0123_0132_1203_1230
Counting sequence:
1, 1, 2, 6, 20, 68, 232, 794, 2732, 9468, 33080, 116548, 413976, 1481704, 5340688, 19373306, 70682572, 259224044, 955146328, 3534264236, 13127716552, 48931485464, 182963030128, 686115032996, 2579799906040, 9723876025688, 36734672589872, 139067034723144, 527495769282992, 2004484164867280, 7629972467313696, 29089271004711994, 111068127606612748, 424672256529518924, 1625888075709526936, 6232570972634733340, 23919596737361168616, 91901608580524007992, 353467725436574449328, 1360850743185073693836, 5244254084003228403752, 20227837182176284640264, 78088859821609864662928, 301706958405772656810296, 1166600239177197293153872, 4514235708136903960463024, 17480657423031162408003808, 67737547514311725028681316, 262655796484197993467628472, 1019104490358952801132506488, 3956523315511758357294127600, 15369571341027506870554789688, 59738333891543000100471149776, 232315742911560364901480321264, 903919436055897935695964277856, 3518829233217619727586450269960, 13704913855689710966302297964656, 53401905713549631750896403897392, 208176920578244463951808561768288, 811889990255153683230910735022480, 3167701929192239508912793254654304, 12364255917169710148052657087585696, 48279475486091251345579907878852672, 188591701117543954964184751465372346, 736958339751633309734646048572318092, 2880837146301839319298235714778179084, 11265363169120625433094343264279186968, 44067450043913034852930128933275693436, 172437847997920571304797328737725804072, 674971005020431950818419681730764423544, 2642844216840564540389588544021753437488, 10351139849292211117657288767272720129276, 40553780779418799723496813895074459444552, 158926978730154755677694108781828892555304, 622993756622206642265627850071878977627088, 2442791308860757623638631978084445680727256, 9580817860726607822618993484926771760339472, 37586285453619769150347164694449176063080944, 147490487223064916919229187981842829831832928, 578900162350529798908265460604077877235107916, 2272719155894672543862661291099527598747874792, 8924580099976640964925273669192651737824603304, 35053170031233553669467863184192082014443056208, 137708882265560389415771268366058835769271587496, 541114902078790236057275255171780215807944911472, 2126707405844547671946053973273839083379411510224, 8360160147113049469029352970715587248723912031008, 32870629669330853594138212550273316950467999594616, 129266521171525828740993120229787452252828708131472, 508448316608001593047906572072673472828026019272144, 2000269201600709563858797882103064086034784730339488, 7870624467168009370835705907586659734167788460923376, 30974715644983778814256651451676607893267312457422752, 121921753070680831502925122209899140642418358218379104, 479986691036154010337831543343433131729519455783465408, 1889947595954856415705211721102838565108377118083820516, 7442886408811908771127741043144412062286844597985413432, 29315858712259150874033755614085903009161572308255559864, 115486716139202715564375401057629387639512788062425321328, 455017661588458699323639080474465057855026014828906293336, 1793039894180262993374340139514375964727560342329140215952
Generating function in Maple syntax:
(-2*(-4*x+1)^(1/2)*x-x^2+(-4*x+1)^(1/2)+3*x-1)/x/(2*x-1)
Generating function in latex syntax:
\frac{-2 \sqrt{-4 x +1}\, x -x^{2}+\sqrt{-4 x +1}+3 x -1}{x \left(2 x -1\right)}
Generating function in sympy syntax:
(-x**2 - 2*x*sqrt(1 - 4*x) + 3*x + sqrt(1 - 4*x) - 1)/(x*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*x*F(x)^2+2*(2*x-1)*(x^2-3*x+1)*F(x)+x^3+10*x^2-9*x+2 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} x F \! \left(x \right)^{2}+2 \left(2 x -1\right) \left(x^{2}-3 x +1\right) F \! \left(x \right)+x^{3}+10 x^{2}-9 x +2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(1+n)+2*(4*n+11)/(n+4)*a(n+2), n >= 4
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(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(1+n \right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}, \quad n \geq 4
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21136/
