0132_1230_3012
Counting sequence:
1, 1, 2, 6, 21, 74, 249, 804, 2551, 8139, 26500, 88531, 303112, 1059129, 3759584, 13505901, 48965424, 178812038, 656851379, 2424911296, 8990618541, 33460049864, 124948929267, 468021157175, 1757950510224, 6619947293526, 24987401091475, 94521153411144, 358269507908905, 1360512529980898, 5175500642823481, 19720139903440314, 75254211223134845, 287590354520510631, 1100534422440316284, 4216819968887541957, 16176618457827579106, 62127422988608178433, 238861286187932232308, 919286658742542318624, 3541413702668302515633, 13655332297604736270035, 52699762216106250833352, 203553241434385742975769, 786853361053770716201258, 3043971215183795348793767, 11784299926822521856460038, 45653073684224674976938032, 176980971926816252921688617, 686533217107277815908315213, 2664794874865127319394450262, 10349580545382821404348119921, 40218747491162202753934167330, 156376618946958147803372968145, 608336336974938640848749835332, 2367750953583811555036761606754, 9220207881428793138977480751927, 35921160738203861216004819602993, 140009621027326597595067370530582, 545954616154904448016839274003319, 2129805580751026220085868968736368, 8311933539335885329337463642403065, 32451671282381519072577949836187568, 126747521841153512695571390071716569, 495226691716970199844696543357169692, 1935645264867889924057418658737901870, 7568326849428202769731798806853243475, 29602051871384720454451280305434418068, 115820975870345006623358778738175134737, 453306478380560983065586287731303418360, 1774728586800843255326415895997661961467, 6950298511446948818287130952144974545799, 27227188901156348688299679244704097318760, 106690678266233726543675016325662316797154, 418187556577337047709545506741689338145031, 1639583211007715859594974626544087228686640, 6429992141371019771036697630527823193238625, 25223134868180904346474732500793111376424806, 98968378479713362806618231537795926577304149, 388418459654978262261808771931997665745178203, 1524778037602314534195255037666087066198802860, 5987068087590635016662123112631064137248105840, 23513653103207411851404517185464407548719767225, 92368094235987606559307076329968430241830383060, 362925545275382724587978553838807747762725381397, 1426279248197656560561073240321625708686247377884, 5606359321754181295075885125371216171515805201663, 22041674156419608092145262199891468323684976018685, 86674934742182522462642363913552381803969637509538, 340899093046183318986596733147423492925723225265460, 1341033693846538100915997840594024285358596707726281, 5276345927430542786333855127177491651273453131497442, 20763703749922432193462189518596070595569033703121467, 81724580285262847944924767954706190912102061451883020, 321717925803339853113840574288743856767509486573842131, 1266691723780768060966446504164805339302993440024502009, 4988134928186722446530317164386295770409006527780093778, 19646064284316297883547195248727816074914974259375989058, 77389422353917655665734896332139647494521731445464051235, 304898253148147005327554437678566451621735465169603859098, 1201418200238278502014724509654142984384917088953479692299
Generating function in Maple syntax:
1/2*(2*(x-1)^6*(x-1/2)*(1-4*x)^(1/2)-6*x^8+24*x^7-45*x^6+28*x^5+15*x^4-36*x^3+25*x^2-8*x+1)/x/(2*x-1)/(x-1)^7
Generating function in latex syntax:
\frac{2 \left(x -1\right)^{6} \left(x -\frac{1}{2}\right) \sqrt{1-4 x}-6 x^{8}+24 x^{7}-45 x^{6}+28 x^{5}+15 x^{4}-36 x^{3}+25 x^{2}-8 x +1}{2 x \left(2 x -1\right) \left(x -1\right)^{7}}
Generating function in sympy syntax:
