0132_0231_2103_2130_3102
Counting sequence:
1, 1, 2, 6, 19, 51, 116, 244, 502, 1043, 2220, 4851, 10835, 24584, 56352, 129974, 300857, 697804, 1620243, 3764257, 8748040, 20333434, 47265658, 109874877, 255422988, 593780569, 1380365723, 3208953498, 7459903408, 17342162000, 40315624933, 93722445602, 217878239419, 506505441487, 1177482279684, 2737314182848, 6363483416838, 14793304149431, 34390259781076, 79947654443423, 185855747898299, 432062194568332, 1004422742329400, 2334999585725706, 5428215467060729, 12619069972032376, 29335778567671611, 68197411225978989, 158539746514592152, 368560195659453878, 856798505175117770, 1991814870720996721, 4630407797472164980, 10764392156149573109, 25024175744225337187, 58174150717848978574, 135238492821245779752, 314391352772264661524, 730871223392151342693, 1699069457453170420542, 3949857278347473170115, 9182304143528229940779, 21346267331342913827828, 49624050985319754693452, 115361922436801666282998, 268183932671108403203419, 623452004125041631647068, 1449350069469709754722443, 3369330132830154403977283, 7832742263676085334030160, 18208916594837656948749808, 42330595389990954582053022, 98406695243973635182571289, 228767811546776653332234212, 531820639542373644213484419, 1236332990777541261158422073, 2874125504794653148380392008, 6681531172371250567037671026, 15532675498301986665510500026, 36109089654958112010836392933, 83943449140641613268525686524, 195144843610310602449414604177, 453656722204606692822028656395, 1054623928533840486835782264706, 2451703184802618677312703896064, 5699518419544781751088575618776, 13249772817562948385476101125381, 30801984798401900331563855823834, 71605927179624585974827940621227, 166463584759632905646832211115463, 386980884718051445322404607694020, 899621411814513110648377341230616, 2091366050767069346947155019169350, 4861836213390233264867114982482559, 11302397950451074211355412250072772, 26274887475339825451279161804146999, 61081702738507561195993775894493547, 141997731215294106896778416324965844, 330104675644207023749626858989754568, 767400267240540418651317520213513202, 1783989181648501315351477258985674265
Generating function in Maple syntax:
-(3*x^9-7*x^8+8*x^7-12*x^5+15*x^4-19*x^3+15*x^2-6*x+1)/(x^3-2*x^2+3*x-1)/(x-1)^4
Generating function in latex syntax:
-\frac{3 x^{9}-7 x^{8}+8 x^{7}-12 x^{5}+15 x^{4}-19 x^{3}+15 x^{2}-6 x +1}{\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-3*x**9 + 7*x**8 - 8*x**7 + 12*x**5 - 15*x**4 + 19*x**3 - 15*x**2 + 6*x - 1)/((x - 1)**4*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^3-2*x^2+3*x-1)*(x-1)^4*F(x)+3*x^9-7*x^8+8*x^7-12*x^5+15*x^4-19*x^3+15*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+3 x^{9}-7 x^{8}+8 x^{7}-12 x^{5}+15 x^{4}-19 x^{3}+15 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/13800*(-46*2^(1/3)*((I-4/23*23^(1/2))*3^(1/2)-12/23*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+4600+115*2^(2/3)*((I-1/23*23^(1/2))*3^(1/2)+3/23*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3))*(11/600*((I-3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)+1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*(-115*2^(2/3)*((I+1/23*23^(1/2))*3^(1/2)+3/23*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+46*2^(1/3)*((I+4/23*23^(1/2))*3^(1/2)-12/23*I*23^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+12*23^(1/2)*3^(1/2))^(1/3)+1/12*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/13800*((10*2^(2/3)*23^(1/2)*3^(1/2)+230*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+(-16*23^(1/2)*3^(1/2)*2^(1/3)+92*2^(1/3))*(11+3*23^(1/2)*3^(1/2))^(2/3))*(1/300*2^(1/3)*(3*23^(1/2)*3^(1/2)-11)*(11+3*23^(1/2)*3^(1/2))^(2/3)-1/6*(44+12*23^(1/2)*3^(1/2))^(1/3)+2/3)^(-n)+1/3*n^3+n^2-40/3*n+23)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(-46 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{4 \sqrt{23}}{23}\right) \sqrt{3}-\frac{12 \,\mathrm{I} \sqrt{23}}{23}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+4600+115 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{\sqrt{23}}{23}\right) \sqrt{3}+\frac{3 \,\mathrm{I} \sqrt{23}}{23}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{11 \left(\left(\mathrm{I}-\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}+1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}-\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(-115 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{\sqrt{23}}{23}\right) \sqrt{3}+\frac{3 \,\mathrm{I} \sqrt{23}}{23}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+46 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{4 \sqrt{23}}{23}\right) \sqrt{3}-\frac{12 \,\mathrm{I} \sqrt{23}}{23}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{600}+\frac{\mathrm{I} \sqrt{3}\, \left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{2}{3}\right)^{-n}}{13800}\\+\\\frac{\left(\left(10 \,2^{\frac{2}{3}} \sqrt{23}\, \sqrt{3}+230 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+\left(-16 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+92 \,2^{\frac{1}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{2^{\frac{1}{3}} \left(3 \sqrt{23}\, \sqrt{3}-11\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}}{300}-\frac{\left(44+12 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{2}{3}\right)^{-n}}{13800}\\+\frac{n^{3}}{3}+n^{2}-\frac{40 n}{3}+23 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 116
