0123_0213_1230
Counting sequence:
1, 1, 2, 6, 21, 77, 284, 1041, 3789, 13730, 49679, 179906, 653083, 2378702, 8696754, 31921462, 117624497, 435047541, 1614769933, 6013417811, 22463101851, 84151166305, 316084324517, 1190187380109, 4491810419947, 16988382790291, 64379012014331, 244422429188511, 929587527276463, 3541152728682579, 13510175395588476, 51617839574141913, 197480878369898381, 756490603168379498, 2901381483710759075, 11140402901484108506, 42821891522986640059, 164769095485047631474, 634612277175701888747, 2446489870641299864904, 9439771980477573875319, 36453977764600584520340, 140889002286124658601953, 544932260839714671396130, 2109243469452411288942775, 8169888033757229623483896, 31666347132111895005262659, 122817528507405555144261086, 476641689298872595202348303, 1850897655899652183234624298, 7191533804780308231790063341, 27957606135178029464566027932, 108744897880604911481049976863, 423194338378234030105363659470, 1647725677318866900549720624569, 6418544250327525342700289124556, 25014256365827826782929438601323, 97528445217732221510604037886718, 380418135013872211438396834078545, 1484469253659582455985380960976092, 5795026924975326706063459740745151, 22631243447935212447208796548758346, 88414764159908771779953286073511682, 345540965730111985800259634149489302, 1350914462229150558614685971810673729, 5283298138245261266552547476244549845, 20669356213137931134045591447962864789, 80888939200266739861752539408237495539, 316655958882344308073739542098616263051, 1239991395262669639757946203095533042537, 4857115896558665996451125711223863181921, 19031083253381745454194848211475370050301, 74588247425468450489156774493708575106323, 292412468253484899087646621588605243006319, 1146665719235585051709062058698536852621723, 4497697266627925748553728740898552147011083, 17646280049416000559473909094270205411973695, 69250495695813846878545472404232718997167791, 271829570641525812971514688008531536113051325, 1067264407309375331299593376524181358517286635, 4191277180662202470726949574933508396931378827, 16463318289259366418530348967956177751307693113, 64681888654757884948554632569728219882504152447, 254179258970452374566396918436552864047553565097, 999050578568282813253576852339881174126464494799, 3927558990396449546721529438655055330243836938745, 15443432288617800554540644878223054082444220730119, 60736375865742529457936512834115446831996247255629, 238910909914280712976254413976215257153624488263751, 939946950914815693019277621460347427518981665201677, 3698700845964645063320245303681496061340676288569811, 14556999866358705399669150538447807195545513546212961, 57301991748333044872364256716227841250213415598768343, 225601061141890717760205361180795116214956919698732389, 888351010672961655191209063192782792575765927329182613, 3498634830959664454452176212233994212444784557178517293, 13781031884596298895890747958877967057372461901560430235, 54291590678113339960066253217673602547622209708353849651, 213919188634645126831177141073437415777911109204847577955, 843008491110038565955938572114725984469913896484407433695, 3322598814909607896510113920853491492368147293843608718047
Generating function in Maple syntax:
1/4*((-3*x^3+5*x^2-4*x+1)*(1-4*x)^(1/2)-8*x^4+15*x^3-13*x^2+6*x-1)/(x-1)^2/x^2/(x-1/2)
Generating function in latex syntax:
\frac{\left(-3 x^{3}+5 x^{2}-4 x +1\right) \sqrt{1-4 x}-8 x^{4}+15 x^{3}-13 x^{2}+6 x -1}{4 \left(x -1\right)^{2} x^{2} \left(x -\frac{1}{2}\right)}
Generating function in sympy syntax:
(-2*x**4 + 15*x**3/4 - 13*x**2/4 + 3*x/2 + sqrt(1 - 4*x)*(-3*x**3 + 5*x**2 - 4*x + 1)/4 - 1/4)/(x**2*(x - 1)**2*(x - 1/2))