(-3*x**8 + 12*x**7 - 45*x**6/2 + 14*x**5 + 15*x**4/2 - 18*x**3 + 25*x**2/2 - 4*x + sqrt(1 - 4*x)*(x - 1)**6*(x - 1/2) + 1/2)/(x*(x - 1)**7*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^14*F(x)^2+(2*x-1)*(6*x^8-24*x^7+45*x^6-28*x^5-15*x^4+36*x^3-25*x^2+8*x-1)*(x-1)^7*F(x)+9*x^15-68*x^14+226*x^13-298*x^12-437*x^11+2873*x^10-6748*x^9+10045*x^8-10605*x^7+8258*x^6-4793*x^5+2056*x^4-634*x^3+133*x^2-17*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{14} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(6 x^{8}-24 x^{7}+45 x^{6}-28 x^{5}-15 x^{4}+36 x^{3}-25 x^{2}+8 x -1\right) \left(x -1\right)^{7} F \! \left(x \right)+9 x^{15}-68 x^{14}+226 x^{13}-298 x^{12}-437 x^{11}+2873 x^{10}-6748 x^{9}+10045 x^{8}-10605 x^{7}+8258 x^{6}-4793 x^{5}+2056 x^{4}-634 x^{3}+133 x^{2}-17 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(6) = 249
a(7) = 804
a(8) = 2551
a(9) = 8139
a(10) = 26500
a(n+4) = -8*(2*n+3)/(n+5)*a(n)+4*(9*n+19)/(n+5)*a(n+1)-2*(14*n+41)/(n+5)*a(n+2)+(35+9*n)/(n+5)*a(n+3)-1/120*(3*n^6-53*n^5+105*n^4+465*n^3+1092*n^2-292*n-840)/(n+5), n >= 11
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) = 74
a \! \left(6\right) = 249
a \! \left(7\right) = 804
a \! \left(8\right) = 2551
a \! \left(9\right) = 8139
a \! \left(10\right) = 26500
a \! \left(n +4\right) = -\frac{8 \left(2 n +3\right) a \! \left(n \right)}{n +5}+\frac{4 \left(9 n +19\right) a \! \left(n +1\right)}{n +5}-\frac{2 \left(14 n +41\right) a \! \left(n +2\right)}{n +5}+\frac{\left(35+9 n \right) a \! \left(n +3\right)}{n +5}-\frac{3 n^{6}-53 n^{5}+105 n^{4}+465 n^{3}+1092 n^{2}-292 n -840}{120 \left(n +5\right)}, \quad n \geq 11
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/294/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[19,x]*F[3,x]
F[3,x] = F[1,x]+F[282,x]+F[4,x]
F[4,x] = F[19,x]*F[5,x]
F[5,x] = F[1,x]+F[272,x]+F[281,x]+F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[1,x]+F[182,x]+F[186,x]+F[265,x]+F[8,x]
F[8,x] = F[19,x]*F[9,x]
F[9,x] = F[10,x,1]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[156,x,k[0]]+F[158,x,k[0]]+F[166,x,k[0]]+F[168,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[19,x]
F[12,x,k[0]] = F[13,x,k[0]]+F[64,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[34,x,k[0]]
F[14,x,k[0]] = F[15,x]+F[24,x,k[0]]
F[15,x] = F[16,x]+F[21,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[19,x]
F[19,x] = F[20,x,1]
F[20,x,k[0]] = k[0]*x
F[21,x] = F[17,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[19,x]*F[21,x]
F[24,x,k[0]] = F[25,x,k[0]]+F[31,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[29,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[20,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[19,x]*F[25,x,k[0]]
F[31,x,k[0]] = F[29,x,k[0]]+F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[19,x]*F[31,x,k[0]]
F[34,x,k[0]] = F[35,x]+F[49,x,k[0]]
F[35,x] = F[21,x]+F[36,x]
F[36,x] = F[37,x]+F[45,x]
F[37,x] = F[38,x]+F[39,x]+F[43,x]
F[38,x] = 0
F[39,x] = F[19,x]*F[40,x]
F[40,x] = F[19,x]+F[41,x]
F[41,x] = F[38,x]+F[39,x]+F[42,x]
F[42,x] = F[17,x]*F[19,x]
F[43,x] = F[19,x]*F[44,x]
F[44,x] = F[17,x]+F[37,x]
F[45,x] = F[46,x]
F[46,x] = F[19,x]*F[47,x]
F[47,x] = F[22,x]+F[48,x]
F[48,x] = F[46,x]
F[49,x,k[0]] = F[50,x,k[0]]+F[56,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[54,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[20,x,k[0]]*F[53,x,k[0]]
F[53,x,k[0]] = F[17,x]+F[51,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[19,x]*F[50,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[19,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[51,x,k[0]]+F[57,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[19,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[54,x,k[0]]+F[63,x,k[0]]
F[63,x,k[0]] = F[61,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[99,x,k[0]]
F[65,x,k[0]] = F[66,x]+F[80,x,k[0]]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[17,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = F[17,x]+F[68,x]
F[71,x] = F[72,x]+F[77,x]
