0132_0213_0231_1203_2130
Counting sequence:
1, 1, 2, 6, 19, 57, 159, 418, 1055, 2594, 6274, 15017, 35699, 84471, 199212, 468645, 1100356, 2579584, 6039693, 14126075, 33009801, 77079432, 179869437, 419508244, 977962904, 2278936471, 5308781009, 12363210805, 28784561950, 67003154815, 155937769834, 362859998090, 844244481199, 1964024960005, 4568593400347, 10626269730582, 24714237286771, 57475945669870, 133659991906278, 310811041143933, 722726524243991, 1680492360258811, 3907384829247832, 9084995803099281, 21122909134318264, 49110518672516972, 114179529645037769, 265458052910444023, 617160802485864405, 1434816200025922764, 3335725785504841089, 7754987233925255152, 18028889280745429804, 41913545059797465371, 97440095651640479557, 226526589715699310985, 526622130102869183066, 1224271320927358891739, 2846132321089056587118, 6616548509109359092070, 15381796321265398852891, 35758712497042686676817, 83129669818458924843767, 193254533704061406881194, 449265279815318271330599, 1044421053542309352464986, 2427996358072389776394794, 5644430693691942605140785, 13121757311961505034205275, 30504480693549314506939935, 70914505724369465733967524, 164856608245876452575058525, 383245884278250099469837004, 890940122658987576404669880, 2071187568849580417672006117, 4814933067875499069321734547, 11193373633319289688316294081, 26021461222522382822558279600, 60492607247735931117525700453, 140628348489346043310100261228, 326921443310816102346454506656, 760000542432947055193982380671, 1766787693629464811513725749337, 4107284648259136041128841705981, 9548281517803064784811405418934, 22197067786223665542206957425687, 51601934642730560015160300801554, 119959969216360527579945188278178, 278873144835470355919855511262055, 648301508087673027951103639234109, 1507118358550943810266079445854579, 3503625513797965552160955295146462, 8144941951349701706591948082534459, 18934694422944157111100288002297446, 44017827355811112043038472935226702, 102329040124654880755027890480125125, 237886169988806889573149212765221951, 553018276879962647818514728656638819, 1285611570401010302196442447691581968, 2988684406660075014789784692070649865, 6947848514514492116323659096573334656
Generating function in Maple syntax:
-(x^6-12*x^5+24*x^4-29*x^3+20*x^2-7*x+1)/(2*x-1)/(x^3-2*x^2+3*x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{x^{6}-12 x^{5}+24 x^{4}-29 x^{3}+20 x^{2}-7 x +1}{\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**6 + 12*x**5 - 24*x**4 + 29*x**3 - 20*x**2 + 7*x - 1)/((x - 1)**3*(2*x - 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^3-2*x^2+3*x-1)*(x-1)^3*F(x)+x^6-12*x^5+24*x^4-29*x^3+20*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{3}-2 x^{2}+3 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{6}-12 x^{5}+24 x^{4}-29 x^{3}+20 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
1/13800*(575*2^(2/3)*((9/23*I-3/23*3^(1/2))*23^(1/2)+I*3^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200-437*((-153/437*I-51/437*3^(1/2))*23^(1/2)+I*3^(1/2)+1)*2^(1/3)*(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*(-575*((9/23*I+3/23*3^(1/2))*23^(1/2)+I*3^(1/2)+1)*2^(2/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200+437*2^(1/3)*((-153/437*I+51/437*3^(1/2))*23^(1/2)+I*3^(1/2)-1)*(11+3*23^(1/2)*3^(1/2))^(2/3))*(-11/600*2^(1/3)*((I+3/11*23^(1/2))*3^(1/2)-9/11*I*23^(1/2)-1)*(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*((150*23^(1/2)*3^(1/2)*2^(2/3)+1150*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+9200+(-102*23^(1/2)*3^(1/2)*2^(1/3)+874*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)-n^2+n-2^n
Explicit closed form in latex syntax:
\frac{\left(575 \,2^{\frac{2}{3}} \left(\left(\frac{9 \,\mathrm{I}}{23}-\frac{3 \sqrt{3}}{23}\right) \sqrt{23}+\mathrm{I} \sqrt{3}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200-437 \left(\left(-\frac{153 \,\mathrm{I}}{437}-\frac{51 \sqrt{3}}{437}\right) \sqrt{23}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{1}{3}} \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(-575 \left(\left(\frac{9 \,\mathrm{I}}{23}+\frac{3 \sqrt{3}}{23}\right) \sqrt{23}+\mathrm{I} \sqrt{3}+1\right) 2^{\frac{2}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200+437 \,2^{\frac{1}{3}} \left(\left(-\frac{153 \,\mathrm{I}}{437}+\frac{51 \sqrt{3}}{437}\right) \sqrt{23}+\mathrm{I} \sqrt{3}-1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(-\frac{11 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{3 \sqrt{23}}{11}\right) \sqrt{3}-\frac{9 \,\mathrm{I} \sqrt{23}}{11}-1\right) \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(150 \sqrt{23}\, \sqrt{3}\, 2^{\frac{2}{3}}+1150 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+9200+\left(-102 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}+874 \,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}-n^{2}+n -2^{n}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 57
a(6) = 159
a(n+4) = -2*a(n)+5*a(n+1)-8*a(n+2)+5*a(n+3)-(n+1)*(n-2), n >= 7
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) = 57
a \! \left(6\right) = 159
a \! \left(n +4\right) = -2 a \! \left(n \right)+5 a \! \left(n +1\right)-8 a \! \left(n +2\right)+5 a \! \left(n +3\right)-\left(n +1\right) \left(n -2\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18158/
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[19,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[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[36,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[5,x]
F[23,x] = F[20,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[20,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[20,x]+F[31,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[30,x]
F[36,x] = F[37,x]+F[38,x]+F[63,x]
F[37,x] = 0
F[38,x] = F[12,x]*F[39,x]
F[39,x] = F[40,x]+F[50,x]
F[40,x] = F[41,x]+F[6,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[13,x]+F[44,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[14,x]+F[45,x]
F[48,x] = F[49,x]
F[49,x] = F[12,x]*F[44,x]
F[50,x] = F[36,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[31,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[54,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[31,x]+F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[57,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[74,x]
F[65,x] = F[20,x]+F[66,x]