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[204,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[14,x]+F[97,x,k[0]]
F[14,x] = F[15,x]+F[46,x]
F[15,x] = F[16,x]+F[29,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[21,x]
F[20,x] = F[1,x]+F[11,x]
F[21,x] = F[17,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[28,x]
F[23,x] = 0
F[24,x] = F[11,x]*F[25,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[11,x]
F[27,x] = F[22,x]
F[28,x] = F[11,x]*F[17,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[1,x]+F[30,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[11,x]*F[30,x]
F[39,x] = F[33,x]+F[40,x]
F[40,x] = 2*F[23,x]+F[41,x]+F[45,x]
F[41,x] = F[11,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[37,x]
F[44,x] = F[40,x]
F[45,x] = F[11,x]*F[33,x]
F[46,x] = F[47,x]+F[74,x]
F[47,x] = F[30,x]+F[48,x]
F[48,x] = F[23,x]+F[49,x]+F[51,x]
F[49,x] = F[11,x]*F[50,x]
F[50,x] = F[17,x]+F[48,x]
F[51,x] = F[11,x]*F[52,x]
F[52,x] = F[53,x]+F[57,x]
F[53,x] = F[30,x]+F[54,x]
F[54,x] = F[23,x]+F[38,x]+F[55,x]
F[55,x] = F[11,x]*F[56,x]
F[56,x] = F[11,x]+F[54,x]
F[57,x] = F[58,x]+F[64,x]
F[58,x] = F[23,x]+F[51,x]+F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[30,x]+F[61,x]
F[61,x] = F[23,x]+F[59,x]+F[62,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[30,x]+F[61,x]
F[64,x] = F[23,x]+F[65,x]+F[69,x]+F[73,x]
F[65,x] = F[11,x]*F[66,x]
F[66,x] = F[37,x]+F[67,x]
F[67,x] = 2*F[23,x]+F[65,x]+F[68,x]
F[68,x] = F[11,x]*F[61,x]
F[69,x] = F[11,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[54,x]
F[72,x] = F[64,x]
F[73,x] = F[11,x]*F[58,x]
F[74,x] = F[75,x]+F[81,x]
F[75,x] = F[23,x]+F[76,x]+F[78,x]
F[76,x] = F[11,x]*F[77,x]
F[77,x] = F[30,x]+F[75,x]
F[78,x] = F[11,x]*F[79,x]
F[79,x] = F[30,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = 2*F[23,x]+F[82,x]+F[84,x]
F[82,x] = F[11,x]*F[83,x]
F[83,x] = F[33,x]+F[81,x]
F[84,x] = F[11,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[80,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[11,x]*F[80,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[84,x]
F[91,x] = 3*F[23,x]+F[92,x]+F[96,x]
F[92,x] = F[11,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[87,x]
F[95,x] = F[91,x]
F[96,x] = F[11,x]*F[90,x]
F[97,x,k[0]] = F[153,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[130,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]+F[103,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[8,x,k[0]]
F[102,x,k[0]] = F[1,x]+F[100,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]+F[106,x,k[0]]+F[23,x]
F[104,x,k[0]] = F[105,x,k[0]]*F[8,x,k[0]]
F[105,x,k[0]] = F[103,x,k[0]]+F[17,x]
F[106,x,k[0]] = F[107,x,k[0]]*F[11,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[113,x,k[0]]
F[108,x,k[0]] = F[100,x,k[0]]+F[109,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[112,x,k[0]]+F[23,x]
F[110,x,k[0]] = F[111,x,k[0]]*F[8,x,k[0]]
F[111,x,k[0]] = F[109,x,k[0]]+F[11,x]
F[112,x,k[0]] = F[100,x,k[0]]*F[11,x]
F[113,x,k[0]] = F[114,x,k[0]]+F[120,x,k[0]]
F[114,x,k[0]] = F[106,x,k[0]]+F[115,x,k[0]]+F[23,x]
F[115,x,k[0]] = F[116,x,k[0]]*F[8,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[30,x]
F[117,x,k[0]] = F[115,x,k[0]]+F[118,x,k[0]]+F[23,x]
F[118,x,k[0]] = F[11,x]*F[119,x,k[0]]
F[119,x,k[0]] = F[100,x,k[0]]+F[117,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]+F[125,x,k[0]]+F[129,x,k[0]]+F[23,x]
F[121,x,k[0]] = F[122,x,k[0]]*F[8,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]+F[37,x]
F[123,x,k[0]] = 2*F[23,x]+F[121,x,k[0]]+F[124,x,k[0]]
F[124,x,k[0]] = F[11,x]*F[117,x,k[0]]
F[125,x,k[0]] = F[11,x]*F[126,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[128,x,k[0]]
F[127,x,k[0]] = F[109,x,k[0]]
F[128,x,k[0]] = F[120,x,k[0]]
F[129,x,k[0]] = F[11,x]*F[114,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]+F[137,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[134,x,k[0]]+F[23,x]
F[132,x,k[0]] = F[133,x,k[0]]*F[8,x,k[0]]
F[133,x,k[0]] = F[131,x,k[0]]+F[30,x]
F[134,x,k[0]] = F[11,x]*F[135,x,k[0]]
F[135,x,k[0]] = F[100,x,k[0]]+F[136,x,k[0]]
F[136,x,k[0]] = F[134,x,k[0]]
F[137,x,k[0]] = 2*F[23,x]+F[138,x,k[0]]+F[140,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]*F[8,x,k[0]]