F[72,x] = F[38,x]+F[73,x]+F[75,x]
F[73,x] = F[19,x]*F[74,x]
F[74,x] = F[17,x]+F[72,x]
F[75,x] = F[19,x]*F[76,x]
F[76,x] = F[17,x]+F[72,x]
F[77,x] = F[78,x]
F[78,x] = F[19,x]*F[79,x]
F[79,x] = F[22,x]+F[77,x]
F[80,x,k[0]] = F[81,x,k[0]]+F[90,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[87,x,k[0]]
F[82,x,k[0]] = F[38,x]+F[83,x,k[0]]+F[85,x,k[0]]
F[83,x,k[0]] = F[19,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[26,x,k[0]]+F[82,x,k[0]]
F[85,x,k[0]] = F[20,x,k[0]]*F[86,x,k[0]]
F[86,x,k[0]] = F[17,x]+F[82,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[19,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[29,x,k[0]]+F[87,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]+F[96,x,k[0]]
F[91,x,k[0]] = 2*F[38,x]+F[92,x,k[0]]+F[94,x,k[0]]
F[92,x,k[0]] = F[19,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[29,x,k[0]]+F[91,x,k[0]]
F[94,x,k[0]] = F[19,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[82,x,k[0]]+F[91,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[19,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[32,x,k[0]]+F[96,x,k[0]]
F[99,x,k[0]] = F[100,x]+F[131,x,k[0]]
F[100,x] = F[101,x]+F[71,x]
F[101,x] = F[102,x]+F[128,x]
F[102,x] = F[103,x]+F[105,x]+F[113,x]+F[38,x]
F[103,x] = F[104,x]*F[19,x]
F[104,x] = F[102,x]+F[37,x]
F[105,x] = F[106,x]*F[19,x]
F[106,x] = F[107,x]+F[110,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[19,x]
F[109,x] = F[107,x]+F[19,x]
F[110,x] = 2*F[38,x]+F[105,x]+F[111,x]
F[111,x] = F[112,x]*F[19,x]
F[112,x] = F[110,x]+F[41,x]
F[113,x] = F[114,x]*F[19,x]
F[114,x] = F[115,x]+F[72,x]
F[115,x] = F[113,x]+F[116,x]+F[121,x]+F[38,x]
F[116,x] = F[117,x]*F[19,x]
F[117,x] = F[118,x]+F[22,x]
F[118,x] = 2*F[38,x]+F[116,x]+F[119,x]
F[119,x] = F[120,x]*F[19,x]
F[120,x] = F[118,x]+F[72,x]
F[121,x] = F[122,x]*F[19,x]
F[122,x] = F[107,x]+F[123,x]
F[123,x] = 2*F[38,x]+F[121,x]+F[124,x]
F[124,x] = F[125,x]*F[19,x]
F[125,x] = F[126,x]+F[127,x]
F[126,x] = F[42,x]
F[127,x] = F[124,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[19,x]
F[130,x] = F[128,x]+F[45,x]
F[131,x,k[0]] = F[132,x,k[0]]+F[141,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[138,x,k[0]]
F[133,x,k[0]] = 2*F[38,x]+F[134,x,k[0]]+F[136,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[19,x]
F[135,x,k[0]] = F[133,x,k[0]]+F[51,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[20,x,k[0]]
F[137,x,k[0]] = F[133,x,k[0]]+F[72,x]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[19,x]
F[140,x,k[0]] = F[138,x,k[0]]+F[54,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]+F[153,x,k[0]]
F[142,x,k[0]] = 3*F[38,x]+F[143,x,k[0]]+F[145,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]*F[19,x]
F[144,x,k[0]] = F[142,x,k[0]]+F[57,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]*F[19,x]
F[146,x,k[0]] = F[133,x,k[0]]+F[147,x,k[0]]
F[147,x,k[0]] = 3*F[38,x]+F[145,x,k[0]]+F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[19,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[54,x,k[0]]
F[150,x,k[0]] = 3*F[38,x]+F[148,x,k[0]]+F[151,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]*F[19,x]
F[152,x,k[0]] = F[133,x,k[0]]+F[150,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]*F[19,x]
F[155,x,k[0]] = F[153,x,k[0]]+F[60,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]*F[19,x]
F[157,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[158,x,k[0]] = F[159,x,k[0]]*F[20,x,k[0]]
F[159,x,k[0]] = F[1,x]+F[158,x,k[0]]+F[160,x,k[0]]+F[164,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]*F[19,x]
F[161,x,k[0]] = F[162,x,k[0]]+F[163,x,k[0]]
F[162,x,k[0]] = F[28,x,k[0]]+F[53,x,k[0]]
F[163,x,k[0]] = F[137,x,k[0]]+F[86,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]*F[19,x]
F[165,x,k[0]] = 1/(-1+k[0])*(F[159,x,k[0]]*k[0]-F[159,x,1])