Implicit equation for the generating function in Maple syntax:
x^2*(2*x-1)^2*(x-1)^4*F(x)^2+(2*x-1)*(8*x^4-15*x^3+13*x^2-6*x+1)*(x-1)^2*F(x)+16*x^6-51*x^5+76*x^4-65*x^3+33*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
x^{2} \left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(8 x^{4}-15 x^{3}+13 x^{2}-6 x +1\right) \left(x -1\right)^{2} F \! \left(x \right)+16 x^{6}-51 x^{5}+76 x^{4}-65 x^{3}+33 x^{2}-9 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 77
a(6) = 284
a(n+6) = -12*(3+2*n)/(8+n)*a(n)-3*(141+41*n)/(8+n)*a(2+n)+2*(94+41*n)/(8+n)*a(n+1)+(469+102*n)/(8+n)*a(n+3)-(268+47*n)/(8+n)*a(n+4)+(75+11*n)/(8+n)*a(n+5)+5/(8+n), 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) = 21
a \! \left(5\right) = 77
a \! \left(6\right) = 284
a \! \left(n +6\right) = -\frac{12 \left(3+2 n \right) a \! \left(n \right)}{8+n}-\frac{3 \left(141+41 n \right) a \! \left(2+n \right)}{8+n}+\frac{2 \left(94+41 n \right) a \! \left(n +1\right)}{8+n}+\frac{\left(469+102 n \right) a \! \left(n +3\right)}{8+n}-\frac{\left(268+47 n \right) a \! \left(n +4\right)}{8+n}+\frac{\left(75+11 n \right) a \! \left(n +5\right)}{8+n}+\frac{5}{8+n}, \quad n \geq 7
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/232/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[232,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[110,x,k[0]]+F[14,x]
F[14,x] = F[15,x]+F[38,x]
F[15,x] = F[16,x]+F[26,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[11,x]*F[20,x]
F[23,x] = F[17,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]*F[23,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[30,x]
F[28,x] = 0
F[29,x] = F[11,x]*F[21,x]
F[30,x] = F[11,x]*F[31,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[11,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[32,x]
F[35,x] = F[27,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[11,x]*F[35,x]
F[38,x] = F[109,x]+F[39,x]
F[39,x] = F[40,x]+F[51,x]
F[40,x] = F[41,x]
F[41,x] = F[11,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[1,x]+F[11,x]
F[44,x] = F[40,x]+F[45,x]
F[45,x] = F[28,x]+F[46,x]+F[50,x]
F[46,x] = F[11,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[11,x]
F[49,x] = F[45,x]
F[50,x] = F[11,x]*F[40,x]
F[51,x] = F[28,x]+F[52,x]+F[95,x]
F[52,x] = F[11,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[17,x]+F[27,x]
F[55,x] = F[51,x]+F[56,x]
F[56,x] = F[28,x]+F[57,x]+F[61,x]+F[86,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[27,x]
F[60,x] = F[56,x]
F[61,x] = F[11,x]*F[62,x]
F[62,x] = F[28,x]+F[63,x]+F[84,x]
F[63,x] = F[11,x]*F[64,x]
F[64,x] = F[65,x]+F[69,x]
F[65,x] = F[21,x]+F[66,x]
F[66,x] = F[28,x]+F[29,x]+F[67,x]
F[67,x] = F[11,x]*F[68,x]
F[68,x] = F[11,x]+F[66,x]
F[69,x] = F[62,x]+F[70,x]
F[70,x] = F[28,x]+F[61,x]+F[71,x]+F[75,x]
F[71,x] = F[11,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[66,x]
F[74,x] = F[70,x]
F[75,x] = F[11,x]*F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[78,x]
F[78,x] = F[11,x]*F[21,x]
F[79,x] = 2*F[28,x]+F[75,x]+F[80,x]
F[80,x] = F[11,x]*F[81,x]
F[81,x] = F[28,x]+F[82,x]+F[84,x]
F[82,x] = F[11,x]*F[83,x]
F[83,x] = F[21,x]+F[81,x]
F[84,x] = F[11,x]*F[85,x]
F[85,x] = F[21,x]+F[81,x]
F[86,x] = F[11,x]*F[87,x]
F[87,x] = F[88,x]+F[91,x]
F[88,x] = F[77,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[11,x]*F[88,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = 2*F[28,x]+F[80,x]+F[86,x]
F[93,x] = F[94,x]
F[94,x] = F[11,x]*F[91,x]
F[95,x] = F[11,x]*F[96,x]
F[96,x] = F[85,x]+F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[28,x]+F[82,x]+F[95,x]
F[99,x] = 2*F[28,x]+F[100,x]+F[108,x]
F[100,x] = F[101,x]*F[11,x]
F[101,x] = F[102,x]+F[105,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[11,x]