F[139,x,k[0]] = F[137,x,k[0]]+F[33,x]
F[140,x,k[0]] = F[11,x]*F[141,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[145,x,k[0]]
F[142,x,k[0]] = F[136,x,k[0]]+F[143,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[11,x]*F[136,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[147,x,k[0]]
F[146,x,k[0]] = F[140,x,k[0]]
F[147,x,k[0]] = 3*F[23,x]+F[148,x,k[0]]+F[152,x,k[0]]
F[148,x,k[0]] = F[11,x]*F[149,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]+F[151,x,k[0]]
F[150,x,k[0]] = F[143,x,k[0]]
F[151,x,k[0]] = F[147,x,k[0]]
F[152,x,k[0]] = F[11,x]*F[146,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[181,x,k[0]]
F[154,x,k[0]] = F[136,x,k[0]]+F[155,x,k[0]]
F[155,x,k[0]] = 2*F[23,x]+F[156,x,k[0]]+F[158,x,k[0]]
F[156,x,k[0]] = F[11,x]*F[157,x,k[0]]
F[157,x,k[0]] = F[103,x,k[0]]+F[155,x,k[0]]
F[158,x,k[0]] = F[11,x]*F[159,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]+F[164,x,k[0]]
F[160,x,k[0]] = F[136,x,k[0]]+F[161,x,k[0]]
F[161,x,k[0]] = 2*F[23,x]+F[144,x,k[0]]+F[162,x,k[0]]
F[162,x,k[0]] = F[11,x]*F[163,x,k[0]]
F[163,x,k[0]] = F[109,x,k[0]]+F[161,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[171,x,k[0]]
F[165,x,k[0]] = 2*F[23,x]+F[158,x,k[0]]+F[166,x,k[0]]
F[166,x,k[0]] = F[11,x]*F[167,x,k[0]]
F[167,x,k[0]] = F[117,x,k[0]]+F[168,x,k[0]]
F[168,x,k[0]] = 2*F[23,x]+F[166,x,k[0]]+F[169,x,k[0]]
F[169,x,k[0]] = F[11,x]*F[170,x,k[0]]
F[170,x,k[0]] = F[136,x,k[0]]+F[168,x,k[0]]
F[171,x,k[0]] = 2*F[23,x]+F[172,x,k[0]]+F[176,x,k[0]]+F[180,x,k[0]]
F[172,x,k[0]] = F[11,x]*F[173,x,k[0]]
F[173,x,k[0]] = F[123,x,k[0]]+F[174,x,k[0]]
F[174,x,k[0]] = 3*F[23,x]+F[172,x,k[0]]+F[175,x,k[0]]
F[175,x,k[0]] = F[11,x]*F[168,x,k[0]]
F[176,x,k[0]] = F[11,x]*F[177,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]+F[179,x,k[0]]
F[178,x,k[0]] = F[161,x,k[0]]
F[179,x,k[0]] = F[171,x,k[0]]
F[180,x,k[0]] = F[11,x]*F[165,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[188,x,k[0]]
F[182,x,k[0]] = 2*F[23,x]+F[183,x,k[0]]+F[185,x,k[0]]
F[183,x,k[0]] = F[11,x]*F[184,x,k[0]]
F[184,x,k[0]] = F[131,x,k[0]]+F[182,x,k[0]]
F[185,x,k[0]] = F[11,x]*F[186,x,k[0]]
F[186,x,k[0]] = F[136,x,k[0]]+F[187,x,k[0]]
F[187,x,k[0]] = F[185,x,k[0]]
F[188,x,k[0]] = 3*F[23,x]+F[189,x,k[0]]+F[191,x,k[0]]
F[189,x,k[0]] = F[11,x]*F[190,x,k[0]]
F[190,x,k[0]] = F[137,x,k[0]]+F[188,x,k[0]]
F[191,x,k[0]] = F[11,x]*F[192,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]+F[196,x,k[0]]
F[193,x,k[0]] = F[187,x,k[0]]+F[194,x,k[0]]
F[194,x,k[0]] = F[195,x,k[0]]
F[195,x,k[0]] = F[11,x]*F[187,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]+F[198,x,k[0]]
F[197,x,k[0]] = F[191,x,k[0]]
F[198,x,k[0]] = 4*F[23,x]+F[199,x,k[0]]+F[203,x,k[0]]
F[199,x,k[0]] = F[11,x]*F[200,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[202,x,k[0]]
F[201,x,k[0]] = F[194,x,k[0]]
F[202,x,k[0]] = F[198,x,k[0]]
F[203,x,k[0]] = F[11,x]*F[197,x,k[0]]
F[204,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_{204}\! \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_{14}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{46}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{29}\! \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_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)
F_{27}\! \left(x \right) = F_{22}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \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_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \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_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{33}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{74}\! \left(x \right)
F_{47}\! \left(x \right) = F_{30}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{23}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{17}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{30}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{58}\! \left(x \right) = F_{23}\! \left(x \right)+F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{30}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right)+F_{59}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{30}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{23}\! \left(x \right)+F_{65}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{37}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)
