0132_0213_0231_0321_2130

Counting sequence:
1, 1, 2, 6, 19, 56, 155, 416, 1101, 2895, 7590, 19875, 52020, 136135, 356256, 932328, 2440033, 6386214, 16715149, 43751574, 114522651, 299779025, 784732004, 2054235169, 5377572454, 14077597613, 36853269342, 96477907210, 252570961231, 661214043252, 1731024998783, 4531759122476, 11864027774089, 31059828840851, 81314366199874, 212880860066943, 557322899258264, 1459076115673779, 3819879594003004, 10000505644072300, 26181511571653853, 68543751684008994, 179449131684349553, 469802294010432354, 1229954774242852503, 3220055464713911445, 8430197142531846976, 22070504032043464637, 57781244527918003402, 151273074222982423513, 396037635552734858042, 1036839076832952788750, 2714477928412856662283, 7106591032750789097008, 18605287062927585064547, 48709252275674848122168, 127522430327727895251781, 333857951727858783968471, 874051233016191231349598, 2288295324205031395421915, 5990833806387885871934460, 15684204036696934829113887, 41061773764063852318213464, 107501107243005472448157168, 281441525881712574280251609, 736823421696013202603390878, 1929028631781599788274137941, 5050262236716091680961450158, 13221757555795167244305859987, 34615009278101666786091641433, 90623267736441652100982514588, 237254788324515419480578450137, 621141084871121123002333442862, 1626168439014812801836596542597, 4257364172018539117091528060822, 11145923944365264735267711998482, 29180407368452140312681231315783, 76395297515586148485299300586860, 200005483754820749894093032079175, 523621150609279875922702142300356, 1370857961148421419607981406759041, 3588952717563303911120054463485211, 9396000157856533144915529101362938, 24599047681711783727687195087873207, 64401142723417113974486193042304096, 168604380127131192899615004916800011, 441411996860865222336106725710887156, 1155631608697380285268541117101491060, 3025482825353698890493032136242605909, 7920816858811451657869334216927157402, 20736967732218042437592364310026157113, 54290086296239871620886061814774915194, 142133291064743699628681206262846621455, 372109786695612868026865721026348305693, 974196068575735381941310588022988609656, 2550478418047116359979470690584746184053, 6677239183394281503123618942868090620306, 17481239127346704237133815687499997346225, 45766478188083306465945091866134973417586, 119818195413606833481162504863047907582486, 313688108001355406706206942176775190350851

Generating function in Maple syntax:
-(x^7-7*x^5+7*x^4-12*x^3+13*x^2-6*x+1)/(x^2-3*x+1)/(x^3+2*x-1)/(x-1)^2

Generating function in latex syntax:
-\frac{x^{7}-7 x^{5}+7 x^{4}-12 x^{3}+13 x^{2}-6 x +1}{\left(x^{2}-3 x +1\right) \left(x^{3}+2 x -1\right) \left(x -1\right)^{2}}

Generating function in sympy syntax:
(-x**7 + 7*x**5 - 7*x**4 + 12*x**3 - 13*x**2 + 6*x - 1)/((x - 1)**2*(x**2 - 3*x + 1)*(x**3 + 2*x - 1))

Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x^3+2*x-1)*(x-1)^2*F(x)+x^7-7*x^5+7*x^4-12*x^3+13*x^2-6*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x^{3}+2 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{7}-7 x^{5}+7 x^{4}-12 x^{3}+13 x^{2}-6 x +1 = 0

Explicit closed form in Maple syntax:
5/4+109/236*Sum(_alpha^(-n+3),_alpha = RootOf(_Z^5-3*_Z^4+3*_Z^3-7*_Z^2+5*_Z-1))-65/59*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^5-3*_Z^4+3*_Z^3-7*_Z^2+5*_Z-1))+191/236*Sum(_alpha^(-n+1),_alpha = RootOf(_Z^5-3*_Z^4+3*_Z^3-7*_Z^2+5*_Z-1))-166/59*Sum(_alpha^(-n),_alpha = RootOf(_Z^5-3*_Z^4+3*_Z^3-7*_Z^2+5*_Z-1))+283/236*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^5-3*_Z^4+3*_Z^3-7*_Z^2+5*_Z-1))-3/2*n-piecewise(n = 0,1,0)

Explicit closed form in latex syntax:
\frac{5}{4}+\frac{109 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +3}\right)}{236}-\frac{65 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{59}+\frac{191 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{236}-\frac{166 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{59}+\frac{283 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}-3 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}-7 \textit{\_Z}^{2}+5 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{236}-\frac{3 n}{2}-\left(\left\{\begin{array}{cc}1 & 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) = 19
a(5) = 56
a(6) = 155
a(7) = 416
a(n+5) = a(n)-3*a(n+1)+3*a(n+2)-7*a(n+3)+5*a(n+4)-3*n-2, n >= 8

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) = 56
a \! \left(6\right) = 155
a \! \left(7\right) = 416
a \! \left(n +5\right) = a \! \left(n \right)-3 a \! \left(n +1\right)+3 a \! \left(n +2\right)-7 a \! \left(n +3\right)+5 a \! \left(n +4\right)-3 n -2, \quad n \geq 8

