0231_0321_1032_3012_3102
Counting sequence:
1, 1, 2, 6, 19, 52, 139, 372, 991, 2636, 7011, 18644, 49575, 131820, 350507, 931988, 2478127, 6589260, 17520627, 46586772, 123872695, 329373420, 875793083, 2328704980, 6191949887, 16464190924, 43777741699, 116403574100, 309513271751, 822985601004, 2188291621963, 5818595388436, 15471453600847, 41138085834060, 109384816045843, 290850625127444, 773362237968855, 2056344733156844, 5467752954537435, 14538575118169428, 38657592657189983, 102789266341624268, 273313275576777379, 726731002809558996, 1932353813879143911, 5138065181721401580, 13661946182941065067, 36326665175361819540, 96591406897107507311, 256833371335458964300, 682911479918749074995, 1815839144967172128916, 4828256512524011261431, 12838175129852692801772, 34136285062163741122811, 90767258279228197570260, 241347151880325521866879, 641734132164206723549644, 1706349932767195364106691, 4537128301459248495496788, 12064074800014105802199559, 32077977767021850828109292, 85294286936976304449411723, 226794701241002671331331860, 603039644953025348768294031, 1603462565021005977766743372, 4263554177477042646964444499, 11336650209881141969232220436, 30143779727281338540962372119, 80151318019397904345085853676, 213119716185839431169598520347, 566678309845639443766207638612, 1506778971915914127392185504927, 4006475686049146560889775689164, 10653086963705486136704152160483, 28326207557291947089082451019988, 75318453450387673436648605578791, 200269288385478266235787966498540, 532509445335928100086389440615851, 1415925085958109813281864058887828, 3764898194023104259121693491388591, 10010740364676174531698029922896716, 26618229095291672949081481454957683, 70776994943305728948104379815589268, 188193699711255479908686300931929655, 500400852556400034663639944589363948, 1330549394710667007132174949741836091, 3537887041400245008745362445936895444, 9407125182623957093950179730794354879, 25013236196069493210910071807009277388, 66509371657563433533261048236686700547, 176846229876444274465332527741971388244, 470228303802590968885746247334648031815, 1250321580796753079303347118884640852972, 3324563925148985676423105540587872514251, 8839906038699906369921050694729681945108, 23505019164142304574871901167816518110415, 62499072217282486872511064111538463194444, 166182975676107091059736130780352808389523, 441875061897781278141727128007877116194324, 1174931243906234621088212515019183967167063
Generating function in Maple syntax:
(x^5+4*x^4-2*x+1)/(x-1)/(2*x^3+x^2+2*x-1)
Generating function in latex syntax:
\frac{x^{5}+4 x^{4}-2 x +1}{\left(x -1\right) \left(2 x^{3}+x^{2}+2 x -1\right)}
Generating function in sympy syntax:
(x**5 + 4*x**4 - 2*x + 1)/((x - 1)*(2*x**3 + x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(2*x^3+x^2+2*x-1)*F(x)+x^5+4*x^4-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(2 x^{3}+x^{2}+2 x -1\right) F \! \left(x \right)+x^{5}+4 x^{4}-2 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/171336*(((-440*59^(1/2)+649*I)*3^(1/2)-1320*I*59^(1/2)+649)*(71+6*59^(1/2)*3^(1/2))^(1/3)-14278+((226*59^(1/2)+3481*I)*3^(1/2)-678*I*59^(1/2)-3481)*(71+6*59^(1/2)*3^(1/2))^(2/3))*(1/1452*((71*I+6*59^(1/2))*3^(1/2)-18*I*59^(1/2)-71)*(71+6*59^(1/2)*3^(1/2))^(2/3)-1/12*I*3^(1/2)*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/12*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/6)^(-n)+1/171336*(((226*59^(1/2)-3481*I)*3^(1/2)+678*I*59^(1/2)-3481)*(71+6*59^(1/2)*3^(1/2))^(2/3)-14278+((-440*59^(1/2)-649*I)*3^(1/2)+1320*I*59^(1/2)+649)*(71+6*59^(1/2)*3^(1/2))^(1/3))*(1/1452*((-71*I+6*59^(1/2))*3^(1/2)+18*I*59^(1/2)-71)*(71+6*59^(1/2)*3^(1/2))^(2/3)+1/12*I*3^(1/2)*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/12*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/6)^(-n)-1+1/171336*((-452*59^(1/2)*3^(1/2)+6962)*(71+6*59^(1/2)*3^(1/2))^(2/3)+880*(71+6*59^(1/2)*3^(1/2))^(1/3)*59^(1/2)*3^(1/2)-1298*(71+6*59^(1/2)*3^(1/2))^(1/3)-14278)*(1/6*(71+6*59^(1/2)*3^(1/2))^(1/3)-1/6+71/726*(71+6*59^(1/2)*3^(1/2))^(2/3)-1/121*(71+6*59^(1/2)*3^(1/2))^(2/3)*59^(1/2)*3^(1/2))^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(\left(\left(-440 \sqrt{59}+649 \,\mathrm{I}\right) \sqrt{3}-1320 \,\mathrm{I} \sqrt{59}+649\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-14278+\left(\left(226 \sqrt{59}+3481 \,\mathrm{I}\right) \sqrt{3}-678 \,\mathrm{I} \sqrt{59}-3481\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(71 \,\mathrm{I}+6 \sqrt{59}\right) \sqrt{3}-18 \,\mathrm{I} \sqrt{59}-71\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{1452}-\frac{\mathrm{I} \sqrt{3}\, \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{1}{6}\right)^{-n}}{171336}\\+\\\frac{\left(\left(\left(226 \sqrt{59}-3481 \,\mathrm{I}\right) \sqrt{3}+678 \,\mathrm{I} \sqrt{59}-3481\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}-14278+\left(\left(-440 \sqrt{59}-649 \,\mathrm{I}\right) \sqrt{3}+1320 \,\mathrm{I} \sqrt{59}+649\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-71 \,\mathrm{I}+6 \sqrt{59}\right) \sqrt{3}+18 \,\mathrm{I} \sqrt{59}-71\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{1452}+\frac{\mathrm{I} \sqrt{3}\, \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{1}{6}\right)^{-n}}{171336}\\-1+\\\frac{\left(\left(-452 \sqrt{59}\, \sqrt{3}+6962\right) \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}+880 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{59}\, \sqrt{3}-1298 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-14278\right) \left(\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{6}+\frac{71 \left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{726}-\frac{\left(71+6 \sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{59}\, \sqrt{3}}{121}\right)^{-n}}{171336} & \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) = 52
