0132_0213_1230_1320_2130
Counting sequence:
1, 1, 2, 6, 19, 56, 150, 373, 884, 2036, 4623, 10452, 23684, 53999, 124112, 287700, 672305, 1582262, 3746076, 8911739, 21280706, 50964298, 122318829, 294052522, 707741098, 1704909565, 4109616542, 9910545186, 23907501487, 57686052500, 139212548514, 335997546433, 811015574192, 1957704569216, 4725878658699, 11408543390976, 27541422714224, 66488801104811, 160514689813868, 387510926746992, 935524418382989, 2258539517612882, 5452569679965480, 13163622588193223, 31779721120733246, 76722908862259222, 185225279527177449, 447173037073654102, 1079570638340912086, 2606313126848921209, 6292194923896062266, 15190699712959212606, 36673588947454817995, 88537868664659619440, 213749311479502289070, 516036467152312606477, 1245822205332930681452, 3007680810982181503628, 7261183716914086888455, 17530048062581694448428, 42321279541360129074908, 102172606649241004413671, 246666492021843423289352, 595505589344532827837196, 1437677668488959561122409, 3470860922662216268657006, 8379399507785759978670900, 20229659928310530363883283, 48838719348075197743135034, 117907098597589973982391906, 284652916499055662853093093, 687212931523017833899888642, 1659078779425598442919494274, 4005370490177815396060851829, 9669819759458504114383979222, 23345010008564643301091792730, 56359839775716996483525741415, 136064689558568717043315078092, 328489218890506883655588937146, 793043127335729240090351502169, 1914575473555641961076140303016, 4622194074436638125512149503768, 11158963622411898771322172328579, 26940121319232521799653922324312, 65039206260831168669067723174088, 157018533840819811784449225802915, 379076273942347771007507005897892, 915171081725313725256831916413096, 2209418437392644811613691607018437, 5334007956510061989940883826492170, 12877434350411881942817039231640384, 31088876657332373268032380713693023, 75055187665074249542112359318131382, 181199251987476976927075806452774446, 437453691640021825672895528268951009, 1056106635267510187882030146441913006, 2549666962175025112719045971235785134, 6155440559617532446365383853337382641, 14860548081410044241327469233893620338, 35876536722437546051647551613897416822, 86613621526285013848382072924286311299
Generating function in Maple syntax:
(3*x^9+5*x^8-4*x^7+7*x^5-12*x^4-4*x^3+12*x^2-6*x+1)/(x^2+2*x-1)/(x^2+x-1)^2/(x-1)^3
Generating function in latex syntax:
\frac{3 x^{9}+5 x^{8}-4 x^{7}+7 x^{5}-12 x^{4}-4 x^{3}+12 x^{2}-6 x +1}{\left(x^{2}+2 x -1\right) \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**9 + 5*x**8 - 4*x**7 + 7*x**5 - 12*x**4 - 4*x**3 + 12*x**2 - 6*x + 1)/((x - 1)**3*(x**2 + x - 1)**2*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+2*x-1)*(x^2+x-1)^2*(x-1)^3*F(x)-3*x^9-5*x^8+4*x^7-7*x^5+12*x^4+4*x^3-12*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+2 x -1\right) \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)-3 x^{9}-5 x^{8}+4 x^{7}-7 x^{5}+12 x^{4}+4 x^{3}-12 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/100*((-60*n+338)*5^(1/2)+140*n-750)*(-1/2*5^(1/2)-1/2)^(-n)+1/100*((60*n-338)*5^(1/2)+140*n-750)*(1/2*5^(1/2)-1/2)^(-n)+1/100*(-50*2^(1/2)-25)*(-1-2^(1/2))^(-n)+1/100*(50*2^(1/2)-25)*(2^(1/2)-1)^(-n)-1/2*n^2+13/2*n+27/2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(-60 n +338\right) \sqrt{5}+140 n -750\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{100}+\\\frac{\left(\left(60 n -338\right) \sqrt{5}+140 n -750\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{100}+\\\frac{\left(-50 \sqrt{2}-25\right) \left(-1-\sqrt{2}\right)^{-n}}{100}+\frac{\left(50 \sqrt{2}-25\right) \left(\sqrt{2}-1\right)^{-n}}{100}-\frac{n^{2}}{2}+\frac{13 n}{2}\\+\frac{27}{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) = 56
a(6) = 150
a(7) = 373
a(8) = 884
a(9) = 2036
a(n+6) = n^2+a(n)+4*a(n+1)+2*a(n+2)-6*a(n+3)-2*a(n+4)+4*a(n+5)-17*n-6, 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 150
a \! \left(7\right) = 373
a \! \left(8\right) = 884
a \! \left(9\right) = 2036
a \! \left(n +6\right) = n^{2}+a \! \left(n \right)+4 a \! \left(n +1\right)+2 a \! \left(n +2\right)-6 a \! \left(n +3\right)-2 a \! \left(n +4\right)+4 a \! \left(n +5\right)-17 n -6, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18462/
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[23,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[21,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[14,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[13,x]
F[23,x] = F[14,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[79,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[49,x]
F[28,x] = F[29,x]+F[6,x]
F[29,x] = F[25,x]+F[30,x]+F[31,x]
F[30,x] = F[10,x]*F[12,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[12,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[12,x]*F[33,x]
F[36,x] = F[37,x]+F[47,x]
F[37,x] = F[25,x]+F[38,x]+F[39,x]
F[38,x] = x^2
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[12,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = x^2
F[44,x] = F[37,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[37,x]
F[47,x] = F[48,x]
F[48,x] = F[12,x]*F[36,x]
F[49,x] = F[24,x]+F[50,x]
F[50,x] = 2*F[25,x]+F[51,x]+F[64,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[25,x]+F[53,x]+F[62,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[10,x]+F[56,x]
F[56,x] = F[25,x]+F[30,x]+F[35,x]
F[57,x] = F[52,x]+F[58,x]
F[58,x] = 2*F[25,x]+F[51,x]+F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[19,x]+F[61,x]
F[61,x] = F[59,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[14,x]+F[52,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[60,x]+F[66,x]
F[66,x] = F[67,x]+F[77,x]
F[67,x] = 2*F[25,x]+F[68,x]+F[69,x]
F[68,x] = F[12,x]*F[19,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[19,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[19,x]
F[74,x] = F[67,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[12,x]*F[67,x]
F[77,x] = F[78,x]
F[78,x] = F[12,x]*F[66,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[63,x]+F[81,x]
F[81,x] = F[82,x]+F[92,x]
