0123_0213_0231_3012
Counting sequence:
1, 1, 2, 6, 20, 67, 223, 742, 2484, 8399, 28731, 99451, 348127, 1231141, 4393821, 15808046, 57278916, 208844951, 765683811, 2820992111, 10438841451, 38779829501, 144575955621, 540728961251, 2028302456175, 7628647166477, 28762701003653, 108691599851157, 411597600536669, 1561689465974345, 5936123217389625, 22601895971913854, 86193220781648996, 329188507098492903, 1258984925934473459, 4821311304626517415, 18486135500206187059, 70963276939173662989, 272709612340732285013, 1049110733624433669015, 4039923137795383646459, 15571637824952173318117, 60073786970170892461453, 231956623233522692624365, 896359886854956726676069, 3466537508194164833517817, 13416285873844254983828233, 51961016793346383464039635, 201381158071671085519641679, 780986663080789943615900029, 3030682738738123402800965941, 11767889490234402537208973581, 45720160255727114639329548517, 177729025021464037579070525401, 691259896615099112355196714345, 2689974691811063624255263795237, 10472991694858181875067706178813, 40794479318646342156830974805977, 158976466069640136442915047511369, 619809466977734954582975219577769, 2417524903424012966122079774827321, 9433326800836761540044467617832081, 36824263386134294255313312934721137, 143804639587994941472850552269549086, 561792598493034562636774762306264996, 2195524600261172134667030376142848391, 8583312211931737335455486563890976531, 33567667861259679399275610035989757911, 131320534699523127061378308121623674371, 513907647910301943953354769034604864941, 2011751901730670182839867921804380649781, 7877651619687163654608733860413597471311, 30856623704437621612727526095086770251971, 120899846384243221203734291254268168362741, 473833081714512385703796636394996201868221, 1857564939548300262098817703279145400500221, 7284143155029525623697260892945193131233941, 28571020106505631911277496856583066994693401, 112094141097733837707033784288725918035472361, 439893119759200116408661262752295274096001351, 1726695736290471605294671556479767237595224411, 6779321944621927421120951533461000202022489621, 26622938854872311194513802287331522856941558781, 104573733826908040262180516091416037220472089381, 410850477560431003845115443437331993718630253101, 1614497207003740725634625081628971879739692630281, 6345720784641732349810909333385374759185033170361, 24946676330392366762176267799362728203308905421341, 98091298411882221097780028124108751725931755708741, 385773494542002324349016859540912969075729348183081, 1517457431580358634103479528839526155427372414290361, 5970092495944367171695413379905859956266315418653721, 23492230580796619065101300150826713634772530285119241, 92457979874441764474536836918704732929500858349840881, 363948428731620118366526886880056539973312815280473361, 1432877309922591439416743867591575953777575561307621171, 5642224026273709056544752406107458970427427061759032591, 22220934204271039164542512117492704042858302377039125981, 87527297122013860674255846996371231658024381427935107861, 344820066968655713228143533780388460938069713832654652061, 1358651250233213573481637597239188700340935266602514166101
Generating function in Maple syntax:
(-(x-1)^2*(-4*x+1)^(1/2)-x^2-2*x+1)/(4*x^3-6*x^2+2*x)
Generating function in latex syntax:
\frac{-\left(x -1\right)^{2} \sqrt{-4 x +1}-x^{2}-2 x +1}{4 x^{3}-6 x^{2}+2 x}
Generating function in sympy syntax:
(-x**2 - 2*x - sqrt(1 - 4*x)*(x - 1)**2 + 1)/(4*x**3 - 6*x**2 + 2*x)
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^2*F(x)^2+(2*x-1)*(x-1)*(x^2+2*x-1)*F(x)+x^4-4*x^3+8*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(x -1\right) \left(x^{2}+2 x -1\right) F \! \left(x \right)+x^{4}-4 x^{3}+8 x^{2}-5 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = 4*(1+2*n)/(4+n)*a(n)-2*(13+7*n)/(4+n)*a(1+n)+(20+7*n)/(4+n)*a(n+2)+6/(4+n), 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{4 \left(1+2 n \right) a \! \left(n \right)}{4+n}-\frac{2 \left(13+7 n \right) a \! \left(1+n \right)}{4+n}+\frac{\left(20+7 n \right) a \! \left(n +2\right)}{4+n}+\frac{6}{4+n}, \quad n \geq 4