a(n+3) = 2*a(n)+a(n+1)+2*a(n+2)+4, n >= 6
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) = 52
a \! \left(n +3\right) = 2 a \! \left(n \right)+a \! \left(n +1\right)+2 a \! \left(n +2\right)+4, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/20807/
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[22,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[14,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[17,x]*F[4,x]
F[22,x] = F[23,x]+F[35,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[1,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[13,x]*F[4,x]
F[29,x] = F[23,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[23,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[23,x]*F[4,x]
F[35,x] = F[36,x]+F[37,x]+F[55,x]
F[36,x] = 0
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[44,x]
F[39,x] = F[17,x]+F[40,x]
F[40,x] = F[36,x]+F[41,x]+F[42,x]
F[41,x] = F[16,x]*F[4,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[20,x]+F[4,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[36,x]+F[37,x]+F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[23,x]+F[45,x]
F[48,x] = 2*F[36,x]+F[49,x]+F[53,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[45,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[45,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[33,x]+F[51,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[22,x]+F[57,x]
F[57,x] = F[58,x]+F[68,x]
F[58,x] = F[36,x]+F[59,x]+F[67,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[4,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = x^2
F[64,x] = F[33,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[33,x]*F[4,x]
F[67,x] = F[32,x]*F[4,x]
F[68,x] = 2*F[36,x]+F[69,x]+F[77,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[20,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[20,x]*F[4,x]
F[74,x] = F[51,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[51,x]
F[77,x] = F[4,x]*F[50,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_{22}\! \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_{14}\! \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_{1}\! \left(x \right)+F_{4}\! \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_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{35}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \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_{23}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{55}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{20}\! \left(x \right)+F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{23}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{33}\! \left(x \right)+F_{51}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{22}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{68}\! \left(x \right)
F_{58}\! \left(x \right) = F_{36}\! \left(x \right)+F_{59}\! \left(x \right)+F_{67}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = x^{2}
F_{64}\! \left(x \right) = F_{33}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{69}\! \left(x \right)+F_{77}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{74}\! \left(x \right) = F_{51}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \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_22(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_14(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_17(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_35(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_1(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_13(x)*F_4(x))
Eq(F_29(x), F_23(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_23(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_23(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_55(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_44(x))
Eq(F_39(x), F_17(x) + F_40(x))
Eq(F_40(x), F_36(x) + F_41(x) + F_42(x))
Eq(F_41(x), F_16(x)*F_4(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_20(x) + F_4(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_36(x) + F_37(x) + F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_23(x) + F_45(x))
Eq(F_48(x), 2*F_36(x) + F_49(x) + F_53(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_45(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_45(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_33(x) + F_51(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_22(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_68(x))
Eq(F_58(x), F_36(x) + F_59(x) + F_67(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_4(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), x**2)
Eq(F_64(x), F_33(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_33(x)*F_4(x))
Eq(F_67(x), F_32(x)*F_4(x))
Eq(F_68(x), 2*F_36(x) + F_69(x) + F_77(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_20(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_20(x)*F_4(x))
Eq(F_74(x), F_51(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_51(x))
Eq(F_77(x), F_4(x)*F_50(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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