F[66,x] = F[37,x]+F[67,x]+F[73,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[10,x]+F[70,x]
F[70,x] = F[18,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = F[56,x]
F[73,x] = F[12,x]*F[65,x]
F[74,x] = F[75,x]+F[87,x]
F[75,x] = F[37,x]+F[76,x]+F[85,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[80,x]
F[78,x] = F[14,x]+F[79,x]
F[79,x] = F[46,x]
F[80,x] = F[31,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[31,x]+F[84,x]
F[84,x] = F[82,x]
F[85,x] = F[12,x]*F[86,x]
F[86,x] = F[20,x]+F[75,x]
F[87,x] = 2*F[37,x]+F[88,x]+F[97,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[92,x]
F[90,x] = F[17,x]+F[91,x]
F[91,x] = F[49,x]
F[92,x] = F[55,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[84,x]+F[96,x]
F[96,x] = F[94,x]
F[97,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_{19}\! \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_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{36}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{63}\! \left(x \right)
F_{37}\! \left(x \right) = 0
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_{50}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{6}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{36}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{31}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{31}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{74}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{37}\! \left(x \right)+F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{18}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{56}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{87}\! \left(x \right)
F_{75}\! \left(x \right) = F_{37}\! \left(x \right)+F_{76}\! \left(x \right)+F_{85}\! \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_{80}\! \left(x \right)
F_{78}\! \left(x \right) = F_{14}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{46}\! \left(x \right)
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{31}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{20}\! \left(x \right)+F_{75}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{37}\! \left(x \right)+F_{88}\! \left(x \right)+F_{97}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{17}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{49}\! \left(x \right)
F_{92}\! \left(x \right) = F_{55}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{84}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{94}\! \left(x \right)
F_{97}\! \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_19(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_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_36(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_5(x))
Eq(F_23(x), F_20(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_20(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_20(x) + F_31(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_30(x))
Eq(F_36(x), F_37(x) + F_38(x) + F_63(x))
Eq(F_37(x), 0)
Eq(F_38(x), F_12(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_50(x))
Eq(F_40(x), F_41(x) + F_6(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_13(x) + F_44(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_14(x) + F_45(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_12(x)*F_44(x))
Eq(F_50(x), F_36(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_31(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_54(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_31(x) + F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_12(x)*F_57(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_74(x))
Eq(F_65(x), F_20(x) + F_66(x))
Eq(F_66(x), F_37(x) + F_67(x) + F_73(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_10(x) + F_70(x))
Eq(F_70(x), F_18(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), F_56(x))
Eq(F_73(x), F_12(x)*F_65(x))
Eq(F_74(x), F_75(x) + F_87(x))
Eq(F_75(x), F_37(x) + F_76(x) + F_85(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_80(x))
Eq(F_78(x), F_14(x) + F_79(x))
Eq(F_79(x), F_46(x))
Eq(F_80(x), F_31(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_31(x) + F_84(x))
Eq(F_84(x), F_82(x))
Eq(F_85(x), F_12(x)*F_86(x))
Eq(F_86(x), F_20(x) + F_75(x))
Eq(F_87(x), 2*F_37(x) + F_88(x) + F_97(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_92(x))
Eq(F_90(x), F_17(x) + F_91(x))
Eq(F_91(x), F_49(x))
Eq(F_92(x), F_55(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_84(x) + F_96(x))
Eq(F_96(x), F_94(x))
Eq(F_97(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": [1, 2, 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]]}], "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": [1, 2, 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]]}], "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": [1, 2, 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]]}], "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, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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": [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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 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, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"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": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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": [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], 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"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]]}], "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": [[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]]}], "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": [1, 0, 2], "pos": [[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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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": [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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"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": [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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 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": [0, 1], "pos": [[0, 0], [1, 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