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21147/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[22,x]*F[3,x]
F[3,x] = F[1,x]+F[210,x]+F[4,x]
F[4,x] = F[22,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[207,x,k[0]]+F[209,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[22,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[47,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[38,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[15,x,k[0]]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[11,x,k[0]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[16,x]+F[26,x,k[0]]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[22,x]
F[18,x] = F[19,x]+F[23,x]
F[19,x] = F[1,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[19,x]*F[22,x]
F[22,x] = x
F[23,x] = F[20,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[22,x]*F[23,x]
F[26,x,k[0]] = F[27,x]+F[28,x,k[0]]+F[32,x,k[0]]
F[27,x] = 0
F[28,x,k[0]] = F[22,x]*F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]+F[34,x,k[0]]
F[30,x,k[0]] = F[12,x,k[0]]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[14,x,k[0]]*F[33,x,k[0]]
F[33,x,k[0]] = F[20,x]+F[31,x,k[0]]
F[34,x,k[0]] = F[31,x,k[0]]+F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[14,x,k[0]]*F[37,x,k[0]]
F[37,x,k[0]] = F[24,x]+F[35,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[42,x,k[0]]
F[39,x,k[0]] = F[22,x]+F[40,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[12,x,k[0]]*F[22,x]
F[42,x,k[0]] = F[43,x]+F[45,x,k[0]]
F[43,x] = F[44,x]
F[44,x] = F[20,x]*F[22,x]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[22,x]*F[31,x,k[0]]
F[47,x,k[0]] = F[204,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[81,x,k[0]]
F[49,x,k[0]] = F[50,x]+F[61,x,k[0]]
F[50,x] = F[51,x]
F[51,x] = F[22,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[1,x]+F[22,x]
F[54,x] = F[50,x]+F[55,x]
F[55,x] = F[27,x]+F[56,x]+F[60,x]
F[56,x] = F[22,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[22,x]
F[59,x] = F[55,x]
F[60,x] = F[22,x]*F[50,x]
F[61,x,k[0]] = F[27,x]+F[62,x,k[0]]+F[80,x,k[0]]
F[62,x,k[0]] = F[22,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[65,x,k[0]]
F[64,x,k[0]] = F[12,x,k[0]]+F[40,x,k[0]]
F[65,x,k[0]] = F[61,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = 2*F[27,x]+F[67,x,k[0]]+F[71,x,k[0]]
F[67,x,k[0]] = F[22,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[70,x,k[0]]
F[69,x,k[0]] = F[40,x,k[0]]
F[70,x,k[0]] = F[66,x,k[0]]
F[71,x,k[0]] = F[22,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]
F[73,x,k[0]] = F[22,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[64,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = F[72,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = 2*F[27,x]+F[71,x,k[0]]+F[77,x,k[0]]
F[77,x,k[0]] = F[22,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[69,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[76,x,k[0]]
F[80,x,k[0]] = F[14,x,k[0]]*F[49,x,k[0]]
F[81,x,k[0]] = F[139,x,k[0]]+F[82,x]
F[82,x] = F[104,x]+F[27,x]+F[83,x]
F[83,x] = F[22,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[16,x]+F[43,x]
F[86,x] = F[82,x]+F[87,x]
F[87,x] = 2*F[27,x]+F[88,x]+F[92,x]
F[88,x] = F[22,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[43,x]
F[91,x] = F[87,x]
F[92,x] = F[22,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[22,x]*F[95,x]
F[95,x] = F[96,x]+F[98,x]
F[96,x] = F[20,x]+F[97,x]
F[97,x] = F[44,x]
F[98,x] = F[93,x]+F[99,x]
F[99,x] = 2*F[27,x]+F[100,x]+F[92,x]
F[100,x] = F[101,x]*F[22,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[97,x]
F[103,x] = F[99,x]
F[104,x] = F[105,x]*F[22,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[50,x]+F[93,x]
F[107,x] = F[108,x]+F[118,x]
F[108,x] = F[109,x]+F[116,x]+F[27,x]
