0231_2103
Counting sequence:
1, 1, 2, 6, 22, 86, 336, 1290, 4870, 18164, 67234, 247786, 911120, 3346618, 12286942, 45104548, 165573482, 607817410, 2231360192, 8191763970, 30074097062, 110410946820, 405353571346, 1488185247962, 5463619641904, 20058759689642, 73642362774478, 270365534734372, 992601463154394, 3644168652828306, 13378949293223584, 49118549940631026, 180330447832761814, 662052732696827268, 2430614602143054658, 8923590292813419626, 32761452034334480144, 120278128455054226778, 441580799649373849662, 1621189198318311724836, 5951921865878906813386, 21851474174780869494754, 80223990567285169141376, 294528808956190525032034, 1081312693276619771830662, 3969856615342844971154180, 14574656937238597962335474, 53508387183854353717020794, 196446990920302982175397872, 721221891981717814519231882, 2647844159061735461539575342, 9721111863939599986032911140, 35689417576866243983053491514, 131027658646825566529351747506, 481045881275383245272102655584, 1766078569073287069170170126674, 6483858678657721080750427185334, 23804390190219511078734830593412, 87393791322658220262961176775970, 320851519434697441189126324830474, 1177952071486155824027071542807760, 4324651742847478724003975164027450, 15877227223105694512692243384637854, 58290553617653261802761941143940132, 214003905928095619885073091011757866, 785679135128533086645142498988667394, 2884488022306130613079666034730845760, 10589909772093386266568785650719904450, 38879062112179894135680987888567615334, 142737898929608780921244990853111010564, 524038047318442993091691459195067035602, 1923917033224326516418638047568547082778, 7063335896451473637539344742000440798640, 25931842758565952545455919436618191583082, 95204373501878150879173297747905063829134, 349526750500254712793836775370355979014692, 1283228331026801113302723467099523903632794, 4711155718963002418757230617463805252233938, 17296211182119113073543026909174001358192160, 63500113157438088382073207208468643244721842, 233129922417691778200130269982261720305097110, 855897068903297686073040414760694640296626564, 3142281286589849451835371750830702953701468418, 11536354128078398318405695613200546120982556586, 42353772444370899153456240470940590077282284176, 155494710057791073214278770440237856836822667546, 570872521160036863152127626812437885762513572094, 2095861880410559489058907863957440932319644366116, 7694602313020889558583673369308835584171565302922, 28249430608446560354340729394257433918189523564066, 103713005199892113287264998900957208657781370615296, 380764752277049296302930955380765479114699162568994, 1397913369660544110354416984116327616424064871820102, 5132202435728147371926239879873753939300119558390532, 18842012969437412943022050742728903712197573692282034, 69175262898622955384204773631511093069748152164707770, 253965274562512900114370761778494966166130334654157680, 932390539348373120539458778072433390439369606076476234, 3423114122054357211718264778572813665360417792531995886, 12567384371786116816781290520621695764097382998664918308, 46139025552974520799559670417660572760312305663315181562
Generating function in Maple syntax:
-(x-1)*(3*x-1)*(x^2-3*x+1)/(2*x^5-10*x^4+25*x^3-22*x^2+8*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right) \left(3 x -1\right) \left(x^{2}-3 x +1\right)}{2 x^{5}-10 x^{4}+25 x^{3}-22 x^{2}+8 x -1}
Generating function in sympy syntax:
(1 - x)*(3*x - 1)*(x**2 - 3*x + 1)/(2*x**5 - 10*x**4 + 25*x**3 - 22*x**2 + 8*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^5-10*x^4+25*x^3-22*x^2+8*x-1)*F(x)+(x-1)*(3*x-1)*(x^2-3*x+1) = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{5}-10 x^{4}+25 x^{3}-22 x^{2}+8 x -1\right) F \! \left(x \right)+\left(x -1\right) \left(3 x -1\right) \left(x^{2}-3 x +1\right) = 0
Explicit closed form in Maple syntax:
-9310/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 1)^(-n+3)-9310/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 2)^(-n+3)-9310/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 3)^(-n+3)-9310/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 4)^(-n+3)-9310/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 5)^(-n+3)+41357/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 1)^(-n+2)+41357/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 2)^(-n+2)+41357/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 3)^(-n+2)+41357/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 4)^(-n+2)+41357/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 5)^(-n+2)-93738/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 1)^(-n+1)-93738/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 2)^(-n+1)-93738/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 3)^(-n+1)-93738/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 4)^(-n+1)-93738/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 5)^(-n+1)-8207/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 1)^(-n-1)-8207/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 2)^(-n-1)-8207/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 3)^(-n-1)-8207/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 4)^(-n-1)-8207/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 5)^(-n-1)+55448/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 1)^(-n)+55448/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 2)^(-n)+55448/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 3)^(-n)+55448/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 4)^(-n)+55448/17539*RootOf(2*_Z^5-10*_Z^4+25*_Z^3-22*_Z^2+8*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
-\frac{9310 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{17539}-\frac{9310 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{17539}-\frac{9310 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{17539}-\frac{9310 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{17539}-\frac{9310 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{17539}+\frac{41357 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{17539}+\frac{41357 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{17539}+\frac{41357 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{17539}+\frac{41357 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{17539}+\frac{41357 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{17539}-\frac{93738 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{17539}-\frac{93738 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{17539}-\frac{93738 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{17539}-\frac{93738 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{17539}-\frac{93738 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{17539}-\frac{8207 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{17539}-\frac{8207 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{17539}-\frac{8207 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{17539}-\frac{8207 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{17539}-\frac{8207 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{17539}+\frac{55448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{17539}+\frac{55448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{17539}+\frac{55448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{17539}+\frac{55448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{17539}+\frac{55448 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-10 \textit{\_Z}^{4}+25 \textit{\_Z}^{3}-22 \textit{\_Z}^{2}+8 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{17539}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(n+5) = 2*a(n)-10*a(n+1)+25*a(n+2)-22*a(n+3)+8*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) = 22
a \! \left(n +5\right) = 2 a \! \left(n \right)-10 a \! \left(n +1\right)+25 a \! \left(n +2\right)-22 a \! \left(n +3\right)+8 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: regular_insertion_encoding_right
Tree: http://permpal.com/tree/14613/
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[15,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[11,x]+F[7,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]+F[18,x]+F[56,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]+F[31,x]
F[20,x] = F[21,x]+F[7,x]
F[21,x] = F[17,x]+F[22,x]+F[24,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[20,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[10,x]+F[26,x]
F[26,x] = F[21,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]+F[27,x]