F_{72}\! \left(x \right) = F_{64}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{81}\! \left(x \right)
F_{75}\! \left(x \right) = F_{23}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{11}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{30}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{30}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{23}\! \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_{33}\! \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_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{80}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right) F_{80}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{84}\! \left(x \right)
F_{91}\! \left(x \right) = 3 F_{23}\! \left(x \right)+F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{11}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{87}\! \left(x \right)
F_{95}\! \left(x \right) = F_{91}\! \left(x \right)
F_{96}\! \left(x \right) = F_{11}\! \left(x \right) F_{90}\! \left(x \right)
F_{97}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{17}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{113}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{11}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{120}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{115}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{125}\! \left(x , y\right)+F_{129}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{37}\! \left(x \right)
F_{123}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{121}\! \left(x , y\right)+F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{117}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{126}\! \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_{109}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{114}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{23}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{138}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{33}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{136}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = 3 F_{23}\! \left(x \right)+F_{148}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{143}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{146}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{156}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{144}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{158}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{166}\! \left(x , y\right)+F_{169}\! \left(x , y\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_{136}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{176}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = 3 F_{23}\! \left(x \right)+F_{172}\! \left(x , y\right)+F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{168}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{171}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{165}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = 2 F_{23}\! \left(x \right)+F_{183}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{185}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = 3 F_{23}\! \left(x \right)+F_{189}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{192}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{196}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{187}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{187}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{191}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = 4 F_{23}\! \left(x \right)+F_{199}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{198}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{197}\! \left(x , y\right)
F_{204}\! \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_204(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_14(x) + F_97(x, k_0))