F[104,x] = F[102,x]+F[21,x]
F[105,x] = 2*F[28,x]+F[100,x]+F[106,x]
F[106,x] = F[107,x]*F[11,x]
F[107,x] = F[105,x]+F[81,x]
F[108,x] = F[11,x]*F[97,x]
F[109,x] = F[45,x]+F[56,x]
F[110,x,k[0]] = F[111,x,k[0]]+F[154,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]+F[135,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[116,x,k[0]]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[8,x,k[0]]
F[115,x,k[0]] = F[1,x]+F[113,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[119,x,k[0]]+F[28,x]
F[117,x,k[0]] = F[118,x,k[0]]*F[8,x,k[0]]
F[118,x,k[0]] = F[116,x,k[0]]+F[17,x]
F[119,x,k[0]] = F[11,x]*F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[126,x,k[0]]
F[121,x,k[0]] = F[113,x,k[0]]+F[122,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]+F[125,x,k[0]]+F[28,x]
F[123,x,k[0]] = F[124,x,k[0]]*F[8,x,k[0]]
F[124,x,k[0]] = F[122,x,k[0]]+F[21,x]
F[125,x,k[0]] = F[11,x]*F[121,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[128,x,k[0]]
F[127,x,k[0]] = F[119,x,k[0]]+F[123,x,k[0]]+F[28,x]
F[128,x,k[0]] = 2*F[28,x]+F[129,x,k[0]]+F[134,x,k[0]]
F[129,x,k[0]] = F[130,x,k[0]]*F[8,x,k[0]]
F[130,x,k[0]] = F[102,x]+F[131,x,k[0]]
F[131,x,k[0]] = 2*F[28,x]+F[129,x,k[0]]+F[132,x,k[0]]
F[132,x,k[0]] = F[11,x]*F[133,x,k[0]]
F[133,x,k[0]] = F[122,x,k[0]]+F[131,x,k[0]]
F[134,x,k[0]] = F[11,x]*F[126,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]+F[140,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]+F[139,x,k[0]]+F[28,x]
F[137,x,k[0]] = F[138,x,k[0]]*F[8,x,k[0]]
F[138,x,k[0]] = F[11,x]+F[136,x,k[0]]
F[139,x,k[0]] = F[11,x]*F[113,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[143,x,k[0]]+F[144,x,k[0]]+F[28,x]
F[141,x,k[0]] = F[142,x,k[0]]*F[8,x,k[0]]
F[142,x,k[0]] = F[140,x,k[0]]+F[27,x]
F[143,x,k[0]] = F[11,x]*F[122,x,k[0]]
F[144,x,k[0]] = F[11,x]*F[145,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[150,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]+F[148,x,k[0]]
F[147,x,k[0]] = F[139,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[11,x]*F[146,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]+F[152,x,k[0]]
F[151,x,k[0]] = 2*F[28,x]+F[143,x,k[0]]+F[144,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]
F[153,x,k[0]] = F[11,x]*F[150,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[231,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[168,x,k[0]]
F[156,x,k[0]] = F[137,x,k[0]]+F[157,x,k[0]]+F[28,x]
F[157,x,k[0]] = F[11,x]*F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]+F[160,x,k[0]]
F[159,x,k[0]] = F[113,x,k[0]]+F[136,x,k[0]]
F[160,x,k[0]] = F[156,x,k[0]]+F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]+F[163,x,k[0]]+F[167,x,k[0]]+F[28,x]
F[162,x,k[0]] = 0
F[163,x,k[0]] = F[11,x]*F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[166,x,k[0]]
F[165,x,k[0]] = F[136,x,k[0]]
F[166,x,k[0]] = F[161,x,k[0]]
F[167,x,k[0]] = F[11,x]*F[156,x,k[0]]
F[168,x,k[0]] = F[141,x,k[0]]+F[169,x,k[0]]+F[220,x,k[0]]+F[28,x]
F[169,x,k[0]] = F[11,x]*F[170,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]+F[172,x,k[0]]
F[171,x,k[0]] = F[116,x,k[0]]+F[140,x,k[0]]
F[172,x,k[0]] = F[168,x,k[0]]+F[173,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]+F[175,x,k[0]]+F[179,x,k[0]]+F[211,x,k[0]]+F[28,x]
F[174,x,k[0]] = 0
F[175,x,k[0]] = F[11,x]*F[176,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[178,x,k[0]]
F[177,x,k[0]] = F[140,x,k[0]]
F[178,x,k[0]] = F[173,x,k[0]]
F[179,x,k[0]] = F[11,x]*F[180,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]+F[187,x,k[0]]+F[209,x,k[0]]+F[28,x]
F[181,x,k[0]] = F[182,x,k[0]]*F[8,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]+F[66,x]
