0132_0213_0321_1230_1302
Counting sequence:
1, 1, 2, 6, 19, 54, 145, 382, 1001, 2619, 6849, 17909, 46831, 122472, 320322, 837880, 2191888, 5734457, 15003746, 39258792, 102730808, 268836405, 703552379, 1841295278, 4819111920, 12613200755, 33013888778, 86413118795, 226189790660, 592073314343, 1549837342951, 4056990486991, 10620092115457, 27800863497303, 72776867067830, 190516646501908, 498742639080222, 1305640521765676, 3418014454808623, 8948020493024134, 23425158169198884, 61325387677241766, 160546201211027887, 420302048820942921, 1100333984812770254, 2880639554918575394, 7541444381589740855, 19743367435749556222, 51687899709363292661, 135318569053302383134, 354263709811920220209, 927463034528367609999, 2428103248849119941741, 6356795231316361909537, 16642162766986109538407, 43569414851781595903620, 114065435010302647957498, 298625386602565142679672, 781807229405960853841756, 2046788175816088020489757, 5358538407850917659750318, 14028783133369535185601520, 36727708903739840274973764, 96154106250839316771520493, 251734058130414668907191155, 659046785550817856666381370, 1725403316862994614637931988, 4517156233521843353320298335, 11826049269882069283165984570, 30960954116036566991106931583, 81056725994088848865329479436, 212209021420168759978389983631, 555569867636423540334945839867, 1454499487407103845249921356643, 3807926051152820509928537432165, 9969272753289157368895006273223, 26099878463210187605030462804082, 68330330681920346616813414924116, 178891039297534403425072232823758, 468342614518971170864430551960024, 1226136402799855869597593359369019, 3210065660600433655984079249114906, 8404058409388291538869112952666772, 22002104523825782606484579793335586, 57602243436819225555195379574276239, 150804598528686565031725646566092609, 394811488782205485554493636924377690, 1033629720507445767004654072481906062, 2706077330284804080521764939381784571, 7084601474234916535016244282495424774, 18547725241683967051142084609154398569, 48558569948377821342406448933313987214, 127127974601491914155291950490558371401, 332825330604367520739735705362031028227, 871347963157895449278281136855349016617, 2281218433209676448684887701635889937485, 5972307044347906758733256317651983837983, 15635702020729931971420310278515117174512, 40934797439116365484919992896711082311266, 107168686626527590045662639843280825482472, 280571253908538616824157633197679107652328
Generating function in Maple syntax:
(2*x^6-6*x^5+6*x^4-12*x^3+13*x^2-6*x+1)/(x-1)/(x^2-3*x+1)/(x^3-2*x^2+3*x-1)
Generating function in latex syntax:
\frac{2 x^{6}-6 x^{5}+6 x^{4}-12 x^{3}+13 x^{2}-6 x +1}{\left(x -1\right) \left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right)}
Generating function in sympy syntax:
(2*x**6 - 6*x**5 + 6*x**4 - 12*x**3 + 13*x**2 - 6*x + 1)/((x - 1)*(x**2 - 3*x + 1)*(x**3 - 2*x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2-3*x+1)*(x^3-2*x^2+3*x-1)*F(x)-2*x^6+6*x^5-6*x^4+12*x^3-13*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}-3 x +1\right) \left(x^{3}-2 x^{2}+3 x -1\right) F \! \left(x \right)-2 x^{6}+6 x^{5}-6 x^{4}+12 x^{3}-13 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/13800*(299*2^(1/3)*((I-77/299*23^(1/2))*3^(1/2)-231/299*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(2/3)+4600-1265*2^(2/3)*((I-1/253*23^(1/2))*3^(1/2)+3/253*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*(1265*2^(2/3)*((I+1/253*23^(1/2))*3^(1/2)+3/253*I*23^(1/2)+1)*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600-299*((I+77/299*23^(1/2))*3^(1/2)-231/299*I*23^(1/2)-1)*2^(1/3)*(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*((-10*3^(1/2)*2^(2/3)*23^(1/2)-2530*2^(2/3))*(11+3*23^(1/2)*3^(1/2))^(1/3)+4600+(154*23^(1/2)*3^(1/2)*2^(1/3)-598*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)+1/5*5^(1/2)*(3/2-1/2*5^(1/2))^(-n)-1/5*5^(1/2)*(3/2+1/2*5^(1/2))^(-n)-2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(299 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{77 \sqrt{23}}{299}\right) \sqrt{3}-\frac{231 \,\mathrm{I} \sqrt{23}}{299}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{2}{3}}+4600-1265 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}-\frac{\sqrt{23}}{253}\right) \sqrt{3}+\frac{3 \,\mathrm{I} \sqrt{23}}{253}-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(1265 \,2^{\frac{2}{3}} \left(\left(\mathrm{I}+\frac{\sqrt{23}}{253}\right) \sqrt{3}+\frac{3 \,\mathrm{I} \sqrt{23}}{253}+1\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600-299 \left(\left(\mathrm{I}+\frac{77 \sqrt{23}}{299}\right) \sqrt{3}-\frac{231 \,\mathrm{I} \sqrt{23}}{299}-1\right) 2^{\frac{1}{3}} \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(-10 \sqrt{3}\, 2^{\frac{2}{3}} \sqrt{23}-2530 \,2^{\frac{2}{3}}\right) \left(11+3 \sqrt{23}\, \sqrt{3}\right)^{\frac{1}{3}}+4600+\left(154 \sqrt{23}\, \sqrt{3}\, 2^{\frac{1}{3}}-598 \,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{\sqrt{5}\, \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{5}-\frac{\sqrt{5}\, \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{5}-2 & \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) = 54
