0231_1032_2103
Counting sequence:
1, 1, 2, 6, 21, 74, 253, 845, 2791, 9188, 30246, 99639, 328422, 1082797, 3570197, 11771589, 38812310, 127966990, 421913905, 1391070390, 4586427029, 15121681789, 49856965951, 164381014292, 541972783322, 1786912535551, 5891543754590, 19424726640545, 64044335343577, 211157508852081, 696197303307338, 2295398766231358, 7568049275682797, 24952252604488538, 82268876346212669, 271244769860537589, 894308132597230391, 2948580488527487820, 9721623432029926238, 32052698755183837791, 105679417092615124326, 348430541912828648013, 1148793642865050320973, 3787632469421602930133, 12488021510667467322078, 41173657293815251481862, 135751692411837210942793, 447580399797182629947846, 1475695888010436215637941, 4865446196655856767700709, 16041629501637218566628751, 52890087911088117880480604, 174381374345862382911080434, 574944472958169153046167431, 1895621870312379821097140478, 6249964029949108166975905409, 20606456903359452801344827761, 67940561589674951760199225057, 224003569889197496471547122706, 738551435976504593841854565174, 2435042547994952824517694816325, 8028462097167168879711679618218, 26470257654727212378663697987261, 87273818052261412500082658911709, 287746323317672430253648823539719, 948714613737390413871584368119348, 3127961490320134389430350159924694, 10313051937064461077791641322305031, 34002669337755692467912210252339238, 112108571657387601346346313124728365, 369627799341743357564419944153999941, 1218682104556248297533453646396000485, 4018058367391630492911547003465302950, 13247747696799573208705330920611965374, 43678514095848762138814498073106890721, 144010335740478628215414093434382090774, 474809576959863285741268036491741566741, 1565471903204765470256394130783669515917, 5161442394264751589804965211280612586335, 17017544380564232916399582317458759179556, 56107730092321687364549856791964726106954, 184990108191417163553330855910510717955727, 609922020947259805726623757948475777182942, 2010944667654663485570426919735242369853089, 6630189298770051214612465849986927371294921, 21860079416702273520527090689592321910784593, 72073820304523962635461109636863552463959386, 237631139131170326276194036894672401606209006, 783482241487803924599161932680961781344340253, 2583181753751206451923746553136410907534027834, 8516884773599595591004814294267322151259289469, 28080612655859952277341587386410427959580477957, 92583242357895596095631673110607008982818888535, 305251771766883885315571869536929191104542036636, 1006430988953968053475517904815140190842566974350, 3318255385264072992877173450799403988884423035951, 10940460819154717218018562979975552146356820738854, 36071269097310319921964909487726826546465277498189, 118928852796815095562104627280539286018815310631933, 392114621457030372782097040162661799389422859807221, 1292822328178614530427762202485367203671685444559598
Generating function in Maple syntax:
-(x^2-3*x+1)*(x-1)^2/(x^5-3*x^4+11*x^3-12*x^2+6*x-1)
Generating function in latex syntax:
-\frac{\left(x^{2}-3 x +1\right) \left(x -1\right)^{2}}{x^{5}-3 x^{4}+11 x^{3}-12 x^{2}+6 x -1}
Generating function in sympy syntax:
(x - 1)**2*(-x**2 + 3*x - 1)/(x**5 - 3*x**4 + 11*x**3 - 12*x**2 + 6*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^5-3*x^4+11*x^3-12*x^2+6*x-1)*F(x)+(x^2-3*x+1)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}-3 x^{4}+11 x^{3}-12 x^{2}+6 x -1\right) F \! \left(x \right)+\left(x^{2}-3 x +1\right) \left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-948/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+3)-948/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n+3)-948/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n+3)-948/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n+3)-948/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 5)^(-n+3)+2174/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+2)+2174/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n+2)+2174/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n+2)+2174/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n+2)+2174/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 5)^(-n+2)-9347/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n+1)-9347/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n+1)-9347/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n+1)-9347/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n+1)-9347/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 5)^(-n+1)-858/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n-1)-858/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n-1)-858/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n-1)-858/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n-1)-858/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 5)^(-n-1)+10862/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 1)^(-n)+10862/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 2)^(-n)+10862/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 3)^(-n)+10862/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 4)^(-n)+10862/26987*RootOf(_Z^5-3*_Z^4+11*_Z^3-12*_Z^2+6*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{948 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{26987}-\frac{948 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{26987}-\frac{948 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{26987}-\frac{948 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{26987}-\frac{948 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{26987}+\frac{2174 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{26987}+\frac{2174 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{26987}+\frac{2174 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{26987}+\frac{2174 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{26987}+\frac{2174 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{26987}-\frac{9347 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{26987}-\frac{9347 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{26987}-\frac{9347 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{26987}-\frac{9347 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{26987}-\frac{9347 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{26987}-\frac{858 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{26987}-\frac{858 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{26987}-\frac{858 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{26987}-\frac{858 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{26987}-\frac{858 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{26987}+\frac{10862 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{26987}+\frac{10862 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{26987}+\frac{10862 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{26987}+\frac{10862 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{26987}+\frac{10862 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+11 \textit{\_Z}^{3}-12 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{26987}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(n+5) = a(n)-3*a(n+1)+11*a(n+2)-12*a(n+3)+6*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) = 21
a \! \left(n +5\right) = a \! \left(n \right)-3 a \! \left(n +1\right)+11 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14761/
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[19,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[6,x]
F[10,x] = F[11,x]+F[7,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[1,x]+F[15,x]
F[18,x] = F[12,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[21,x]+F[22,x]+F[43,x]
F[21,x] = 0
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[30,x]
F[24,x] = F[15,x]+F[25,x]
F[25,x] = F[21,x]+F[26,x]+F[28,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[24,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[18,x]+F[7,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[2,x]+F[31,x]
F[34,x] = 2*F[21,x]+F[35,x]+F[37,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[30,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[20,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[31,x]+F[39,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[19,x]+F[45,x]
F[45,x] = F[20,x]+F[46,x]
F[46,x] = 2*F[21,x]+F[40,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[56,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[15,x]+F[50,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[49,x]
F[56,x] = F[57,x]+F[60,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[31,x]+F[57,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[56,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_{19}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{7}\! \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_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \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_{22}\! \left(x \right)+F_{43}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{7}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{35}\! \left(x \right)+F_{37}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{31}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{56}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{15}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{31}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{56}\! \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_19(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_6(x))
Eq(F_10(x), F_11(x) + F_7(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_1(x) + F_15(x))
Eq(F_18(x), F_12(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_43(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_30(x))
Eq(F_24(x), F_15(x) + F_25(x))
Eq(F_25(x), F_21(x) + F_26(x) + F_28(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_24(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_18(x) + F_7(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_2(x) + F_31(x))
Eq(F_34(x), 2*F_21(x) + F_35(x) + F_37(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_20(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_31(x) + F_39(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_19(x) + F_45(x))
Eq(F_45(x), F_20(x) + F_46(x))
Eq(F_46(x), 2*F_21(x) + F_40(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_56(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_15(x) + F_50(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_49(x))
Eq(F_56(x), F_57(x) + F_60(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_31(x) + F_57(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_56(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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