F[183,x,k[0]] = F[143,x,k[0]]+F[181,x,k[0]]+F[184,x,k[0]]+F[28,x]
F[184,x,k[0]] = F[11,x]*F[185,x,k[0]]
F[185,x,k[0]] = F[147,x,k[0]]+F[186,x,k[0]]
F[186,x,k[0]] = 2*F[28,x]+F[143,x,k[0]]+F[184,x,k[0]]
F[187,x,k[0]] = F[11,x]*F[188,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[190,x,k[0]]
F[189,x,k[0]] = F[122,x,k[0]]+F[183,x,k[0]]
F[190,x,k[0]] = F[180,x,k[0]]+F[191,x,k[0]]
F[191,x,k[0]] = F[179,x,k[0]]+F[192,x,k[0]]+F[193,x,k[0]]+F[197,x,k[0]]+F[28,x]
F[192,x,k[0]] = 0
F[193,x,k[0]] = F[11,x]*F[194,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]+F[196,x,k[0]]
F[195,x,k[0]] = F[183,x,k[0]]
F[196,x,k[0]] = F[191,x,k[0]]
F[197,x,k[0]] = F[11,x]*F[198,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]+F[204,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]
F[200,x,k[0]] = F[11,x]*F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]
F[202,x,k[0]] = F[11,x]*F[203,x,k[0]]
F[203,x,k[0]] = F[113,x,k[0]]+F[201,x,k[0]]
F[204,x,k[0]] = 3*F[28,x]+F[197,x,k[0]]+F[205,x,k[0]]
F[205,x,k[0]] = F[11,x]*F[206,x,k[0]]
F[206,x,k[0]] = 2*F[28,x]+F[207,x,k[0]]+F[209,x,k[0]]
F[207,x,k[0]] = F[11,x]*F[208,x,k[0]]
F[208,x,k[0]] = F[122,x,k[0]]+F[206,x,k[0]]
F[209,x,k[0]] = F[11,x]*F[210,x,k[0]]
F[210,x,k[0]] = F[201,x,k[0]]+F[206,x,k[0]]
F[211,x,k[0]] = F[11,x]*F[212,x,k[0]]
F[212,x,k[0]] = F[213,x,k[0]]+F[216,x,k[0]]
F[213,x,k[0]] = F[199,x,k[0]]+F[214,x,k[0]]
F[214,x,k[0]] = F[215,x,k[0]]
F[215,x,k[0]] = F[11,x]*F[213,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[218,x,k[0]]
F[217,x,k[0]] = 3*F[28,x]+F[205,x,k[0]]+F[211,x,k[0]]
F[218,x,k[0]] = F[219,x,k[0]]
F[219,x,k[0]] = F[11,x]*F[216,x,k[0]]
F[220,x,k[0]] = F[11,x]*F[221,x,k[0]]
F[221,x,k[0]] = F[210,x,k[0]]+F[222,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]+F[224,x,k[0]]
F[223,x,k[0]] = 2*F[28,x]+F[207,x,k[0]]+F[220,x,k[0]]
F[224,x,k[0]] = 3*F[28,x]+F[225,x,k[0]]+F[230,x,k[0]]
F[225,x,k[0]] = F[11,x]*F[226,x,k[0]]
F[226,x,k[0]] = F[131,x,k[0]]+F[227,x,k[0]]
F[227,x,k[0]] = 3*F[28,x]+F[225,x,k[0]]+F[228,x,k[0]]
F[228,x,k[0]] = F[11,x]*F[229,x,k[0]]
F[229,x,k[0]] = F[206,x,k[0]]+F[227,x,k[0]]
F[230,x,k[0]] = F[11,x]*F[222,x,k[0]]
F[231,x,k[0]] = F[161,x,k[0]]+F[173,x,k[0]]
F[232,x] = F[11,x]*F[14,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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{232}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{109}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{51}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{28}\! \left(x \right)+F_{46}\! \left(x \right)+F_{50}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{51}\! \left(x \right) = F_{28}\! \left(x \right)+F_{52}\! \left(x \right)+F_{95}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{28}\! \left(x \right)+F_{57}\! \left(x \right)+F_{61}\! \left(x \right)+F_{86}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{27}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{28}\! \left(x \right)+F_{63}\! \left(x \right)+F_{84}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{62}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{28}\! \left(x \right)+F_{61}\! \left(x \right)+F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{66}\! \left(x \right)
F_{74}\! \left(x \right) = F_{70}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{75}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{28}\! \left(x \right)+F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{21}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right)+F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{77}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{11}\! \left(x \right) F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{80}\! \left(x \right)+F_{86}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right) F_{91}\! \left(x \right)