F[109,x] = F[110,x]*F[22,x]
F[110,x] = F[111,x]+F[96,x]
F[111,x] = F[108,x]+F[112,x]
F[112,x] = 2*F[27,x]+F[113,x]+F[92,x]
F[113,x] = F[114,x]*F[22,x]
F[114,x] = F[102,x]+F[115,x]
F[115,x] = F[112,x]
F[116,x] = F[117,x]*F[22,x]
F[117,x] = F[108,x]+F[50,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[22,x]
F[120,x] = F[121,x]+F[124,x]
F[121,x] = F[122,x]+F[24,x]
F[122,x] = F[123,x]
F[123,x] = F[22,x]*F[24,x]
F[124,x] = F[118,x]+F[125,x]
F[125,x] = 3*F[27,x]+F[126,x]+F[130,x]
F[126,x] = F[127,x]*F[22,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[122,x]
F[129,x] = F[125,x]
F[130,x] = F[131,x]*F[22,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[22,x]
F[133,x] = F[121,x]+F[134,x]
F[134,x] = F[131,x]+F[135,x]
F[135,x] = 3*F[27,x]+F[130,x]+F[136,x]
F[136,x] = F[137,x]*F[22,x]
F[137,x] = F[128,x]+F[138,x]
F[138,x] = F[135,x]
F[139,x,k[0]] = F[140,x,k[0]]+F[161,x,k[0]]+F[194,x,k[0]]+F[27,x]
F[140,x,k[0]] = F[141,x,k[0]]*F[22,x]
F[141,x,k[0]] = F[142,x,k[0]]+F[143,x,k[0]]
F[142,x,k[0]] = F[26,x,k[0]]+F[45,x,k[0]]
F[143,x,k[0]] = F[139,x,k[0]]+F[144,x,k[0]]
F[144,x,k[0]] = 3*F[27,x]+F[145,x,k[0]]+F[149,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]*F[22,x]
F[146,x,k[0]] = F[147,x,k[0]]+F[148,x,k[0]]
F[147,x,k[0]] = F[45,x,k[0]]
F[148,x,k[0]] = F[144,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]*F[22,x]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]*F[22,x]
F[152,x,k[0]] = F[153,x,k[0]]+F[155,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[31,x,k[0]]
F[154,x,k[0]] = F[46,x,k[0]]
F[155,x,k[0]] = F[150,x,k[0]]+F[156,x,k[0]]
F[156,x,k[0]] = 3*F[27,x]+F[149,x,k[0]]+F[157,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]*F[22,x]
F[158,x,k[0]] = F[159,x,k[0]]+F[160,x,k[0]]
F[159,x,k[0]] = F[154,x,k[0]]
F[160,x,k[0]] = F[156,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]*F[22,x]
F[162,x,k[0]] = F[163,x,k[0]]+F[164,x,k[0]]
F[163,x,k[0]] = F[150,x,k[0]]+F[72,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[173,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[22,x]
F[167,x,k[0]] = F[153,x,k[0]]+F[168,x,k[0]]
F[168,x,k[0]] = F[165,x,k[0]]+F[169,x,k[0]]
F[169,x,k[0]] = 3*F[27,x]+F[149,x,k[0]]+F[170,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]*F[22,x]
F[171,x,k[0]] = F[159,x,k[0]]+F[172,x,k[0]]
F[172,x,k[0]] = F[169,x,k[0]]
F[173,x,k[0]] = F[174,x,k[0]]
F[174,x,k[0]] = F[175,x,k[0]]*F[22,x]
F[175,x,k[0]] = F[176,x,k[0]]+F[179,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[35,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[22,x]*F[35,x,k[0]]
F[179,x,k[0]] = F[173,x,k[0]]+F[180,x,k[0]]
F[180,x,k[0]] = 4*F[27,x]+F[181,x,k[0]]+F[185,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[22,x]
F[182,x,k[0]] = F[183,x,k[0]]+F[184,x,k[0]]
F[183,x,k[0]] = F[177,x,k[0]]
F[184,x,k[0]] = F[180,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]*F[22,x]
F[186,x,k[0]] = F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]*F[22,x]
F[188,x,k[0]] = F[176,x,k[0]]+F[189,x,k[0]]
F[189,x,k[0]] = F[186,x,k[0]]+F[190,x,k[0]]
F[190,x,k[0]] = 4*F[27,x]+F[185,x,k[0]]+F[191,x,k[0]]
F[191,x,k[0]] = F[192,x,k[0]]*F[22,x]
F[192,x,k[0]] = F[183,x,k[0]]+F[193,x,k[0]]
F[193,x,k[0]] = F[190,x,k[0]]
F[194,x,k[0]] = F[14,x,k[0]]*F[195,x,k[0]]
F[195,x,k[0]] = F[108,x]+F[196,x,k[0]]
F[196,x,k[0]] = 2*F[27,x]+F[194,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]*F[22,x]
F[198,x,k[0]] = F[153,x,k[0]]+F[199,x,k[0]]
F[199,x,k[0]] = F[196,x,k[0]]+F[200,x,k[0]]
F[200,x,k[0]] = 3*F[27,x]+F[149,x,k[0]]+F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[22,x]
F[202,x,k[0]] = F[159,x,k[0]]+F[203,x,k[0]]
F[203,x,k[0]] = F[200,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]+F[206,x,k[0]]
F[205,x,k[0]] = F[55,x]+F[66,x,k[0]]
F[206,x,k[0]] = F[144,x,k[0]]+F[87,x]
F[207,x,k[0]] = F[208,x,k[0]]*F[22,x]
F[208,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[209,x,k[0]] = F[14,x,k[0]]*F[6,x,k[0]]
