0321_1302_2031_2103
Counting sequence:
1, 1, 2, 6, 20, 65, 205, 637, 1970, 6089, 18829, 58249, 180233, 557705, 1725742, 5340028, 16523747, 51129602, 158210758, 489552901, 1514827943, 4687346138, 14504099068, 44880169924, 138873130946, 429716431271, 1329675580990, 4114427611495, 12731311916423, 39394617775352, 121899134975941, 377193635761930, 1167153802101305, 3611534948112956, 11175206436332308, 34579546007115448, 106999813280441069, 331090525008417521, 1024496514428851045, 3170109165915252424, 9809298501540090497, 30353004283540592663, 93921585615116759035, 290622442577823488365, 899275747707416895479, 2782637373912302347178, 8610340904259317713990, 26643058553952168084631, 82441865775393131839370, 255100637892781901207702, 789360294569266262219491, 2442524957167538275587661, 7557927865679815080487676, 23386567025731029118227620, 72365273520616602140488534, 223920544043593414819656808, 692879437959894376967378105, 2143983338367361084433472584, 6634147736771084496410058313, 20528105515418737608380432191, 63520309280490474315206491316, 196551488302638957799445085167, 608191112284900967610302499694, 1881931458554001084010932545953, 5823278149181720236111621931930, 18019024151279542641432759697046, 55756435300968717204215074014736, 172527660286772745575071411591273, 533853956110262810544152103062249, 1651909299534091205787650406430361, 5111518426817842054364358885600538, 15816619371939760250545982093665021, 48941513551885935825181828452852125, 151440184050890330089002189434789045, 468602780767162913692922819375518201, 1450001976152687912286415118207449921, 4486754703855210405370528389090124526, 13883407128851408114568141868922126168, 42959556790529236868918910122397590311, 132930159182862569335186574669009274886, 411327037346827628522220234309530096822, 1272773106513593880994677895342995100145, 3938353751587533747730437180574406531179, 12186484922776721047875191516976563634478, 37708754505153434832981211799758280356976, 116682552462054379548080898431312087250488, 361051915602235418091267609006522659899234, 1117206326133779208729586739317387177376935, 3456982005126379760059049663642314962019538, 10696971816409651006804900055343162420522119, 33099740140787701666828390008704920000191103, 102420836119899136689099906460566216347957428, 316921753067563383353561182725552101267046977, 980653950626199328384427210989364078183061386, 3034446709859498675065725677500185605105965465, 9389516892373122406498804074903680946130655884, 29054070116209868548790047881611863720792754540, 89902281447867996328842558127698493701801071180, 278185472025219632845828537964258369821055951293, 860791913170402267398576630708015184914955093957, 2663556484043808872608713143918413976694276441425
Generating function in Maple syntax:
(x^3-2*x^2+3*x-1)*(x-1)^2/(3*x^5-9*x^4+15*x^3-13*x^2+6*x-1)
Generating function in latex syntax:
\frac{\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{2}}{3 x^{5}-9 x^{4}+15 x^{3}-13 x^{2}+6 x -1}
Generating function in sympy syntax:
(x - 1)**2*(x**3 - 2*x**2 + 3*x - 1)/(3*x**5 - 9*x**4 + 15*x**3 - 13*x**2 + 6*x - 1)
Implicit equation for the generating function in Maple syntax:
(3*x^5-9*x^4+15*x^3-13*x^2+6*x-1)*F(x)-(x^3-2*x^2+3*x-1)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x^{5}-9 x^{4}+15 x^{3}-13 x^{2}+6 x -1\right) F \! \left(x \right)-\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-29/73*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+3)-29/73*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+3)-29/73*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+3)-29/73*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+3)-29/73*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+3)+236/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+2)+236/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+2)+236/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+2)+236/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+2)+236/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+2)-316/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+1)-316/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+1)-316/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+1)-316/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+1)-316/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+1)-25/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n-1)-25/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n-1)-25/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n-1)-25/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n-1)-25/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n-1)+209/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n)+209/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n)+209/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n)+209/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n)+209/219*RootOf(3*_Z^5-9*_Z^4+15*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n)+piecewise(n = 0,1/3,0)
Explicit closed form in latex syntax:
-\frac{29 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{73}-\frac{29 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{73}-\frac{29 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{73}-\frac{29 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{73}-\frac{29 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{73}+\frac{236 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{219}+\frac{236 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{219}+\frac{236 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{219}+\frac{236 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{219}+\frac{236 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{219}-\frac{316 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{219}-\frac{316 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{219}-\frac{316 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{219}-\frac{316 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{219}-\frac{316 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{219}-\frac{25 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{219}-\frac{25 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{219}-\frac{25 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{219}-\frac{25 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{219}-\frac{25 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{219}+\frac{209 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{219}+\frac{209 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{219}+\frac{209 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{219}+\frac{209 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{219}+\frac{209 \mathit{RootOf}\! \left(3 \textit{\_Z}^{5}-9 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{219}+\left(\left\{\begin{array}{cc}\frac{1}{3} & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(n+5) = 3*a(n)-9*a(n+1)+15*a(n+2)-13*a(n+3)+6*a(n+4), n >= 6
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) = 20
a \! \left(5\right) = 65
a \! \left(n +5\right) = 3 a \! \left(n \right)-9 a \! \left(n +1\right)+15 a \! \left(n +2\right)-13 a \! \left(n +3\right)+6 a \! \left(n +4\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15943/
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[21,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[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = F[15,x]+F[16,x]+F[19,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[7,x]
F[18,x] = F[16,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[10,x]
F[21,x] = F[2,x]+F[22,x]
F[22,x] = F[15,x]+F[23,x]+F[47,x]
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[25,x]
F[29,x] = F[30,x]+F[44,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[2,x]+F[30,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[2,x]+F[35,x]
F[38,x] = 2*F[15,x]+F[39,x]+F[42,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[30,x]+F[41,x]
F[41,x] = F[39,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[34,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[29,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[21,x]+F[49,x]
F[49,x] = F[35,x]+F[50,x]
F[50,x] = 2*F[15,x]+F[39,x]+F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[49,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_{21}\! \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_{14}\! \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_{11}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{7}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{47}\! \left(x \right)
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_{25}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{44}\! \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_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{29}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{21}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{35}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{39}\! \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_{49}\! \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_21(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_14(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_11(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_7(x))
Eq(F_18(x), F_16(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_10(x))
Eq(F_21(x), F_2(x) + F_22(x))
Eq(F_22(x), F_15(x) + F_23(x) + F_47(x))
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_25(x))
Eq(F_29(x), F_30(x) + F_44(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_34(x))
Eq(F_33(x), F_2(x) + F_30(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_2(x) + F_35(x))
Eq(F_38(x), 2*F_15(x) + F_39(x) + F_42(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_30(x) + F_41(x))
Eq(F_41(x), F_39(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_34(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_29(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_21(x) + F_49(x))
Eq(F_49(x), F_35(x) + F_50(x))
Eq(F_50(x), 2*F_15(x) + F_39(x) + F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_49(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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{"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "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": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, 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