F_{95}\! \left(x \right) = F_{11}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{85}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{28}\! \left(x \right)+F_{82}\! \left(x \right)+F_{95}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{100}\! \left(x \right)+F_{108}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{11}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{105}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{11}\! \left(x \right)
F_{104}\! \left(x \right) = F_{102}\! \left(x \right)+F_{21}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{100}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{11}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{81}\! \left(x \right)
F_{108}\! \left(x \right) = F_{11}\! \left(x \right) F_{97}\! \left(x \right)
F_{109}\! \left(x \right) = F_{45}\! \left(x \right)+F_{56}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{154}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{135}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{116}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{113}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{17}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{21}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{121}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{123}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{128}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{102}\! \left(x \right)+F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{133}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{131}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{126}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{139}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{136}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{113}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{143}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{27}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{122}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{146}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{150}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{231}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{157}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{157}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{163}\! \left(x , y\right)+F_{167}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{162}\! \left(x , y\right) = 0
F_{163}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{156}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{169}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{170}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)+F_{175}\! \left(x , y\right)+F_{179}\! \left(x , y\right)+F_{211}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{174}\! \left(x , y\right) = 0
F_{175}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{209}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{181}\! \left(x , y\right)+F_{184}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{184}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{185}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{188}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{179}\! \left(x , y\right)+F_{192}\! \left(x , y\right)+F_{193}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{28}\! \left(x \right)
F_{192}\! \left(x , y\right) = 0