F[210,x] = F[211,x]*F[22,x]
F[211,x] = F[212,x]+F[215,x]
F[212,x] = F[213,x]+F[214,x]
F[213,x] = F[1,x]+F[16,x]
F[214,x] = F[22,x]+F[43,x]
F[215,x] = F[216,x]+F[217,x]
F[216,x] = F[50,x]+F[82,x]
F[217,x] = F[55,x]+F[87,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_{22}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{210}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{22}\! \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_{207}\! \left(x , y\right)+F_{209}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{20}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right) F_{23}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{35}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x \right)+F_{45}\! \left(x , y\right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{27}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{22}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{22}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right) F_{50}\! \left(x \right)
F_{61}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{62}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{71}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{104}\! \left(x \right)+F_{27}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{22}\! \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_{16}\! \left(x \right)+F_{43}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{22}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{43}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)
F_{92}\! \left(x \right) = F_{22}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{22}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{20}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{44}\! \left(x \right)
F_{98}\! \left(x \right) = F_{93}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{100}\! \left(x \right)+F_{92}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{22}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{99}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{22}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{50}\! \left(x \right)+F_{93}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{118}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{116}\! \left(x \right)+F_{27}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{22}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{96}\! \left(x \right)
F_{111}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{113}\! \left(x \right)+F_{92}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{22}\! \left(x \right)
F_{114}\! \left(x \right) = F_{102}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{112}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{22}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right)+F_{50}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{22}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{124}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{24}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{22}\! \left(x \right) F_{24}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{126}\! \left(x \right)+F_{130}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{22}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{122}\! \left(x \right)
F_{129}\! \left(x \right) = F_{125}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{22}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{22}\! \left(x \right)
F_{133}\! \left(x \right) = F_{121}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{130}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{22}\! \left(x \right)
