1016558763051758835426366920394451, 2844842405085147130945429586604239, 7961299045295403936719597976415970, 22279716575978294389546451219894522, 62349846159748617264573706567328473, 174486210490477054691248449828379478, 488300124643800968629158591352937100, 1366509198961397321457511193257842100, 3824179631754730455889038350887049241, 10701976881709137186361371546924938635, 29949510798498633541488024954796560445, 83813785713031460051375507512124495607, 234553102480128211349001431705330102952, 656397481810676752759105650525813786029, 1836930100568167949153511937286371163464, 5140653777441859354542722985909979487017, 14386133283652719177958300027810321505233, 40259632298756048501090668162796796491354, 112666688183185068994962935088660428310454, 315298026866461706758021843165327348074171, 882362367696904315110691026786069620418254, 2469293435373866778006476671486608799521348, 6910324253623384637127848865844313590014716, 19338560823163385009742510791509338549541163, 54119013954387986278231962401690399193617013, 151452204648398440119813636421396799376623427
Generating function in Maple syntax:
(x^3+x^2+x-1)/(3*x^5+3*x^4+2*x^3+x^2+2*x-1)
Generating function in latex syntax:
\frac{x^{3}+x^{2}+x -1}{3 x^{5}+3 x^{4}+2 x^{3}+x^{2}+2 x -1}
Generating function in sympy syntax:
(x**3 + x**2 + x - 1)/(3*x**5 + 3*x**4 + 2*x**3 + x**2 + 2*x - 1)
Implicit equation for the generating function in Maple syntax:
(3*x^5+3*x^4+2*x^3+x^2+2*x-1)*F(x)-x^3-x^2-x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x^{5}+3 x^{4}+2 x^{3}+x^{2}+2 x -1\right) F \! \left(x \right)-x^{3}-x^{2}-x +1 = 0
Explicit closed form in Maple syntax:
-23598/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+3)-23598/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+3)-23598/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+3)-23598/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+3)-23598/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+3)+2346/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+2)+2346/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+2)+2346/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+2)+2346/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+2)+2346/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+2)+39573/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+1)+39573/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+1)+39573/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+1)+39573/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+1)+39573/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+1)+12169/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n-1)+12169/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n-1)+12169/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n-1)+12169/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n-1)+12169/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n-1)+97472/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n)+97472/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n)+97472/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n)+97472/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n)+97472/471343*RootOf(3*_Z^5+3*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{23598 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{471343}-\frac{23598 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{471343}-\frac{23598 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{471343}-\frac{23598 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{471343}-\frac{23598 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{471343}+\frac{2346 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{471343}+\frac{2346 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{471343}+\frac{2346 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{471343}+\frac{2346 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{471343}+\frac{2346 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{471343}+\frac{39573 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{471343}+\frac{39573 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{471343}+\frac{39573 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{471343}+\frac{39573 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{471343}+\frac{39573 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{471343}+\frac{12169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{471343}+\frac{12169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{471343}+\frac{12169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{471343}+\frac{12169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{471343}+\frac{12169 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{471343}+\frac{97472 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{471343}+\frac{97472 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{471343}+\frac{97472 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{471343}+\frac{97472 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{471343}+\frac{97472 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{471343}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+5) = 3*a(n)+3*a(n+1)+2*a(n+2)+a(n+3)+2*a(n+4), n >= 5
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(n +5\right) = 3 a \! \left(n \right)+3 a \! \left(n +1\right)+2 a \! \left(n +2\right)+a \! \left(n +3\right)+2 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16091/
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[16,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[18,x]+F[19,x]+F[38,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[26,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[23,x]
F[23,x] = F[10,x]*F[4,x]
F[24,x] = F[13,x]+F[18,x]+F[25,x]
F[25,x] = F[11,x]*F[4,x]
F[26,x] = F[27,x]+F[32,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[2,x]*F[4,x]
F[32,x] = 2*F[18,x]+F[33,x]+F[35,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[30,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[17,x]+F[37,x]
F[37,x] = F[33,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[50,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[18,x]+F[31,x]+F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[4,x]+F[45,x]
F[45,x] = F[13,x]+F[18,x]+F[46,x]
F[46,x] = F[4,x]*F[7,x]
F[47,x] = F[30,x]+F[48,x]
F[48,x] = 2*F[18,x]+F[33,x]+F[49,x]
F[49,x] = F[17,x]*F[4,x]
F[50,x] = F[17,x]+F[51,x]
F[51,x] = 2*F[18,x]+F[33,x]+F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[55,x]
F[55,x] = F[15,x]*F[4,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[30,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_{16}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{47}\! \left(x \right) = F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \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_{30}\! \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_16(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_38(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_26(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_10(x)*F_4(x))
Eq(F_24(x), F_13(x) + F_18(x) + F_25(x))
Eq(F_25(x), F_11(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_32(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_2(x)*F_4(x))
Eq(F_32(x), 2*F_18(x) + F_33(x) + F_35(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_17(x) + F_37(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_50(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_18(x) + F_31(x) + F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_4(x) + F_45(x))
Eq(F_45(x), F_13(x) + F_18(x) + F_46(x))
Eq(F_46(x), F_4(x)*F_7(x))
Eq(F_47(x), F_30(x) + F_48(x))
Eq(F_48(x), 2*F_18(x) + F_33(x) + F_49(x))
Eq(F_49(x), F_17(x)*F_4(x))
Eq(F_50(x), F_17(x) + F_51(x))
Eq(F_51(x), 2*F_18(x) + F_33(x) + F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_15(x)*F_4(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_30(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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3], "pos": [[0, 0], [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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [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, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 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