F_{193}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)+F_{196}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = 3 F_{28}\! \left(x \right)+F_{197}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{207}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{208}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{212}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)+F_{216}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{213}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = 3 F_{28}\! \left(x \right)+F_{205}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{216}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)+F_{224}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = 2 F_{28}\! \left(x \right)+F_{207}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = 3 F_{28}\! \left(x \right)+F_{225}\! \left(x , y\right)+F_{230}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{226}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{227}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = 3 F_{28}\! \left(x \right)+F_{225}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{229}\! \left(x , y\right)
F_{229}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{227}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{222}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{232}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_232(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_110(x, k_0) + F_14(x))
Eq(F_14(x), F_15(x) + F_38(x))
Eq(F_15(x), F_16(x) + F_26(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_11(x)*F_20(x))
Eq(F_23(x), F_17(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_23(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_30(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_11(x)*F_21(x))
Eq(F_30(x), F_11(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_11(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_32(x))
Eq(F_35(x), F_27(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_11(x)*F_35(x))
Eq(F_38(x), F_109(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_51(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_11(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_1(x) + F_11(x))
Eq(F_44(x), F_40(x) + F_45(x))
Eq(F_45(x), F_28(x) + F_46(x) + F_50(x))
Eq(F_46(x), F_11(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_11(x))
Eq(F_49(x), F_45(x))
Eq(F_50(x), F_11(x)*F_40(x))
Eq(F_51(x), F_28(x) + F_52(x) + F_95(x))
Eq(F_52(x), F_11(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_17(x) + F_27(x))
Eq(F_55(x), F_51(x) + F_56(x))
Eq(F_56(x), F_28(x) + F_57(x) + F_61(x) + F_86(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_27(x))
Eq(F_60(x), F_56(x))
Eq(F_61(x), F_11(x)*F_62(x))
Eq(F_62(x), F_28(x) + F_63(x) + F_84(x))
Eq(F_63(x), F_11(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_69(x))
Eq(F_65(x), F_21(x) + F_66(x))
Eq(F_66(x), F_28(x) + F_29(x) + F_67(x))
Eq(F_67(x), F_11(x)*F_68(x))
Eq(F_68(x), F_11(x) + F_66(x))
Eq(F_69(x), F_62(x) + F_70(x))
Eq(F_70(x), F_28(x) + F_61(x) + F_71(x) + F_75(x))
Eq(F_71(x), F_11(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_66(x))
Eq(F_74(x), F_70(x))
Eq(F_75(x), F_11(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_11(x)*F_21(x))
Eq(F_79(x), 2*F_28(x) + F_75(x) + F_80(x))
Eq(F_80(x), F_11(x)*F_81(x))
Eq(F_81(x), F_28(x) + F_82(x) + F_84(x))
Eq(F_82(x), F_11(x)*F_83(x))
Eq(F_83(x), F_21(x) + F_81(x))
Eq(F_84(x), F_11(x)*F_85(x))
Eq(F_85(x), F_21(x) + F_81(x))
Eq(F_86(x), F_11(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_91(x))