F[31,x] = F[32,x]+F[41,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[2,x]+F[32,x]
F[36,x] = F[32,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[32,x]+F[37,x]
F[41,x] = 2*F[17,x]+F[42,x]+F[44,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[31,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[51,x]
F[46,x] = F[16,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[32,x]+F[47,x]
F[51,x] = F[41,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[37,x]+F[52,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[15,x]+F[58,x]
F[58,x] = F[16,x]+F[59,x]
F[59,x] = 2*F[17,x]+F[48,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = F[11,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[62,x]
F[66,x] = F[37,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[66,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_{15}\! \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_{11}\! \left(x \right)+F_{7}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{56}\! \left(x \right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{31}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \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_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \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_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{31}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)+F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{41}\! \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_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{37}\! \left(x \right)+F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{48}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{37}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{66}\! \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_15(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_11(x) + F_7(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x) + F_18(x) + F_56(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_31(x))
Eq(F_20(x), F_21(x) + F_7(x))
Eq(F_21(x), F_17(x) + F_22(x) + F_24(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_20(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_10(x) + F_26(x))
Eq(F_26(x), F_21(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x) + F_27(x))
Eq(F_31(x), F_32(x) + F_41(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_2(x) + F_32(x))
Eq(F_36(x), F_32(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_32(x) + F_37(x))
Eq(F_41(x), 2*F_17(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_31(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_51(x))
Eq(F_46(x), F_16(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_32(x) + F_47(x))
Eq(F_51(x), F_41(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_55(x))
Eq(F_55(x), F_37(x) + F_52(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_15(x) + F_58(x))
Eq(F_58(x), F_16(x) + F_59(x))
Eq(F_59(x), 2*F_17(x) + F_48(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), F_11(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_62(x))
Eq(F_66(x), F_37(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_66(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [2], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "regular_insertion_encoding_right", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}]}
Specification JSON:
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0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"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]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": 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0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"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]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 3], [1, 3], [1, 2], [1, 3]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], 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{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 4]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 2], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"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, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[0, 4]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 4]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 2], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 4], [0, 4], [0, 4]]}, {"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, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[0, 4]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14614/
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[15,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[11,x]+F[7,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]+F[18,x]+F[56,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]+F[31,x]
F[20,x] = F[21,x]+F[7,x]
F[21,x] = F[17,x]+F[22,x]+F[24,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[20,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[10,x]+F[26,x]
F[26,x] = F[21,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[11,x]+F[27,x]
F[31,x] = F[32,x]+F[41,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[2,x]+F[32,x]
F[36,x] = F[32,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[32,x]+F[37,x]
F[41,x] = 2*F[17,x]+F[42,x]+F[44,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[31,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[51,x]
F[46,x] = F[16,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[32,x]+F[47,x]
F[51,x] = F[41,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[37,x]+F[52,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[15,x]+F[58,x]
F[58,x] = F[16,x]+F[59,x]
F[59,x] = 2*F[17,x]+F[48,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[66,x]
F[62,x] = F[11,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[62,x]
F[66,x] = F[37,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[66,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_{15}\! \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_{11}\! \left(x \right)+F_{7}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{56}\! \left(x \right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{31}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \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_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{41}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \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_{40}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{31}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)+F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{41}\! \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_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{37}\! \left(x \right)+F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{48}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{37}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{66}\! \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_15(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_11(x) + F_7(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x) + F_18(x) + F_56(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_31(x))
Eq(F_20(x), F_21(x) + F_7(x))
Eq(F_21(x), F_17(x) + F_22(x) + F_24(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_20(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_10(x) + F_26(x))
Eq(F_26(x), F_21(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_11(x) + F_27(x))
Eq(F_31(x), F_32(x) + F_41(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_2(x) + F_32(x))
Eq(F_36(x), F_32(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_32(x) + F_37(x))
Eq(F_41(x), 2*F_17(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_31(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_51(x))
Eq(F_46(x), F_16(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_32(x) + F_47(x))
Eq(F_51(x), F_41(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_55(x))
Eq(F_55(x), F_37(x) + F_52(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_15(x) + F_58(x))
Eq(F_58(x), F_16(x) + F_59(x))
Eq(F_59(x), 2*F_17(x) + F_48(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_66(x))
Eq(F_62(x), F_11(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_62(x))
Eq(F_66(x), F_37(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_66(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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