F[166,x,k[0]] = F[167,x,k[0]]*F[19,x]
F[167,x,k[0]] = 1/(-1+k[0])*(F[159,x,k[0]]*k[0]-F[159,x,1])
F[168,x,k[0]] = F[169,x,k[0]]*F[19,x]
F[169,x,k[0]] = F[14,x,k[0]]+F[170,x,k[0]]
F[170,x,k[0]] = F[171,x]+F[175,x,k[0]]
F[171,x] = F[172,x]+F[76,x]
F[172,x] = F[173,x]+F[22,x]
F[173,x] = F[174,x]
F[174,x] = F[172,x]*F[19,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[51,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[176,x,k[0]]*F[19,x]
F[179,x,k[0]] = F[180,x,k[0]]+F[54,x,k[0]]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[179,x,k[0]]*F[19,x]
F[182,x] = F[183,x]*F[19,x]
F[183,x] = F[184,x]+F[185,x]
F[184,x] = F[15,x]+F[35,x]
F[185,x] = F[100,x]+F[66,x]
F[186,x] = F[187,x]*F[19,x]
F[187,x] = F[1,x]+F[182,x]+F[186,x]+F[188,x]+F[263,x]+F[8,x]
F[188,x] = F[189,x]*F[19,x]
F[189,x] = F[190,x]+F[220,x]
F[190,x] = F[191,x]+F[217,x]
F[191,x] = F[192,x]+F[204,x]
F[192,x] = F[1,x]+F[193,x]
F[193,x] = F[194,x]
F[194,x] = F[19,x]*F[195,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[1,x]+F[19,x]
F[197,x] = F[193,x]+F[198,x]
F[198,x] = F[199,x]+F[203,x]+F[38,x]
F[199,x] = F[19,x]*F[200,x]
F[200,x] = F[201,x]+F[202,x]
F[201,x] = F[19,x]
F[202,x] = F[198,x]
F[203,x] = F[19,x]*F[193,x]
F[204,x] = F[193,x]+F[205,x]
F[205,x] = F[206,x]
F[206,x] = F[19,x]*F[207,x]
F[207,x] = F[208,x]+F[209,x]
F[208,x] = F[126,x]+F[17,x]
F[209,x] = F[210,x]+F[211,x]
F[210,x] = F[206,x]
F[211,x] = 2*F[38,x]+F[212,x]+F[216,x]
F[212,x] = F[19,x]*F[213,x]
F[213,x] = F[214,x]+F[215,x]
F[214,x] = F[126,x]
F[215,x] = F[211,x]
F[216,x] = F[19,x]*F[210,x]
F[217,x] = F[218,x]+F[219,x]
F[218,x] = F[17,x]
F[219,x] = F[210,x]
F[220,x] = F[221,x]+F[250,x]
F[221,x] = F[222,x]+F[226,x]
F[222,x] = F[17,x]+F[223,x]
F[223,x] = F[224,x]
F[224,x] = F[19,x]*F[225,x]
F[225,x] = F[193,x]+F[223,x]
F[226,x] = F[227,x]+F[247,x]
F[227,x] = F[228,x]+F[230,x]+F[38,x]
F[228,x] = F[19,x]*F[229,x]
F[229,x] = F[193,x]+F[227,x]
F[230,x] = F[19,x]*F[231,x]
F[231,x] = F[232,x]+F[233,x]
F[232,x] = F[107,x]+F[17,x]
F[233,x] = F[234,x]+F[243,x]
F[234,x] = F[235,x]+F[38,x]+F[73,x]
F[235,x] = F[19,x]*F[236,x]
F[236,x] = F[232,x]+F[237,x]
F[237,x] = F[234,x]+F[238,x]
F[238,x] = 2*F[38,x]+F[124,x]+F[239,x]
F[239,x] = F[19,x]*F[240,x]
F[240,x] = F[241,x]+F[242,x]
F[241,x] = F[107,x]
F[242,x] = F[238,x]
F[243,x] = 2*F[38,x]+F[111,x]+F[244,x]
F[244,x] = F[19,x]*F[245,x]
F[245,x] = F[241,x]+F[246,x]
F[246,x] = F[243,x]
F[247,x] = F[248,x]
F[248,x] = F[19,x]*F[249,x]
F[249,x] = F[205,x]+F[247,x]
F[250,x] = F[251,x]+F[252,x]
F[251,x] = F[72,x]
F[252,x] = F[253,x]
F[253,x] = 2*F[38,x]+F[254,x]+F[256,x]
F[254,x] = F[19,x]*F[255,x]
F[255,x] = F[210,x]+F[253,x]
F[256,x] = F[19,x]*F[257,x]
F[257,x] = F[258,x]+F[259,x]
F[258,x] = F[22,x]
F[259,x] = F[260,x]
F[260,x] = F[19,x]*F[261,x]
F[261,x] = F[258,x]+F[262,x]
F[262,x] = F[260,x]
F[263,x] = F[264,x]
F[264,x] = F[16,x]^2*F[19,x]*F[192,x]
F[265,x] = F[19,x]*F[266,x]
F[266,x] = F[267,x]+F[269,x]
F[267,x] = F[192,x]+F[268,x]
F[268,x] = F[17,x]+F[210,x]
F[269,x] = F[270,x]+F[271,x]
F[270,x] = F[17,x]+F[227,x]
F[271,x] = F[253,x]+F[72,x]
F[272,x] = F[19,x]*F[273,x]
F[273,x] = F[1,x]+F[274,x]+F[276,x]+F[280,x]
F[274,x] = F[275,x,1]
F[275,x,k[0]] = F[159,x,k[0]]*F[19,x]
F[276,x] = F[19,x]*F[277,x]
F[277,x] = F[278,x]+F[279,x]
F[278,x] = F[195,x]+F[207,x]
F[279,x] = F[231,x]+F[257,x]
F[280,x] = F[19,x]*F[273,x]
F[281,x] = F[19,x]*F[277,x]
F[282,x] = F[19,x]*F[283,x]
F[283,x] = F[1,x]+F[284,x]+F[289,x]+F[306,x]
F[284,x] = F[19,x]*F[285,x]
F[285,x] = F[286,x]+F[287,x]
F[286,x] = F[16,x]+F[44,x]
F[287,x] = F[288,x]+F[76,x]
F[288,x] = F[102,x]+F[72,x]
F[289,x] = F[19,x]*F[290,x]
F[290,x] = F[1,x]+F[291,x]+F[301,x]+F[306,x]+F[308,x]
F[291,x] = F[19,x]*F[292,x]
F[292,x] = F[293,x,1]