F_{137}\! \left(x \right) = F_{128}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{135}\! \left(x \right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{194}\! \left(x , y\right)+F_{27}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = 3 F_{27}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{149}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{22}\! \left(x \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_{45}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = 3 F_{27}\! \left(x \right)+F_{149}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right) F_{22}\! \left(x \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_{154}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{173}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{167}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{169}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = 3 F_{27}\! \left(x \right)+F_{149}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{171}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{169}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = 4 F_{27}\! \left(x \right)+F_{181}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{184}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{177}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{186}\! \left(x , y\right) = F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{188}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{186}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = 4 F_{27}\! \left(x \right)+F_{185}\! \left(x , y\right)+F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{192}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{192}\! \left(x , y\right) = F_{183}\! \left(x , y\right)+F_{193}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{195}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{108}\! \left(x \right)+F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = 2 F_{27}\! \left(x \right)+F_{194}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{198}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{199}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{196}\! \left(x , y\right)+F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = 3 F_{27}\! \left(x \right)+F_{149}\! \left(x , y\right)+F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{159}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{200}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{55}\! \left(x \right)+F_{66}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{87}\! \left(x \right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{208}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{209}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right) F_{22}\! \left(x \right)
F_{211}\! \left(x \right) = F_{212}\! \left(x \right)+F_{215}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)+F_{214}\! \left(x \right)
F_{213}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{214}\! \left(x \right) = F_{22}\! \left(x \right)+F_{43}\! \left(x \right)
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)+F_{217}\! \left(x \right)
F_{216}\! \left(x \right) = F_{50}\! \left(x \right)+F_{82}\! \left(x \right)
F_{217}\! \left(x \right) = F_{55}\! \left(x \right)+F_{87}\! \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_22(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_210(x) + F_4(x))
Eq(F_4(x), F_22(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_207(x, k_0) + F_209(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_22(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_47(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_38(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_15(x, k_0))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_11(x, k_0)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_16(x) + F_26(x, k_0))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_22(x))
Eq(F_18(x), F_19(x) + F_23(x))
Eq(F_19(x), F_1(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_19(x)*F_22(x))
Eq(F_22(x), x)
Eq(F_23(x), F_20(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_22(x)*F_23(x))