Eq(F_88(x), F_77(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_11(x)*F_88(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), 2*F_28(x) + F_80(x) + F_86(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_11(x)*F_91(x))
Eq(F_95(x), F_11(x)*F_96(x))
Eq(F_96(x), F_85(x) + F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_28(x) + F_82(x) + F_95(x))
Eq(F_99(x), F_100(x) + F_108(x) + 2*F_28(x))
Eq(F_100(x), F_101(x)*F_11(x))
Eq(F_101(x), F_102(x) + F_105(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_11(x))
Eq(F_104(x), F_102(x) + F_21(x))
Eq(F_105(x), F_100(x) + F_106(x) + 2*F_28(x))
Eq(F_106(x), F_107(x)*F_11(x))
Eq(F_107(x), F_105(x) + F_81(x))
Eq(F_108(x), F_11(x)*F_97(x))
Eq(F_109(x), F_45(x) + F_56(x))
Eq(F_110(x, k_0), F_111(x, k_0) + F_154(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0) + F_135(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_116(x, k_0))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_8(x, k_0))
Eq(F_115(x, k_0), F_1(x) + F_113(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_119(x, k_0) + F_28(x))
Eq(F_117(x, k_0), F_118(x, k_0)*F_8(x, k_0))
Eq(F_118(x, k_0), F_116(x, k_0) + F_17(x))
Eq(F_119(x, k_0), F_11(x)*F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_126(x, k_0))
Eq(F_121(x, k_0), F_113(x, k_0) + F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_125(x, k_0) + F_28(x))
Eq(F_123(x, k_0), F_124(x, k_0)*F_8(x, k_0))
Eq(F_124(x, k_0), F_122(x, k_0) + F_21(x))
Eq(F_125(x, k_0), F_11(x)*F_121(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_128(x, k_0))
Eq(F_127(x, k_0), F_119(x, k_0) + F_123(x, k_0) + F_28(x))
Eq(F_128(x, k_0), F_129(x, k_0) + F_134(x, k_0) + 2*F_28(x))
Eq(F_129(x, k_0), F_130(x, k_0)*F_8(x, k_0))
Eq(F_130(x, k_0), F_102(x) + F_131(x, k_0))
Eq(F_131(x, k_0), F_129(x, k_0) + F_132(x, k_0) + 2*F_28(x))
Eq(F_132(x, k_0), F_11(x)*F_133(x, k_0))
Eq(F_133(x, k_0), F_122(x, k_0) + F_131(x, k_0))
Eq(F_134(x, k_0), F_11(x)*F_126(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0) + F_140(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0) + F_139(x, k_0) + F_28(x))
Eq(F_137(x, k_0), F_138(x, k_0)*F_8(x, k_0))
Eq(F_138(x, k_0), F_11(x) + F_136(x, k_0))
Eq(F_139(x, k_0), F_11(x)*F_113(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_143(x, k_0) + F_144(x, k_0) + F_28(x))
Eq(F_141(x, k_0), F_142(x, k_0)*F_8(x, k_0))
Eq(F_142(x, k_0), F_140(x, k_0) + F_27(x))
Eq(F_143(x, k_0), F_11(x)*F_122(x, k_0))
Eq(F_144(x, k_0), F_11(x)*F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_150(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0) + F_148(x, k_0))
Eq(F_147(x, k_0), F_139(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_11(x)*F_146(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0) + F_152(x, k_0))
Eq(F_151(x, k_0), F_143(x, k_0) + F_144(x, k_0) + 2*F_28(x))
Eq(F_152(x, k_0), F_153(x, k_0))
Eq(F_153(x, k_0), F_11(x)*F_150(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_231(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_168(x, k_0))
Eq(F_156(x, k_0), F_137(x, k_0) + F_157(x, k_0) + F_28(x))
Eq(F_157(x, k_0), F_11(x)*F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0) + F_160(x, k_0))
Eq(F_159(x, k_0), F_113(x, k_0) + F_136(x, k_0))
Eq(F_160(x, k_0), F_156(x, k_0) + F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0) + F_163(x, k_0) + F_167(x, k_0) + F_28(x))
Eq(F_162(x, k_0), 0)
Eq(F_163(x, k_0), F_11(x)*F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_166(x, k_0))
Eq(F_165(x, k_0), F_136(x, k_0))
Eq(F_166(x, k_0), F_161(x, k_0))
Eq(F_167(x, k_0), F_11(x)*F_156(x, k_0))
Eq(F_168(x, k_0), F_141(x, k_0) + F_169(x, k_0) + F_220(x, k_0) + F_28(x))
