0231_2031_2103_3012
Counting sequence:
1, 1, 2, 6, 20, 61, 169, 444, 1127, 2793, 6809, 16407, 39200, 93070, 219925, 517810, 1215794, 2848498, 6662628, 15563529, 36318377, 84682984, 197329379, 459591001, 1069993589, 2490328579, 5794636776, 13480690734, 31356818817, 72928894498, 169600054854, 394384386926, 917038639064, 2132235402445, 4957543406373, 11526173041228, 26797460995755, 62300878671673, 144839953695477, 336726723012383, 782821663582580, 1819889246587382, 4230820565316489, 9835632567497978, 22865380697465014, 53156129532579994, 123574054360329648, 287276746192196705, 667840947467299605, 1552548348525548216, 3609248990539646751, 8390507947967049905, 19505604975132428593, 45345104603425167883, 105414715881116962084, 245059734831979604030, 569695229414038281541, 1324381582029666714954, 3078815213160552152706, 7157379895551312618590, 16638894871715494657252, 38680747448340005554853, 89921846128343880336889, 209042963431759253985860, 485965991600961271302007, 1129733978884636120530321, 2626313072886395401122825, 6105437539424483760482223, 14193420979138482389012752, 32995701902142319691500326, 76705703072950717017415061, 178319129677524863452299626, 414541690828700029012372354, 963692527313080738503235722, 2240313350392150104683410420, 5208096724960736164154386497, 12107356070534599064797279753, 28146188239212615395808584592, 65431949535372881988323648243, 152110828628333262472728935921, 353614775844553525263306151733, 822054621267402565259658235419, 1911045143417661674812501278872, 4442640968485083705121735517206, 10327887248940944016454388172817, 24009424969922518052414372646138, 55815141410998905539333022936278, 129754461598426585663438361342262, 301642527046818772546236184162616, 701233799545178477277028221580869, 1630170806490849167543900449615877, 3789687348073724749773767023908100, 8809954231970470941228127488830347, 20480658808435869165690083688963313, 47611755313451979017264582962626293, 110683902562833131538245462763700903, 257308855883602412949387214489893108, 598170517863554112521905782954390558, 1390577744432201370018252526896570905, 3232701053537541289709857764004875490, 7515118189767090117910533182208897110
Generating function in Maple syntax:
-(x^9+x^8-x^7+5*x^5-5*x^4+6*x^3-9*x^2+5*x-1)/(x^3-2*x^2+3*x-1)/(x^3+x^2+x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{x^{9}+x^{8}-x^{7}+5 x^{5}-5 x^{4}+6 x^{3}-9 x^{2}+5 x -1}{\left(x^{3}-2 x^{2}+3 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-x**9 - x**8 + x**7 - 5*x**5 + 5*x**4 - 6*x**3 + 9*x**2 - 5*x + 1)/((x - 1)**2*(x**3 - 2*x**2 + 3*x - 1)*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(x^3-2*x^2+3*x-1)*(x^3+x^2+x-1)*(x-1)^2*F(x)+x^9+x^8-x^7+5*x^5-5*x^4+6*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-2 x^{2}+3 x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{9}+x^{8}-x^{7}+5 x^{5}-5 x^{4}+6 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
4-10510/2783*Sum(_alpha^(-n+4),_alpha = RootOf(_Z^6-_Z^5+2*_Z^4-_Z^3+4*_Z^2-4*_Z+1))+4827/2783*Sum(_alpha^(-n+3),_alpha = RootOf(_Z^6-_Z^5+2*_Z^4-_Z^3+4*_Z^2-4*_Z+1))-18484/2783*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^6-_Z^5+2*_Z^4-_Z^3+4*_Z^2-4*_Z+1))+765/2783*Sum(_alpha^(1-n),_alpha = RootOf(_Z^6-_Z^5+2*_Z^4-_Z^3+4*_Z^2-4*_Z+1))-40419/2783*Sum(_alpha^(-n),_alpha = RootOf(_Z^6-_Z^5+2*_Z^4-_Z^3+4*_Z^2-4*_Z+1))+20781/2783*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^6-_Z^5+2*_Z^4-_Z^3+4*_Z^2-4*_Z+1))-n-piecewise(n = 0,4,n = 1,1,0)
Explicit closed form in latex syntax:
4-\frac{10510 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-\textit{\_Z}^{5}+2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +4}\right)}{2783}+\frac{4827 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-\textit{\_Z}^{5}+2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +3}\right)}{2783}-\frac{18484 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-\textit{\_Z}^{5}+2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{2783}+\frac{765 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-\textit{\_Z}^{5}+2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{2783}-\frac{40419 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-\textit{\_Z}^{5}+2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{2783}+\frac{20781 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}-\textit{\_Z}^{5}+2 \textit{\_Z}^{4}-\textit{\_Z}^{3}+4 \textit{\_Z}^{2}-4 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{2783}-n -\left(\left\{\begin{array}{cc}4 & n =0 \\ 1 & n =1 \\ 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) = 61
a(6) = 169
a(7) = 444
a(8) = 1127
a(9) = 2793
a(n+6) = -a(n)+a(n+1)-2*a(n+2)+a(n+3)-4*a(n+4)+4*a(n+5)-2*n+6, n >= 10
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) = 61
a \! \left(6\right) = 169
a \! \left(7\right) = 444
a \! \left(8\right) = 1127
a \! \left(9\right) = 2793
a \! \left(n +6\right) = -a \! \left(n \right)+a \! \left(n +1\right)-2 a \! \left(n +2\right)+a \! \left(n +3\right)-4 a \! \left(n +4\right)+4 a \! \left(n +5\right)-2 n +6, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15929/
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[29,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[22,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[4,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,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[7,x]