Eq(F_26(x, k_0), F_27(x) + F_28(x, k_0) + F_32(x, k_0))
Eq(F_27(x), 0)
Eq(F_28(x, k_0), F_22(x)*F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0) + F_34(x, k_0))
Eq(F_30(x, k_0), F_12(x, k_0) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_14(x, k_0)*F_33(x, k_0))
Eq(F_33(x, k_0), F_20(x) + F_31(x, k_0))
Eq(F_34(x, k_0), F_31(x, k_0) + F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_14(x, k_0)*F_37(x, k_0))
Eq(F_37(x, k_0), F_24(x) + F_35(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_42(x, k_0))
Eq(F_39(x, k_0), F_22(x) + F_40(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_12(x, k_0)*F_22(x))
Eq(F_42(x, k_0), F_43(x) + F_45(x, k_0))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_20(x)*F_22(x))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_22(x)*F_31(x, k_0))
Eq(F_47(x, k_0), F_204(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_81(x, k_0))
Eq(F_49(x, k_0), F_50(x) + F_61(x, k_0))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_22(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_1(x) + F_22(x))
Eq(F_54(x), F_50(x) + F_55(x))
Eq(F_55(x), F_27(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_22(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_22(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_22(x)*F_50(x))
Eq(F_61(x, k_0), F_27(x) + F_62(x, k_0) + F_80(x, k_0))
Eq(F_62(x, k_0), F_22(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_65(x, k_0))
Eq(F_64(x, k_0), F_12(x, k_0) + F_40(x, k_0))
Eq(F_65(x, k_0), F_61(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), 2*F_27(x) + F_67(x, k_0) + F_71(x, k_0))
Eq(F_67(x, k_0), F_22(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_70(x, k_0))
Eq(F_69(x, k_0), F_40(x, k_0))
Eq(F_70(x, k_0), F_66(x, k_0))
Eq(F_71(x, k_0), F_22(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0))
Eq(F_73(x, k_0), F_22(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_64(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), F_72(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), 2*F_27(x) + F_71(x, k_0) + F_77(x, k_0))
Eq(F_77(x, k_0), F_22(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_69(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_76(x, k_0))
Eq(F_80(x, k_0), F_14(x, k_0)*F_49(x, k_0))
Eq(F_81(x, k_0), F_139(x, k_0) + F_82(x))
Eq(F_82(x), F_104(x) + F_27(x) + F_83(x))
Eq(F_83(x), F_22(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_16(x) + F_43(x))
Eq(F_86(x), F_82(x) + F_87(x))
Eq(F_87(x), 2*F_27(x) + F_88(x) + F_92(x))
Eq(F_88(x), F_22(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_43(x))
Eq(F_91(x), F_87(x))
Eq(F_92(x), F_22(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_22(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_98(x))
Eq(F_96(x), F_20(x) + F_97(x))
Eq(F_97(x), F_44(x))
Eq(F_98(x), F_93(x) + F_99(x))
Eq(F_99(x), F_100(x) + 2*F_27(x) + F_92(x))
Eq(F_100(x), F_101(x)*F_22(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_97(x))
Eq(F_103(x), F_99(x))
Eq(F_104(x), F_105(x)*F_22(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_50(x) + F_93(x))
Eq(F_107(x), F_108(x) + F_118(x))
Eq(F_108(x), F_109(x) + F_116(x) + F_27(x))
Eq(F_109(x), F_110(x)*F_22(x))
Eq(F_110(x), F_111(x) + F_96(x))
Eq(F_111(x), F_108(x) + F_112(x))
Eq(F_112(x), F_113(x) + 2*F_27(x) + F_92(x))
Eq(F_113(x), F_114(x)*F_22(x))
Eq(F_114(x), F_102(x) + F_115(x))
Eq(F_115(x), F_112(x))
Eq(F_116(x), F_117(x)*F_22(x))
Eq(F_117(x), F_108(x) + F_50(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_22(x))
Eq(F_120(x), F_121(x) + F_124(x))
Eq(F_121(x), F_122(x) + F_24(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_22(x)*F_24(x))
Eq(F_124(x), F_118(x) + F_125(x))
Eq(F_125(x), F_126(x) + F_130(x) + 3*F_27(x))
Eq(F_126(x), F_127(x)*F_22(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_122(x))
Eq(F_129(x), F_125(x))
Eq(F_130(x), F_131(x)*F_22(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_22(x))
