0123_0132_0231_1023_2103

Counting sequence:
1, 1, 2, 6, 19, 55, 157, 453, 1310, 3785, 10932, 31576, 91209, 263462, 761019, 2198228, 6349657, 18341205, 52979205, 153032262, 442038972, 1276844836, 3688210403, 10653523112, 30773069400, 88889073632, 256759158748, 741657696576, 2142303867841, 6188118701331, 17874594559904, 51631383640431, 149139034605303, 430793251598710, 1244361183603848, 3594380249722109, 10382491474199995, 29990185156445141, 86627685459974343, 250227060920279168, 722789506430149595, 2087802449040396194, 6030689471057397328, 17419854791835649839, 50317852117070370234, 145344853440569976351, 419833628281880708902, 1212703933190172494629, 3502937188698719330359, 10118355034677911264413, 29227217929598289081904, 84423828278073824665666, 243861143345697126735018, 704401333685023961208567, 2034687577076823686891656, 5877265329202163441672024, 16976683859970116271459646, 49037737576583758921824560, 141647198384839790250623064, 409152823964190820411755357, 1181852061083823365141400471, 3413820490727756692072020160, 9860938375167858235626711077, 28483661019366880986169089453, 82276038466003458316773974538, 237657178305015019614994500958, 686480966426691539135406306771, 1982923977416338757732700348271, 5727744384057186915057057028881, 16544787446589238184723114262461, 47790189872077201696260912480506, 138043613759451725714558742735861, 398743745333029760277726137945228, 1151785078006375619753408795712564, 3326970971820943363496560677635305, 9610070540675924753107002398821346, 27759020616347504933635003197773355, 80182889638249025049076569807033468, 231611045634418389959530984883024513, 669016503419694779077032982441874217, 1932477272929343054006224541379029769, 5582027336096495238107595609062442770, 16123878721583184713536993247494273620, 46574380484873495985466756646371404160, 134531706359595875329118936924861799887, 388599479533660804649887007640760668524, 1122483015938204187537469374748783984236, 3242330953664047013382651394846252441188, 9365584925399675277196721831824000402756, 27052815473926513697296986093476945331392, 78142991697348363966130420301374478673909, 225718729989384267950837831466653730827323, 651996346202719263093439576910791820486608, 1883313961059806202248359088473624435539131, 5440017412030068204276116629611564947382675, 15713678151961910423069572968089177102250718, 45389501974277927105463190031301840751773832, 131109143864942623033921392553572821317008805, 378713289578271043579346693988684185583267411, 1093926414857366555712796710386609792500801961, 3159844225311683801422610105648679269605773407

Generating function in Maple syntax:
(x^4-x^3-2*x+1)/(x^6-2*x^3+x^2-3*x+1)

Generating function in latex syntax:
\frac{x^{4}-x^{3}-2 x +1}{x^{6}-2 x^{3}+x^{2}-3 x +1}

Generating function in sympy syntax:
(x**4 - x**3 - 2*x + 1)/(x**6 - 2*x**3 + x**2 - 3*x + 1)

Implicit equation for the generating function in Maple syntax:
(x^6-2*x^3+x^2-3*x+1)*F(x)-x^4+x^3+2*x-1 = 0

Implicit equation for the generating function in latex syntax:
\left(x^{6}-2 x^{3}+x^{2}-3 x +1\right) F \! \left(x \right)-x^{4}+x^{3}+2 x -1 = 0

