0132_0231_0312_1230_2130
Counting sequence:
1, 1, 2, 6, 19, 58, 170, 485, 1363, 3801, 10560, 29286, 81153, 224798, 622604, 1724257, 4775069, 13223673, 36620342, 101412574, 280841223, 777731626, 2153766438, 5964409141, 16517192863, 45740936161, 126670025060, 350786332206, 971429908069, 2690173417438, 7449876676856, 20630886521633, 57132956305945, 158217859073553, 438151507436874, 1213369619543574, 3360175210267995, 9305307518697914, 25769116965369986, 71362218587680741, 197622846316370891, 547275437326802697, 1515565684251718760, 4197044461744725334, 11622843138309260841, 32187050637434776894, 89135353235739796164, 246841852208093873473, 683577254025976602229, 1893025263105575730505, 5242340387498844463934, 14517573153416934264750, 40203404335857534062095, 111334980241654512386794, 308319109542522937364414, 853825752721771833769973, 2364493128864447076333783, 6547972743414092332597329, 18133250854099601755229772, 50216272947749160009427422, 139063540732561970605651533, 385107600104036353562758718, 1066475532527296250092053872, 2953382538210414367319056321, 8178779682207983205427875761, 22649432040940831499056626849, 62722898978824925659061063186, 173698044577741928683554440614, 481020666795341691890658887715, 1332086854787108072647483287994, 3688937942143724454735345419226, 10215747638439406983449211859813, 28290391827961604568259773450691, 78344365787589131176065453914041, 216958453173245195943385800153872, 600821385560108061222351720000966, 1663850069294668118899734813765841, 4607687275497141491420238521453278, 12760033142756864416583332470597884, 35336262222068119877229493704109217, 97856440798944636706525387163186125, 270993093317522654658930000256050201, 750459101375691447147494107309076934, 2078240651608496323490077708834370046, 5755255946767320177981669019450086807, 15937986290069155657602423456824970794, 44136943575048643118315679059859199190, 122228100381844093875326282742202717237, 338485343860552794165265592623573927055, 937364874774862931738786174188378266945, 2595837380845880094926419212683763594932, 7188632611623330147205737056486486448910, 19907425328798973278429578130964074022837, 55129480755619469783009416549089499218718, 152669649549682766217804408572790910086504, 422786893222227802148833387300247305068001, 1170820510872620110011705169877040504340681, 3242344288945315294104086530903665118045105, 8978999249185553574449387810134202154867290, 24865473969483965539255782069375981850902198, 68859766948211658337422044928897408515889259
Generating function in Maple syntax:
-(x^5-4*x^4+7*x^3-9*x^2+5*x-1)/(x^3-x^2+3*x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{x^{5}-4 x^{4}+7 x^{3}-9 x^{2}+5 x -1}{\left(x^{3}-x^{2}+3 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**5 + 4*x**4 - 7*x**3 + 9*x**2 - 5*x + 1)/((x - 1)**3*(x**3 - x**2 + 3*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^3-x^2+3*x-1)*(x-1)^3*F(x)+x^5-4*x^4+7*x^3-9*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-x^{2}+3 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{5}-4 x^{4}+7 x^{3}-9 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
1/29184*(((-80*3^(1/2)-240*I)*19^(1/2)+304*I*3^(1/2)+304)*(1+3*19^(1/2)*3^(1/2))^(1/3)+4864+((39*I-13*3^(1/2))*19^(1/2)+209*I*3^(1/2)-209)*(1+3*19^(1/2)*3^(1/2))^(2/3))*(1/384*((I+3*19^(1/2))*3^(1/2)-9*I*19^(1/2)-1)*(1+3*19^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(1+3*19^(1/2)*3^(1/2))^(1/3)-1/6*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)+1/29184*(((240*I-80*3^(1/2))*19^(1/2)-304*I*3^(1/2)+304)*(1+3*19^(1/2)*3^(1/2))^(1/3)+4864+((-39*I-13*3^(1/2))*19^(1/2)-209*I*3^(1/2)-209)*(1+3*19^(1/2)*3^(1/2))^(2/3))*(1/384*((-I+3*19^(1/2))*3^(1/2)+9*I*19^(1/2)-1)*(1+3*19^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(1+3*19^(1/2)*3^(1/2))^(1/3)-1/6*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)+1/29184*((160*19^(1/2)*3^(1/2)-608)*(1+3*19^(1/2)*3^(1/2))^(1/3)+26*(1+3*19^(1/2)*3^(1/2))^(2/3)*19^(1/2)*3^(1/2)+418*(1+3*19^(1/2)*3^(1/2))^(2/3)+4864)*(1/3*(1+3*19^(1/2)*3^(1/2))^(1/3)+1/3+1/192*(1+3*19^(1/2)*3^(1/2))^(2/3)-1/64*(1+3*19^(1/2)*3^(1/2))^(2/3)*19^(1/2)*3^(1/2))^(-n)-1/4*n^2-1/4*n+1/2
Explicit closed form in latex syntax:
\frac{\left(\left(\left(-80 \sqrt{3}-240 \,\mathrm{I}\right) \sqrt{19}+304 \,\mathrm{I} \sqrt{3}+304\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}+4864+\left(\left(39 \,\mathrm{I}-13 \sqrt{3}\right) \sqrt{19}+209 \,\mathrm{I} \sqrt{3}-209\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(\mathrm{I}+3 \sqrt{19}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{19}-1\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}-\frac{\mathrm{I} \sqrt{3}\, \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{29184}+\frac{\left(\left(\left(240 \,\mathrm{I}-80 \sqrt{3}\right) \sqrt{19}-304 \,\mathrm{I} \sqrt{3}+304\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}+4864+\left(\left(-39 \,\mathrm{I}-13 \sqrt{3}\right) \sqrt{19}-209 \,\mathrm{I} \sqrt{3}-209\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(-\mathrm{I}+3 \sqrt{19}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{19}-1\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{384}+\frac{\mathrm{I} \sqrt{3}\, \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{29184}+\frac{\left(\left(160 \sqrt{19}\, \sqrt{3}-608\right) \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}+26 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{19}\, \sqrt{3}+418 \left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}+4864\right) \left(\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}+\frac{1}{3}+\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}}}{192}-\frac{\left(1+3 \sqrt{19}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{19}\, \sqrt{3}}{64}\right)^{-n}}{29184}-\frac{n^{2}}{4}-\frac{n}{4}+\frac{1}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(n+3) = a(n)-a(n+1)+3*a(n+2)+1/2*n*(n+3), 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) = 58
a \! \left(n +3\right) = a \! \left(n \right)-a \! \left(n +1\right)+3 a \! \left(n +2\right)+\frac{n \left(n +3\right)}{2}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18607/
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[20,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[19,x]
F[19,x] = F[10,x]+F[17,x]
F[20,x] = F[21,x]+F[27,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[16,x]+F[24,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[24,x]
F[27,x] = F[28,x]+F[29,x]+F[68,x]
F[28,x] = 0
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[42,x]
F[31,x] = F[32,x]+F[6,x]