Eq(F_14(x), F_15(x) + F_46(x))
Eq(F_15(x), F_16(x) + F_29(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_21(x))
Eq(F_20(x), F_1(x) + F_11(x))
Eq(F_21(x), F_17(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_28(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_11(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_11(x))
Eq(F_27(x), F_22(x))
Eq(F_28(x), F_11(x)*F_17(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_1(x) + F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_11(x)*F_30(x))
Eq(F_39(x), F_33(x) + F_40(x))
Eq(F_40(x), 2*F_23(x) + F_41(x) + F_45(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_37(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_11(x)*F_33(x))
Eq(F_46(x), F_47(x) + F_74(x))
Eq(F_47(x), F_30(x) + F_48(x))
Eq(F_48(x), F_23(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_11(x)*F_50(x))
Eq(F_50(x), F_17(x) + F_48(x))
Eq(F_51(x), F_11(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_57(x))
Eq(F_53(x), F_30(x) + F_54(x))
Eq(F_54(x), F_23(x) + F_38(x) + F_55(x))
Eq(F_55(x), F_11(x)*F_56(x))
Eq(F_56(x), F_11(x) + F_54(x))
Eq(F_57(x), F_58(x) + F_64(x))
Eq(F_58(x), F_23(x) + F_51(x) + F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_30(x) + F_61(x))
Eq(F_61(x), F_23(x) + F_59(x) + F_62(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_30(x) + F_61(x))
Eq(F_64(x), F_23(x) + F_65(x) + F_69(x) + F_73(x))
Eq(F_65(x), F_11(x)*F_66(x))
Eq(F_66(x), F_37(x) + F_67(x))
Eq(F_67(x), 2*F_23(x) + F_65(x) + F_68(x))
Eq(F_68(x), F_11(x)*F_61(x))
Eq(F_69(x), F_11(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_54(x))
Eq(F_72(x), F_64(x))
Eq(F_73(x), F_11(x)*F_58(x))
Eq(F_74(x), F_75(x) + F_81(x))
Eq(F_75(x), F_23(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_11(x)*F_77(x))
Eq(F_77(x), F_30(x) + F_75(x))
Eq(F_78(x), F_11(x)*F_79(x))
Eq(F_79(x), F_30(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), 2*F_23(x) + F_82(x) + F_84(x))
Eq(F_82(x), F_11(x)*F_83(x))
Eq(F_83(x), F_33(x) + F_81(x))
Eq(F_84(x), F_11(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_80(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_11(x)*F_80(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_84(x))
Eq(F_91(x), 3*F_23(x) + F_92(x) + F_96(x))
Eq(F_92(x), F_11(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_87(x))
Eq(F_95(x), F_91(x))
Eq(F_96(x), F_11(x)*F_90(x))
Eq(F_97(x, k_0), F_153(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_130(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + F_103(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0)*F_8(x, k_0))
Eq(F_102(x, k_0), F_1(x) + F_100(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0) + F_106(x, k_0) + F_23(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_8(x, k_0))
Eq(F_105(x, k_0), F_103(x, k_0) + F_17(x))
Eq(F_106(x, k_0), F_107(x, k_0)*F_11(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_113(x, k_0))
Eq(F_108(x, k_0), F_100(x, k_0) + F_109(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_112(x, k_0) + F_23(x))
Eq(F_110(x, k_0), F_111(x, k_0)*F_8(x, k_0))
Eq(F_111(x, k_0), F_109(x, k_0) + F_11(x))
Eq(F_112(x, k_0), F_100(x, k_0)*F_11(x))
Eq(F_113(x, k_0), F_114(x, k_0) + F_120(x, k_0))
Eq(F_114(x, k_0), F_106(x, k_0) + F_115(x, k_0) + F_23(x))
Eq(F_115(x, k_0), F_116(x, k_0)*F_8(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_30(x))
Eq(F_117(x, k_0), F_115(x, k_0) + F_118(x, k_0) + F_23(x))
Eq(F_118(x, k_0), F_11(x)*F_119(x, k_0))
Eq(F_119(x, k_0), F_100(x, k_0) + F_117(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0) + F_125(x, k_0) + F_129(x, k_0) + F_23(x))
Eq(F_121(x, k_0), F_122(x, k_0)*F_8(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0) + F_37(x))
Eq(F_123(x, k_0), F_121(x, k_0) + F_124(x, k_0) + 2*F_23(x))
Eq(F_124(x, k_0), F_11(x)*F_117(x, k_0))
Eq(F_125(x, k_0), F_11(x)*F_126(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_109(x, k_0))
Eq(F_128(x, k_0), F_120(x, k_0))
Eq(F_129(x, k_0), F_11(x)*F_114(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_137(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_134(x, k_0) + F_23(x))
