0132_1203_1320_2103
Counting sequence:
1, 1, 2, 6, 20, 62, 178, 488, 1301, 3404, 8786, 22442, 56847, 143008, 357671, 890090, 2205430, 5443658, 13391080, 32841708, 80325794, 195982714, 477103259, 1159108952, 2810787134, 6804386362, 16446183209, 39692437204, 95667111761, 230287727780, 553692960842, 1329812842974, 3190549203788, 7647528447866, 18313965030498, 43819964899580, 104763708644273, 250275318091556, 597463119050570, 1425300182811306, 3397963810617267, 8095845842626520, 19277454450309147, 45876799426349486, 109119830006871230, 259413046436404642, 616406555554791968, 1463993327446803848, 3475488835764568946, 8247183591783140174, 19562120070205526231, 46382457330071025072, 109932431749305005782, 260458452285564146138, 616875548422726882061, 1460524178702626187500, 3456824666475234220325, 8179154100446948769928, 19346688333506097138450, 45748473980258609413238, 108149027453865112123204, 255592873131642933299894, 603891426013483263457874, 1426450449154644363224912, 3368571313644462039878029, 7952970911563933711835132, 18772012885108490824242754, 44298922190718121738174634, 104515155633953895470245271, 246531251405690528442535760, 581398579344322598441505807, 1370843245389002069682893234, 3231587580075711077979287558, 7616592587505948115896643386, 17948346476043055891094466968, 42287231951822544100115018660, 99613282348913386539512240258, 234612110584244389494168559586, 552472558304625451827625111635, 1300768338915803893542061796616, 3062104081556227195525847367662, 7207296691298055989811280759290, 16961293409320446559781444810417, 39909955344311350710899596059716, 93894631404671401012678872851065, 220871157756795643661767235756972, 519490261690836089924277239879258, 1221679682474943009260512132234958, 2872633115385138843969238186494716, 6753783476514697019090796295998194, 15876673296444729546983468874231426, 37318011263626378472720016409748452, 87705180713540092500231540661570217, 206101382018242490689506072535693268, 484268868350429394014665894605408826, 1137740570927985716569300909033866410, 2672711049890386906219815029981649595, 6277891925592627722756446307804957448, 14744487561827672517762428986969544195, 34625853418830909317494330755643190518, 81306852083980145702709043454238033614
Generating function in Maple syntax:
(x^9-2*x^8-x^7+9*x^6-21*x^5+29*x^4-30*x^3+20*x^2-7*x+1)/(x-1)^2/(x^3-2*x^2+3*x-1)^2
Generating function in latex syntax:
\frac{x^{9}-2 x^{8}-x^{7}+9 x^{6}-21 x^{5}+29 x^{4}-30 x^{3}+20 x^{2}-7 x +1}{\left(x -1\right)^{2} \left(x^{3}-2 x^{2}+3 x -1\right)^{2}}
Generating function in sympy syntax:
(x**9 - 2*x**8 - x**7 + 9*x**6 - 21*x**5 + 29*x**4 - 30*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**2*(x**3 - 2*x**2 + 3*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(x-1)^2*(x^3-2*x^2+3*x-1)^2*F(x)+x^9-2*x^8-x^7+9*x^6-21*x^5+29*x^4-30*x^3+20*x^2-7*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right)^{2} \left(x^{3}-2 x^{2}+3 x -1\right)^{2} F \! \left(x \right)+x^{9}-2 x^{8}-x^{7}+9 x^{6}-21 x^{5}+29 x^{4}-30 x^{3}+20 x^{2}-7 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/317400*(644*(((3/14*n-90/161)*23^(1/2)+I*n-205/14*I)*3^(1/2)+(9/14*I*n-270/161*I)*23^(1/2)+n-205/14)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+3565*2^(2/3)*(((3/31*n-645/713)*23^(1/2)+I*n-5*I)*3^(1/2)+(-9/31*I*n+1935/713*I)*23^(1/2)-n+5)*(11+3*23^(1/2)*3^(1/2))^(1/3)+101200*n-423200)*(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)+1/317400*(-3565*2^(2/3)*(((-3/31*n+645/713)*23^(1/2)+I*n-5*I)*3^(1/2)+(-9/31*I*n+1935/713*I)*23^(1/2)+n-5)*(11+3*23^(1/2)*3^(1/2))^(1/3)-644*(((-3/14*n+90/161)*23^(1/2)+I*n-205/14*I)*3^(1/2)+(9/14*I*n-270/161*I)*23^(1/2)-n+205/14)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+101200*n-423200)*(-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)+1/317400*(-690*2^(2/3)*(3^(1/2)*(n-215/23)*23^(1/2)-31/3*n+155/3)*(11+3*23^(1/2)*3^(1/2))^(1/3)-276*(3^(1/2)*(n-60/23)*23^(1/2)+14/3*n-205/3)*2^(1/3)*(11+3*23^(1/2)*3^(1/2))^(2/3)+101200*n-423200)*(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+1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(644 \left(\left(\left(\frac{3 n}{14}-\frac{90}{161}\right) \sqrt{23}+\mathrm{I} n -\frac{205 \,\mathrm{I}}{14}\right) \sqrt{3}+\left(\frac{9 \,\mathrm{I} n}{14}-\frac{270 \,\mathrm{I}}{161}\right) \sqrt{23}+n -\frac{205}{14}\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+3565 \,2^{\frac{2}{3}} \left(\left(\left(\frac{3 n}{31}-\frac{645}{713}\right) \sqrt{23}+\mathrm{I} n -5 \,\mathrm{I}\right) \sqrt{3}+\left(-\frac{9 \,\mathrm{I} n}{31}+\frac{1935 \,\mathrm{I}}{713}\right) \sqrt{23}-n +5\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+101200 n -423200\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}}{317400}\\+\\\frac{\left(-3565 \,2^{\frac{2}{3}} \left(\left(\left(-\frac{3 n}{31}+\frac{645}{713}\right) \sqrt{23}+\mathrm{I} n -5 \,\mathrm{I}\right) \sqrt{3}+\left(-\frac{9 \,\mathrm{I} n}{31}+\frac{1935 \,\mathrm{I}}{713}\right) \sqrt{23}+n -5\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-644 \left(\left(\left(-\frac{3 n}{14}+\frac{90}{161}\right) \sqrt{23}+\mathrm{I} n -\frac{205 \,\mathrm{I}}{14}\right) \sqrt{3}+\left(\frac{9 \,\mathrm{I} n}{14}-\frac{270 \,\mathrm{I}}{161}\right) \sqrt{23}-n +\frac{205}{14}\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+101200 n -423200\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}}{317400}\\+\\\frac{\left(-690 \,2^{\frac{2}{3}} \left(\sqrt{3}\, \left(n -\frac{215}{23}\right) \sqrt{23}-\frac{31 n}{3}+\frac{155}{3}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}-276 \left(\sqrt{3}\, \left(n -\frac{60}{23}\right) \sqrt{23}+\frac{14 n}{3}-\frac{205}{3}\right) 2^{\frac{1}{3}} \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+101200 n -423200\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}}{317400}\\-n +1 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 178