F[82,x] = F[25,x]+F[83,x]+F[87,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[12,x]
F[86,x] = F[19,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[18,x]+F[89,x]
F[89,x] = F[82,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[12,x]*F[82,x]
F[92,x] = 2*F[25,x]+F[93,x]+F[97,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[34,x]
F[96,x] = F[61,x]
F[97,x] = F[12,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_{23}\! \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_{21}\! \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_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{79}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{49}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{37}\! \left(x \right) = F_{25}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = x^{2}
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = x^{2}
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{49}\! \left(x \right) = F_{24}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{51}\! \left(x \right)+F_{64}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{25}\! \left(x \right)+F_{53}\! \left(x \right)+F_{62}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{10}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)+F_{35}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{51}\! \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_{19}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right)+F_{52}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{60}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{77}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \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_{19}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{67}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{63}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{92}\! \left(x \right)
F_{82}\! \left(x \right) = F_{25}\! \left(x \right)+F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right)
F_{86}\! \left(x \right) = F_{19}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{34}\! \left(x \right)
F_{96}\! \left(x \right) = F_{61}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \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_23(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_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_14(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_13(x))
Eq(F_23(x), F_14(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_79(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_49(x))
Eq(F_28(x), F_29(x) + F_6(x))
Eq(F_29(x), F_25(x) + F_30(x) + F_31(x))
Eq(F_30(x), F_10(x)*F_12(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_12(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_12(x)*F_33(x))
Eq(F_36(x), F_37(x) + F_47(x))
Eq(F_37(x), F_25(x) + F_38(x) + F_39(x))
Eq(F_38(x), x**2)
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_12(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), x**2)
Eq(F_44(x), F_37(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_37(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_12(x)*F_36(x))
Eq(F_49(x), F_24(x) + F_50(x))
Eq(F_50(x), 2*F_25(x) + F_51(x) + F_64(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_25(x) + F_53(x) + F_62(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_10(x) + F_56(x))
Eq(F_56(x), F_25(x) + F_30(x) + F_35(x))
Eq(F_57(x), F_52(x) + F_58(x))
Eq(F_58(x), 2*F_25(x) + F_51(x) + F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_19(x) + F_61(x))
Eq(F_61(x), F_59(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_14(x) + F_52(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_60(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_77(x))
Eq(F_67(x), 2*F_25(x) + F_68(x) + F_69(x))
Eq(F_68(x), F_12(x)*F_19(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_19(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_19(x))
Eq(F_74(x), F_67(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_12(x)*F_67(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_12(x)*F_66(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_63(x) + F_81(x))
Eq(F_81(x), F_82(x) + F_92(x))
Eq(F_82(x), F_25(x) + F_83(x) + F_87(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_12(x))
Eq(F_86(x), F_19(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_18(x) + F_89(x))
Eq(F_89(x), F_82(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_12(x)*F_82(x))
Eq(F_92(x), 2*F_25(x) + F_93(x) + F_97(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_34(x))
Eq(F_96(x), F_61(x))
Eq(F_97(x), F_12(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, 1, 3], "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, 2, 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, 1, 3], "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, 2, 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, 1, 3], "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, 2, 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": [[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, 0, 2], "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], [1, 0], [1, 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, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "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": "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": [[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, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 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, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [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": [[0, 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"ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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": [[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": [[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, 0, 2], "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], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 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