Eq(F_132(x, k_0), F_133(x, k_0)*F_8(x, k_0))
Eq(F_133(x, k_0), F_131(x, k_0) + F_30(x))
Eq(F_134(x, k_0), F_11(x)*F_135(x, k_0))
Eq(F_135(x, k_0), F_100(x, k_0) + F_136(x, k_0))
Eq(F_136(x, k_0), F_134(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0) + F_140(x, k_0) + 2*F_23(x))
Eq(F_138(x, k_0), F_139(x, k_0)*F_8(x, k_0))
Eq(F_139(x, k_0), F_137(x, k_0) + F_33(x))
Eq(F_140(x, k_0), F_11(x)*F_141(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_145(x, k_0))
Eq(F_142(x, k_0), F_136(x, k_0) + F_143(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_11(x)*F_136(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_147(x, k_0))
Eq(F_146(x, k_0), F_140(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0) + F_152(x, k_0) + 3*F_23(x))
Eq(F_148(x, k_0), F_11(x)*F_149(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_151(x, k_0))
Eq(F_150(x, k_0), F_143(x, k_0))
Eq(F_151(x, k_0), F_147(x, k_0))
Eq(F_152(x, k_0), F_11(x)*F_146(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_181(x, k_0))
Eq(F_154(x, k_0), F_136(x, k_0) + F_155(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_158(x, k_0) + 2*F_23(x))
Eq(F_156(x, k_0), F_11(x)*F_157(x, k_0))
Eq(F_157(x, k_0), F_103(x, k_0) + F_155(x, k_0))
Eq(F_158(x, k_0), F_11(x)*F_159(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0) + F_164(x, k_0))
Eq(F_160(x, k_0), F_136(x, k_0) + F_161(x, k_0))
Eq(F_161(x, k_0), F_144(x, k_0) + F_162(x, k_0) + 2*F_23(x))
Eq(F_162(x, k_0), F_11(x)*F_163(x, k_0))
Eq(F_163(x, k_0), F_109(x, k_0) + F_161(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_171(x, k_0))
Eq(F_165(x, k_0), F_158(x, k_0) + F_166(x, k_0) + 2*F_23(x))
Eq(F_166(x, k_0), F_11(x)*F_167(x, k_0))
Eq(F_167(x, k_0), F_117(x, k_0) + F_168(x, k_0))
Eq(F_168(x, k_0), F_166(x, k_0) + F_169(x, k_0) + 2*F_23(x))
Eq(F_169(x, k_0), F_11(x)*F_170(x, k_0))
Eq(F_170(x, k_0), F_136(x, k_0) + F_168(x, k_0))
Eq(F_171(x, k_0), F_172(x, k_0) + F_176(x, k_0) + F_180(x, k_0) + 2*F_23(x))
Eq(F_172(x, k_0), F_11(x)*F_173(x, k_0))
Eq(F_173(x, k_0), F_123(x, k_0) + F_174(x, k_0))
Eq(F_174(x, k_0), F_172(x, k_0) + F_175(x, k_0) + 3*F_23(x))
Eq(F_175(x, k_0), F_11(x)*F_168(x, k_0))
Eq(F_176(x, k_0), F_11(x)*F_177(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0) + F_179(x, k_0))
Eq(F_178(x, k_0), F_161(x, k_0))
Eq(F_179(x, k_0), F_171(x, k_0))
Eq(F_180(x, k_0), F_11(x)*F_165(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_188(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0) + F_185(x, k_0) + 2*F_23(x))
Eq(F_183(x, k_0), F_11(x)*F_184(x, k_0))
Eq(F_184(x, k_0), F_131(x, k_0) + F_182(x, k_0))
Eq(F_185(x, k_0), F_11(x)*F_186(x, k_0))
Eq(F_186(x, k_0), F_136(x, k_0) + F_187(x, k_0))
Eq(F_187(x, k_0), F_185(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_191(x, k_0) + 3*F_23(x))
Eq(F_189(x, k_0), F_11(x)*F_190(x, k_0))
Eq(F_190(x, k_0), F_137(x, k_0) + F_188(x, k_0))
Eq(F_191(x, k_0), F_11(x)*F_192(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0) + F_196(x, k_0))
Eq(F_193(x, k_0), F_187(x, k_0) + F_194(x, k_0))
Eq(F_194(x, k_0), F_195(x, k_0))
Eq(F_195(x, k_0), F_11(x)*F_187(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0) + F_198(x, k_0))
Eq(F_197(x, k_0), F_191(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_203(x, k_0) + 4*F_23(x))
Eq(F_199(x, k_0), F_11(x)*F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_202(x, k_0))
Eq(F_201(x, k_0), F_194(x, k_0))
Eq(F_202(x, k_0), F_198(x, k_0))
Eq(F_203(x, k_0), F_11(x)*F_197(x, k_0))
Eq(F_204(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 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], "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": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [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_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"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": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 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], 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