F[32,x] = F[18,x]+F[28,x]+F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[13,x]+F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[14,x]+F[36,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[17,x]+F[39,x]
F[42,x] = F[27,x]+F[43,x]
F[43,x] = 2*F[28,x]+F[44,x]+F[59,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[46,x]+F[56,x]
F[46,x] = F[28,x]+F[47,x]+F[57,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[10,x]+F[50,x]
F[50,x] = F[18,x]+F[28,x]+F[51,x]
F[51,x] = F[12,x]*F[13,x]
F[52,x] = F[46,x]+F[53,x]
F[53,x] = 2*F[28,x]+F[44,x]+F[54,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[25,x]+F[56,x]
F[56,x] = F[44,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[21,x]+F[46,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[55,x]+F[61,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[63,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[25,x]+F[62,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[56,x]+F[65,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[58,x]+F[70,x]
F[70,x] = F[71,x]+F[81,x]
F[71,x] = F[28,x]+F[72,x]+F[79,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[14,x]+F[36,x]
F[75,x] = F[25,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[25,x]+F[76,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[21,x]+F[71,x]
F[81,x] = 2*F[28,x]+F[82,x]+F[91,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[86,x]
F[84,x] = F[17,x]+F[85,x]
F[85,x] = F[40,x]
F[86,x] = F[56,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[56,x]+F[90,x]
F[90,x] = F[88,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[46,x]+F[81,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_{20}\! \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_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{27}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{16}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{68}\! \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_{42}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{6}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{27}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{44}\! \left(x \right)+F_{59}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right)+F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{10}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{44}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{44}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{21}\! \left(x \right)+F_{46}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{55}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \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_{25}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{56}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{58}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{81}\! \left(x \right)
F_{71}\! \left(x \right) = F_{28}\! \left(x \right)+F_{72}\! \left(x \right)+F_{79}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{75}\! \left(x \right) = F_{25}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{25}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{21}\! \left(x \right)+F_{71}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{82}\! \left(x \right)+F_{91}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{17}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{40}\! \left(x \right)
F_{86}\! \left(x \right) = F_{56}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{56}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{46}\! \left(x \right)+F_{81}\! \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_20(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_19(x))
Eq(F_19(x), F_10(x) + F_17(x))
Eq(F_20(x), F_21(x) + F_27(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_16(x) + F_24(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_24(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_68(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_42(x))
Eq(F_31(x), F_32(x) + F_6(x))
Eq(F_32(x), F_18(x) + F_28(x) + F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_13(x) + F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_14(x) + F_36(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_17(x) + F_39(x))
Eq(F_42(x), F_27(x) + F_43(x))
Eq(F_43(x), 2*F_28(x) + F_44(x) + F_59(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_56(x))
Eq(F_46(x), F_28(x) + F_47(x) + F_57(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_10(x) + F_50(x))
Eq(F_50(x), F_18(x) + F_28(x) + F_51(x))
Eq(F_51(x), F_12(x)*F_13(x))
Eq(F_52(x), F_46(x) + F_53(x))
Eq(F_53(x), 2*F_28(x) + F_44(x) + F_54(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_25(x) + F_56(x))
Eq(F_56(x), F_44(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_21(x) + F_46(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_55(x) + F_61(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_25(x) + F_62(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_56(x) + F_65(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_58(x) + F_70(x))
Eq(F_70(x), F_71(x) + F_81(x))
Eq(F_71(x), F_28(x) + F_72(x) + F_79(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_14(x) + F_36(x))
Eq(F_75(x), F_25(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_25(x) + F_76(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_21(x) + F_71(x))
Eq(F_81(x), 2*F_28(x) + F_82(x) + F_91(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_86(x))
Eq(F_84(x), F_17(x) + F_85(x))
Eq(F_85(x), F_40(x))
Eq(F_86(x), F_56(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_56(x) + F_90(x))
Eq(F_90(x), F_88(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_46(x) + F_81(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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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], [0, 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, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 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], [0, 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, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 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], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 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, 2], "pos": [[0, 0], [0, 0], [0, 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, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 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[[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "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": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 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