F[29,x] = F[30,x]+F[43,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[14,x]+F[33,x]
F[33,x] = F[30,x]+F[34,x]
F[34,x] = F[35,x]+F[36,x]+F[42,x]
F[35,x] = 0
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[21,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[30,x]+F[39,x]
F[42,x] = F[33,x]*F[4,x]
F[43,x] = F[35,x]+F[44,x]+F[69,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[25,x]+F[46,x]
F[46,x] = F[47,x]+F[66,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[30,x]+F[47,x]
F[51,x] = F[52,x]+F[59,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[41,x]+F[55,x]
F[55,x] = F[52,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[39,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[47,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[47,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[47,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[29,x]+F[71,x]
F[71,x] = F[72,x]+F[79,x]
F[72,x] = F[35,x]+F[36,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[33,x]+F[75,x]
F[75,x] = F[72,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[38,x]
F[79,x] = 2*F[35,x]+F[80,x]+F[84,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[26,x]
F[83,x] = F[63,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[46,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_{29}\! \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_{22}\! \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_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \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_{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_{7}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{43}\! \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_{14}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{42}\! \left(x \right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{30}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{35}\! \left(x \right)+F_{44}\! \left(x \right)+F_{69}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{25}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{66}\! \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_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \left(x \right)+F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \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_{41}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{52}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{39}\! \left(x \right)
F_{59}\! \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_{62}\! \left(x \right) = F_{47}\! \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_{47}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{47}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{29}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{79}\! \left(x \right)
F_{72}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{33}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{72}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{38}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{26}\! \left(x \right)
F_{83}\! \left(x \right) = F_{63}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{46}\! \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_29(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_22(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) + F_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_4(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(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_7(x))
Eq(F_29(x), F_30(x) + F_43(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_14(x) + F_33(x))
Eq(F_33(x), F_30(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_36(x) + F_42(x))
Eq(F_35(x), 0)
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_21(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_30(x) + F_39(x))
Eq(F_42(x), F_33(x)*F_4(x))
Eq(F_43(x), F_35(x) + F_44(x) + F_69(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_25(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_66(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) + F_51(x))
Eq(F_50(x), F_30(x) + F_47(x))
Eq(F_51(x), F_52(x) + F_59(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_41(x) + F_55(x))
Eq(F_55(x), F_52(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_39(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_47(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_47(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_47(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_29(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_79(x))
Eq(F_72(x), F_35(x) + F_36(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_33(x) + F_75(x))
Eq(F_75(x), F_72(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_38(x))
Eq(F_79(x), 2*F_35(x) + F_80(x) + F_84(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_26(x))
Eq(F_83(x), F_63(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_46(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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"pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [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": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "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": [], 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