a(7) = 488
a(8) = 1301
a(9) = 3404
a(n+6) = -a(n)+4*a(n+1)-10*a(n+2)+14*a(n+3)-13*a(n+4)+6*a(n+5)-n-1, 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) = 62
a \! \left(6\right) = 178
a \! \left(7\right) = 488
a \! \left(8\right) = 1301
a \! \left(9\right) = 3404
a \! \left(n +6\right) = -a \! \left(n \right)+4 a \! \left(n +1\right)-10 a \! \left(n +2\right)+14 a \! \left(n +3\right)-13 a \! \left(n +4\right)+6 a \! \left(n +5\right)-n -1, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15563/
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[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[7,x]
F[14,x] = F[15,x]+F[16,x]+F[23,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[22,x]+F[7,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[22,x]+F[28,x]
F[28,x] = F[26,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[15,x]+F[31,x]+F[72,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[45,x]
F[33,x] = F[34,x]+F[7,x]
F[34,x] = F[15,x]+F[16,x]+F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[24,x]+F[37,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[18,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[38,x]+F[44,x]
F[44,x] = F[42,x]
F[45,x] = F[46,x]+F[52,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[2,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[49,x]
F[52,x] = 2*F[15,x]+F[53,x]+F[70,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[50,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[55,x]
F[58,x] = F[59,x]+F[66,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[59,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[38,x]+F[7,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[59,x]+F[69,x]
F[69,x] = F[67,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[61,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[49,x]+F[74,x]
F[74,x] = F[62,x]+F[75,x]
F[75,x] = F[60,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_{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_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \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_{22}\! \left(x \right)+F_{7}\! \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_{22}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{72}\! \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_{45}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{7}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{52}\! \left(x \right)
F_{46}\! \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_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{53}\! \left(x \right)+F_{70}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \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_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{66}\! \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_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{38}\! \left(x \right)+F_{7}\! \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_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{61}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{49}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{62}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{60}\! \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_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_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_23(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_22(x) + F_7(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_22(x) + F_28(x))
Eq(F_28(x), F_26(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_15(x) + F_31(x) + F_72(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_45(x))
Eq(F_33(x), F_34(x) + F_7(x))
Eq(F_34(x), F_15(x) + F_16(x) + F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_24(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_18(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_38(x) + F_44(x))
Eq(F_44(x), F_42(x))
Eq(F_45(x), F_46(x) + F_52(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_2(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_49(x))
Eq(F_52(x), 2*F_15(x) + F_53(x) + F_70(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_50(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_55(x))
Eq(F_58(x), F_59(x) + F_66(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_59(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_38(x) + F_7(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_59(x) + F_69(x))
Eq(F_69(x), F_67(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_61(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_49(x) + F_74(x))
Eq(F_74(x), F_62(x) + F_75(x))
Eq(F_75(x), F_60(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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[0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], 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