Eq(F_133(x), F_121(x) + F_134(x))
Eq(F_134(x), F_131(x) + F_135(x))
Eq(F_135(x), F_130(x) + F_136(x) + 3*F_27(x))
Eq(F_136(x), F_137(x)*F_22(x))
Eq(F_137(x), F_128(x) + F_138(x))
Eq(F_138(x), F_135(x))
Eq(F_139(x, k_0), F_140(x, k_0) + F_161(x, k_0) + F_194(x, k_0) + F_27(x))
Eq(F_140(x, k_0), F_141(x, k_0)*F_22(x))
Eq(F_141(x, k_0), F_142(x, k_0) + F_143(x, k_0))
Eq(F_142(x, k_0), F_26(x, k_0) + F_45(x, k_0))
Eq(F_143(x, k_0), F_139(x, k_0) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0) + F_149(x, k_0) + 3*F_27(x))
Eq(F_145(x, k_0), F_146(x, k_0)*F_22(x))
Eq(F_146(x, k_0), F_147(x, k_0) + F_148(x, k_0))
Eq(F_147(x, k_0), F_45(x, k_0))
Eq(F_148(x, k_0), F_144(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0)*F_22(x))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0)*F_22(x))
Eq(F_152(x, k_0), F_153(x, k_0) + F_155(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_31(x, k_0))
Eq(F_154(x, k_0), F_46(x, k_0))
Eq(F_155(x, k_0), F_150(x, k_0) + F_156(x, k_0))
Eq(F_156(x, k_0), F_149(x, k_0) + F_157(x, k_0) + 3*F_27(x))
Eq(F_157(x, k_0), F_158(x, k_0)*F_22(x))
Eq(F_158(x, k_0), F_159(x, k_0) + F_160(x, k_0))
Eq(F_159(x, k_0), F_154(x, k_0))
Eq(F_160(x, k_0), F_156(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0)*F_22(x))
Eq(F_162(x, k_0), F_163(x, k_0) + F_164(x, k_0))
Eq(F_163(x, k_0), F_150(x, k_0) + F_72(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_173(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_22(x))
Eq(F_167(x, k_0), F_153(x, k_0) + F_168(x, k_0))
Eq(F_168(x, k_0), F_165(x, k_0) + F_169(x, k_0))
Eq(F_169(x, k_0), F_149(x, k_0) + F_170(x, k_0) + 3*F_27(x))
Eq(F_170(x, k_0), F_171(x, k_0)*F_22(x))
Eq(F_171(x, k_0), F_159(x, k_0) + F_172(x, k_0))
Eq(F_172(x, k_0), F_169(x, k_0))
Eq(F_173(x, k_0), F_174(x, k_0))
Eq(F_174(x, k_0), F_175(x, k_0)*F_22(x))
Eq(F_175(x, k_0), F_176(x, k_0) + F_179(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_35(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_22(x)*F_35(x, k_0))
Eq(F_179(x, k_0), F_173(x, k_0) + F_180(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0) + F_185(x, k_0) + 4*F_27(x))
Eq(F_181(x, k_0), F_182(x, k_0)*F_22(x))
Eq(F_182(x, k_0), F_183(x, k_0) + F_184(x, k_0))
Eq(F_183(x, k_0), F_177(x, k_0))
Eq(F_184(x, k_0), F_180(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0)*F_22(x))
Eq(F_186(x, k_0), F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0)*F_22(x))
Eq(F_188(x, k_0), F_176(x, k_0) + F_189(x, k_0))
Eq(F_189(x, k_0), F_186(x, k_0) + F_190(x, k_0))
Eq(F_190(x, k_0), F_185(x, k_0) + F_191(x, k_0) + 4*F_27(x))
Eq(F_191(x, k_0), F_192(x, k_0)*F_22(x))
Eq(F_192(x, k_0), F_183(x, k_0) + F_193(x, k_0))
Eq(F_193(x, k_0), F_190(x, k_0))
Eq(F_194(x, k_0), F_14(x, k_0)*F_195(x, k_0))
Eq(F_195(x, k_0), F_108(x) + F_196(x, k_0))
Eq(F_196(x, k_0), F_194(x, k_0) + F_197(x, k_0) + 2*F_27(x))
Eq(F_197(x, k_0), F_198(x, k_0)*F_22(x))
Eq(F_198(x, k_0), F_153(x, k_0) + F_199(x, k_0))
Eq(F_199(x, k_0), F_196(x, k_0) + F_200(x, k_0))
Eq(F_200(x, k_0), F_149(x, k_0) + F_201(x, k_0) + 3*F_27(x))
Eq(F_201(x, k_0), F_202(x, k_0)*F_22(x))
Eq(F_202(x, k_0), F_159(x, k_0) + F_203(x, k_0))
Eq(F_203(x, k_0), F_200(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0) + F_206(x, k_0))
Eq(F_205(x, k_0), F_55(x) + F_66(x, k_0))
Eq(F_206(x, k_0), F_144(x, k_0) + F_87(x))
Eq(F_207(x, k_0), F_208(x, k_0)*F_22(x))
Eq(F_208(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_209(x, k_0), F_14(x, k_0)*F_6(x, k_0))
Eq(F_210(x), F_211(x)*F_22(x))
Eq(F_211(x), F_212(x) + F_215(x))
Eq(F_212(x), F_213(x) + F_214(x))
Eq(F_213(x), F_1(x) + F_16(x))
Eq(F_214(x), F_22(x) + F_43(x))
Eq(F_215(x), F_216(x) + F_217(x))
Eq(F_216(x), F_50(x) + F_82(x))
Eq(F_217(x), F_55(x) + F_87(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, 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