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18130/
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[12,x]*F[4,x]
F[4,x] = F[16,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[12,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[13,x]
F[16,x] = F[17,x]+F[32,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[20,x]+F[5,x]
F[20,x] = F[17,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[17,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[24,x]
F[27,x] = F[28,x]+F[30,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[17,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[27,x]
F[32,x] = F[33,x]+F[34,x]+F[72,x]
F[33,x] = 0
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[48,x]
F[36,x] = F[37,x]+F[6,x]
F[37,x] = F[33,x]+F[38,x]+F[46,x]
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[10,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[40,x]
F[43,x] = F[14,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[43,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[13,x]
F[48,x] = F[32,x]+F[49,x]
F[49,x] = 2*F[33,x]+F[50,x]+F[70,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[52,x]+F[67,x]
F[52,x] = F[53,x]+F[65,x]
F[53,x] = F[33,x]+F[54,x]+F[63,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]+F[58,x]
F[56,x] = F[10,x]+F[57,x]
F[57,x] = F[15,x]+F[33,x]+F[38,x]
F[58,x] = F[53,x]+F[59,x]
F[59,x] = 2*F[33,x]+F[50,x]+F[60,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[28,x]+F[62,x]
F[62,x] = F[60,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[17,x]+F[53,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[52,x]
F[67,x] = F[62,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[67,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[61,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[64,x]+F[74,x]
F[74,x] = F[102,x]+F[75,x]
F[75,x] = F[29,x]+F[33,x]+F[76,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[90,x]
F[78,x] = F[12,x]+F[79,x]
F[79,x] = F[33,x]+F[80,x]+F[87,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[12,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[82,x]
F[85,x] = F[86,x]+F[88,x]
F[86,x] = F[87,x]
F[87,x] = x^2
F[88,x] = F[89,x]
F[89,x] = F[12,x]*F[85,x]
F[90,x] = F[28,x]+F[91,x]
F[91,x] = 2*F[33,x]+F[92,x]+F[99,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[97,x]
F[94,x] = F[28,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[12,x]*F[94,x]
F[97,x] = F[100,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[12,x]*F[28,x]
F[100,x] = F[101,x]
F[101,x] = F[12,x]*F[97,x]
F[102,x] = 2*F[33,x]+F[103,x]+F[107,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[14,x]
F[106,x] = F[62,x]
F[107,x] = F[12,x]*F[74,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{16}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = F_{17}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{72}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{48}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{6}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{50}\! \left(x \right)+F_{70}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{65}\! \left(x \right)
F_{53}\! \left(x \right) = F_{33}\! \left(x \right)+F_{54}\! \left(x \right)+F_{63}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{10}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{58}\! \left(x \right) = F_{53}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{28}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{17}\! \left(x \right)+F_{53}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{67}\! \left(x \right) = F_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{61}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{64}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{102}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{90}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{33}\! \left(x \right)+F_{80}\! \left(x \right)+F_{87}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = x^{2}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{28}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{92}\! \left(x \right)+F_{99}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{94}\! \left(x \right) = F_{28}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{97}\! \left(x \right) = F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{33}\! \left(x \right)+F_{103}\! \left(x \right)+F_{107}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{14}\! \left(x \right)
F_{106}\! \left(x \right) = F_{62}\! \left(x \right)
F_{107}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_16(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_12(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_13(x))
Eq(F_16(x), F_17(x) + F_32(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_5(x))
Eq(F_20(x), F_17(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_17(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_24(x))
Eq(F_27(x), F_28(x) + F_30(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_17(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_27(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_72(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_48(x))
Eq(F_36(x), F_37(x) + F_6(x))
Eq(F_37(x), F_33(x) + F_38(x) + F_46(x))
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_10(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_40(x))
Eq(F_43(x), F_14(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_43(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_13(x))
Eq(F_48(x), F_32(x) + F_49(x))
Eq(F_49(x), 2*F_33(x) + F_50(x) + F_70(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_67(x))
Eq(F_52(x), F_53(x) + F_65(x))
Eq(F_53(x), F_33(x) + F_54(x) + F_63(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_58(x))
Eq(F_56(x), F_10(x) + F_57(x))
Eq(F_57(x), F_15(x) + F_33(x) + F_38(x))
Eq(F_58(x), F_53(x) + F_59(x))
Eq(F_59(x), 2*F_33(x) + F_50(x) + F_60(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_28(x) + F_62(x))
Eq(F_62(x), F_60(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_17(x) + F_53(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_52(x))
Eq(F_67(x), F_62(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_67(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_61(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_64(x) + F_74(x))
Eq(F_74(x), F_102(x) + F_75(x))
Eq(F_75(x), F_29(x) + F_33(x) + F_76(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_90(x))
Eq(F_78(x), F_12(x) + F_79(x))
Eq(F_79(x), F_33(x) + F_80(x) + F_87(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_12(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_82(x))
Eq(F_85(x), F_86(x) + F_88(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), x**2)
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_12(x)*F_85(x))
Eq(F_90(x), F_28(x) + F_91(x))
Eq(F_91(x), 2*F_33(x) + F_92(x) + F_99(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_97(x))
Eq(F_94(x), F_28(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_12(x)*F_94(x))
Eq(F_97(x), F_100(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_12(x)*F_28(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_12(x)*F_97(x))
Eq(F_102(x), F_103(x) + F_107(x) + 2*F_33(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_14(x))
Eq(F_106(x), F_62(x))
Eq(F_107(x), F_12(x)*F_74(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], 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