a(6) = 145
a(n+5) = a(n)-5*a(n+1)+10*a(n+2)-12*a(n+3)+6*a(n+4)-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) = 54
a \! \left(6\right) = 145
a \! \left(n +5\right) = a \! \left(n \right)-5 a \! \left(n +1\right)+10 a \! \left(n +2\right)-12 a \! \left(n +3\right)+6 a \! \left(n +4\right)-2, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18259/
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[12,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[16,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[33,x]
F[28,x] = 0
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[24,x]
F[32,x] = F[27,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[20,x]+F[35,x]
F[35,x] = F[28,x]+F[36,x]+F[40,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[12,x]
F[39,x] = F[35,x]
F[40,x] = F[12,x]*F[20,x]
F[41,x] = F[28,x]+F[42,x]+F[69,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[48,x]
F[44,x] = F[45,x]+F[6,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[10,x]
F[48,x] = F[41,x]+F[49,x]
F[49,x] = 2*F[28,x]+F[50,x]+F[54,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[45,x]
F[53,x] = F[49,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[28,x]+F[57,x]+F[67,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[10,x]+F[60,x]
F[60,x] = F[46,x]
F[61,x] = F[56,x]+F[62,x]
F[62,x] = 2*F[28,x]+F[54,x]+F[63,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[60,x]
F[66,x] = F[62,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[20,x]+F[56,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[68,x]+F[71,x]
F[71,x] = F[72,x]+F[74,x]
F[72,x] = F[28,x]+F[36,x]+F[73,x]
F[73,x] = F[12,x]*F[34,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[71,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_{12}\! \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_{41}\! \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_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \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_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{41}\! \left(x \right) = F_{28}\! \left(x \right)+F_{42}\! \left(x \right)+F_{69}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{6}\! \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_{10}\! \left(x \right)
F_{48}\! \left(x \right) = F_{41}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{45}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{28}\! \left(x \right)+F_{57}\! \left(x \right)+F_{67}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{10}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{46}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{54}\! \left(x \right)+F_{63}\! \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_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{60}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \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_12(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_41(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_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_16(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_33(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_24(x))
Eq(F_32(x), F_27(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_20(x) + F_35(x))
Eq(F_35(x), F_28(x) + F_36(x) + F_40(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_12(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_12(x)*F_20(x))
Eq(F_41(x), F_28(x) + F_42(x) + F_69(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_48(x))
Eq(F_44(x), F_45(x) + F_6(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_10(x))
Eq(F_48(x), F_41(x) + F_49(x))
Eq(F_49(x), 2*F_28(x) + F_50(x) + F_54(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_45(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_28(x) + F_57(x) + F_67(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_10(x) + F_60(x))
Eq(F_60(x), F_46(x))
Eq(F_61(x), F_56(x) + F_62(x))
Eq(F_62(x), 2*F_28(x) + F_54(x) + F_63(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_60(x))
Eq(F_66(x), F_62(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_20(x) + F_56(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_68(x) + F_71(x))
Eq(F_71(x), F_72(x) + F_74(x))
Eq(F_72(x), F_28(x) + F_36(x) + F_73(x))
Eq(F_73(x), F_12(x)*F_34(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_71(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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 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": 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"RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 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3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 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], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], 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