Eq(F_169(x, k_0), F_11(x)*F_170(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0) + F_172(x, k_0))
Eq(F_171(x, k_0), F_116(x, k_0) + F_140(x, k_0))
Eq(F_172(x, k_0), F_168(x, k_0) + F_173(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0) + F_175(x, k_0) + F_179(x, k_0) + F_211(x, k_0) + F_28(x))
Eq(F_174(x, k_0), 0)
Eq(F_175(x, k_0), F_11(x)*F_176(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_178(x, k_0))
Eq(F_177(x, k_0), F_140(x, k_0))
Eq(F_178(x, k_0), F_173(x, k_0))
Eq(F_179(x, k_0), F_11(x)*F_180(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0) + F_187(x, k_0) + F_209(x, k_0) + F_28(x))
Eq(F_181(x, k_0), F_182(x, k_0)*F_8(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0) + F_66(x))
Eq(F_183(x, k_0), F_143(x, k_0) + F_181(x, k_0) + F_184(x, k_0) + F_28(x))
Eq(F_184(x, k_0), F_11(x)*F_185(x, k_0))
Eq(F_185(x, k_0), F_147(x, k_0) + F_186(x, k_0))
Eq(F_186(x, k_0), F_143(x, k_0) + F_184(x, k_0) + 2*F_28(x))
Eq(F_187(x, k_0), F_11(x)*F_188(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_190(x, k_0))
Eq(F_189(x, k_0), F_122(x, k_0) + F_183(x, k_0))
Eq(F_190(x, k_0), F_180(x, k_0) + F_191(x, k_0))
Eq(F_191(x, k_0), F_179(x, k_0) + F_192(x, k_0) + F_193(x, k_0) + F_197(x, k_0) + F_28(x))
Eq(F_192(x, k_0), 0)
Eq(F_193(x, k_0), F_11(x)*F_194(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0) + F_196(x, k_0))
Eq(F_195(x, k_0), F_183(x, k_0))
Eq(F_196(x, k_0), F_191(x, k_0))
Eq(F_197(x, k_0), F_11(x)*F_198(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_204(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0))
Eq(F_200(x, k_0), F_11(x)*F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0))
Eq(F_202(x, k_0), F_11(x)*F_203(x, k_0))
Eq(F_203(x, k_0), F_113(x, k_0) + F_201(x, k_0))
Eq(F_204(x, k_0), F_197(x, k_0) + F_205(x, k_0) + 3*F_28(x))
Eq(F_205(x, k_0), F_11(x)*F_206(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0) + F_209(x, k_0) + 2*F_28(x))
Eq(F_207(x, k_0), F_11(x)*F_208(x, k_0))
Eq(F_208(x, k_0), F_122(x, k_0) + F_206(x, k_0))
Eq(F_209(x, k_0), F_11(x)*F_210(x, k_0))
Eq(F_210(x, k_0), F_201(x, k_0) + F_206(x, k_0))
Eq(F_211(x, k_0), F_11(x)*F_212(x, k_0))
Eq(F_212(x, k_0), F_213(x, k_0) + F_216(x, k_0))
Eq(F_213(x, k_0), F_199(x, k_0) + F_214(x, k_0))
Eq(F_214(x, k_0), F_215(x, k_0))
Eq(F_215(x, k_0), F_11(x)*F_213(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_218(x, k_0))
Eq(F_217(x, k_0), F_205(x, k_0) + F_211(x, k_0) + 3*F_28(x))
Eq(F_218(x, k_0), F_219(x, k_0))
Eq(F_219(x, k_0), F_11(x)*F_216(x, k_0))
Eq(F_220(x, k_0), F_11(x)*F_221(x, k_0))
Eq(F_221(x, k_0), F_210(x, k_0) + F_222(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0) + F_224(x, k_0))
Eq(F_223(x, k_0), F_207(x, k_0) + F_220(x, k_0) + 2*F_28(x))
Eq(F_224(x, k_0), F_225(x, k_0) + F_230(x, k_0) + 3*F_28(x))
Eq(F_225(x, k_0), F_11(x)*F_226(x, k_0))
Eq(F_226(x, k_0), F_131(x, k_0) + F_227(x, k_0))
Eq(F_227(x, k_0), F_225(x, k_0) + F_228(x, k_0) + 3*F_28(x))
Eq(F_228(x, k_0), F_11(x)*F_229(x, k_0))
Eq(F_229(x, k_0), F_206(x, k_0) + F_227(x, k_0))
Eq(F_230(x, k_0), F_11(x)*F_222(x, k_0))
Eq(F_231(x, k_0), F_161(x, k_0) + F_173(x, k_0))
Eq(F_232(x), F_11(x)*F_14(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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{"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "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, 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]]}], "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, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 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, 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