a(7) = 244
a(8) = 502
a(9) = 1043
a(n+3) = -1/3*n^3-2*n^2+a(n)-2*a(n+1)+3*a(n+2)+31/3*n-9, 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) = 19
a \! \left(5\right) = 51
a \! \left(6\right) = 116
a \! \left(7\right) = 244
a \! \left(8\right) = 502
a \! \left(9\right) = 1043
a \! \left(n +3\right) = -\frac{n^{3}}{3}-2 n^{2}+a \! \left(n \right)-2 a \! \left(n +1\right)+3 a \! \left(n +2\right)+\frac{31 n}{3}-9, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19248/
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[24,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[18,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,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[11,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[4,x]
F[24,x] = F[25,x]+F[37,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[1,x]+F[14,x]
F[29,x] = F[25,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[25,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[33,x]*F[4,x]
F[36,x] = F[30,x]
F[37,x] = F[38,x]+F[39,x]+F[56,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[42,x]+F[7,x]
F[42,x] = F[19,x]+F[38,x]+F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[13,x]+F[45,x]
F[45,x] = F[46,x]+F[50,x]
F[46,x] = F[19,x]+F[38,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[17,x]+F[49,x]
F[49,x] = F[46,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[22,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[53,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[66,x]
F[58,x] = F[25,x]+F[59,x]
F[59,x] = F[38,x]+F[60,x]+F[65,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[11,x]+F[63,x]
F[63,x] = F[19,x]+F[38,x]+F[64,x]
F[64,x] = F[13,x]*F[4,x]
F[65,x] = F[4,x]*F[58,x]
F[66,x] = F[67,x]+F[74,x]
F[67,x] = F[38,x]+F[68,x]+F[71,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[14,x]+F[46,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[33,x]+F[73,x]
F[73,x] = F[67,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[18,x]+F[78,x]
F[78,x] = F[51,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_{24}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \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_{11}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \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_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{25}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{56}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{7}\! \left(x \right)
F_{42}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{17}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{46}\! \left(x \right)
F_{50}\! \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_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{22}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{66}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{38}\! \left(x \right)+F_{60}\! \left(x \right)+F_{65}\! \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_{11}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{67}\! \left(x \right) = F_{38}\! \left(x \right)+F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right)+F_{46}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{33}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{67}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{18}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{51}\! \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_24(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(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_11(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_37(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_1(x) + F_14(x))
Eq(F_29(x), F_25(x) + F_30(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_36(x))
Eq(F_33(x), F_25(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_33(x)*F_4(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_56(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_42(x) + F_7(x))
Eq(F_42(x), F_19(x) + F_38(x) + F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_13(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_50(x))
Eq(F_46(x), F_19(x) + F_38(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_17(x) + F_49(x))
Eq(F_49(x), F_46(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_22(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_53(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_66(x))
Eq(F_58(x), F_25(x) + F_59(x))
Eq(F_59(x), F_38(x) + F_60(x) + F_65(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_11(x) + F_63(x))
Eq(F_63(x), F_19(x) + F_38(x) + F_64(x))
Eq(F_64(x), F_13(x)*F_4(x))
Eq(F_65(x), F_4(x)*F_58(x))
Eq(F_66(x), F_67(x) + F_74(x))
Eq(F_67(x), F_38(x) + F_68(x) + F_71(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_14(x) + F_46(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_33(x) + F_73(x))
Eq(F_73(x), F_67(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_18(x) + F_78(x))
Eq(F_78(x), F_51(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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2], "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, 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]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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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