Explicit closed form in Maple syntax:
-12496/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+4)-12496/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+4)-12496/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+4)-12496/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+4)-12496/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+4)-12496/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+4)-39891/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+3)-39891/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+3)-39891/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+3)-39891/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+3)-39891/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+3)-39891/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+3)+1261/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+2)+1261/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+2)+1261/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+2)+1261/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+2)+1261/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+2)+1261/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+2)+6686/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n+1)+6686/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n+1)+6686/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n+1)+6686/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n+1)+6686/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n+1)+6686/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 6)^(-n+1)+677/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n-1)+677/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n-1)+677/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n-1)+677/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n-1)+677/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n-1)+677/95561*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 6)^(-n-1)+109502/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 1)^(-n)+109502/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 2)^(-n)+109502/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 3)^(-n)+109502/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 4)^(-n)+109502/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 5)^(-n)+109502/477805*RootOf(_Z^6-2*_Z^3+_Z^2-3*_Z+1,index = 6)^(-n)

Explicit closed form in latex syntax:
-\frac{12496 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{477805}-\frac{12496 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{477805}-\frac{12496 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{477805}-\frac{12496 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{477805}-\frac{12496 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{477805}-\frac{12496 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{477805}-\frac{39891 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{477805}-\frac{39891 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{477805}-\frac{39891 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{477805}-\frac{39891 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{477805}-\frac{39891 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{477805}-\frac{39891 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{477805}+\frac{1261 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{477805}+\frac{1261 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{477805}+\frac{1261 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{477805}+\frac{1261 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{477805}+\frac{1261 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{477805}+\frac{1261 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{477805}+\frac{6686 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{95561}+\frac{6686 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{95561}+\frac{6686 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{95561}+\frac{6686 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{95561}+\frac{6686 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{95561}+\frac{6686 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{95561}+\frac{677 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{95561}+\frac{677 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{95561}+\frac{677 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{95561}+\frac{677 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{95561}+\frac{677 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{95561}+\frac{677 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{95561}+\frac{109502 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{477805}+\frac{109502 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{477805}+\frac{109502 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{477805}+\frac{109502 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{477805}+\frac{109502 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{477805}+\frac{109502 \mathit{RootOf}\! \left(\textit{\_Z}^{6}-2 \textit{\_Z}^{3}+\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{477805}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(n) = 2*a(n+3)-a(n+4)+3*a(n+5)-a(n+6), 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) = 19
a \! \left(5\right) = 55
a \! \left(n \right) = 2 a \! \left(n +3\right)-a \! \left(n +4\right)+3 a \! \left(n +5\right)-a \! \left(n +6\right), \quad n \geq 6

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16077/
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[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[4,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]+F[18,x]+F[38,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[20,x]+F[27,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[1,x]+F[21,x]
F[24,x] = F[13,x]+F[17,x]+F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[24,x]+F[7,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[2,x]+F[28,x]
F[31,x] = 2*F[17,x]+F[32,x]+F[36,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[2,x]*F[4,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[16,x]+F[31,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[17,x]+F[35,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[17,x]+F[46,x]
F[46,x] = F[4,x]*F[7,x]
F[47,x] = F[34,x]+F[48,x]
F[48,x] = 2*F[17,x]+F[32,x]+F[49,x]
F[49,x] = F[16,x]*F[4,x]
F[50,x] = F[16,x]+F[51,x]
F[51,x] = F[32,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_{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_{4}\! \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_{38}\! \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_{27}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \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_{17}\! \left(x \right)+F_{35}\! \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_{17}\! \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_{34}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{16}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{32}\! \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_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_4(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x) + F_18(x) + F_38(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_27(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_1(x) + F_21(x))
Eq(F_24(x), F_13(x) + F_17(x) + F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_24(x) + F_7(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_2(x) + F_28(x))
Eq(F_31(x), 2*F_17(x) + F_32(x) + F_36(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_2(x)*F_4(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_16(x) + F_31(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_17(x) + F_35(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_17(x) + F_46(x))
Eq(F_46(x), F_4(x)*F_7(x))
Eq(F_47(x), F_34(x) + F_48(x))
Eq(F_48(x), 2*F_17(x) + F_32(x) + F_49(x))
Eq(F_49(x), F_16(x)*F_4(x))
Eq(F_50(x), F_16(x) + F_51(x))
Eq(F_51(x), F_32(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, 2, 3], "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": 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