F[293,x,k[0]] = F[294,x,k[0]]+F[297,x,k[0]]
F[294,x,k[0]] = F[295,x,k[0]]+F[296,x,k[0]]
F[295,x,k[0]] = F[16,x]+F[25,x,k[0]]
F[296,x,k[0]] = F[44,x]+F[59,x,k[0]]
F[297,x,k[0]] = F[298,x,k[0]]+F[299,x,k[0]]
F[298,x,k[0]] = F[76,x]+F[95,x,k[0]]
F[299,x,k[0]] = F[288,x]+F[300,x,k[0]]
F[300,x,k[0]] = F[133,x,k[0]]+F[142,x,k[0]]
F[301,x] = F[302,x,1]
F[302,x,k[0]] = F[19,x]*F[303,x,k[0]]
F[303,x,k[0]] = 1/(-1+k[0])*(F[304,x,k[0]]*k[0]-F[304,x,1])
F[304,x,k[0]] = F[1,x]+F[158,x,k[0]]+F[166,x,k[0]]+F[302,x,k[0]]+F[305,x,k[0]]
F[305,x,k[0]] = F[19,x]*F[293,x,k[0]]
F[306,x] = F[19,x]*F[307,x]
F[307,x] = F[159,x,1]
F[308,x] = F[166,x,1]
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_{19}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{282}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{19}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{272}\! \left(x \right)+F_{281}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{182}\! \left(x \right)+F_{186}\! \left(x \right)+F_{265}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{19}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{156}\! \left(x , y\right)+F_{158}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{168}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{24}\! \left(x , y\right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \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_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = y x
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_{23}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x \right)+F_{49}\! \left(x , y\right)
F_{35}\! \left(x \right) = F_{21}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{19}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{22}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{46}\! \left(x \right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{51}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{17}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{17}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{77}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{19}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{17}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{17}\! \left(x \right)+F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{22}\! \left(x \right)+F_{77}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{83}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = 2 F_{38}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x \right)+F_{131}\! \left(x , y\right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{71}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{128}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{105}\! \left(x \right)+F_{113}\! \left(x \right)+F_{38}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{19}\! \left(x \right)
F_{104}\! \left(x \right) = F_{102}\! \left(x \right)+F_{37}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{19}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{110}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{19}\! \left(x \right)
F_{109}\! \left(x \right) = F_{107}\! \left(x \right)+F_{19}\! \left(x \right)
F_{110}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{19}\! \left(x \right)
F_{112}\! \left(x \right) = F_{110}\! \left(x \right)+F_{41}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{19}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{72}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)+F_{121}\! \left(x \right)+F_{38}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{19}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{22}\! \left(x \right)
F_{118}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{19}\! \left(x \right)
F_{120}\! \left(x \right) = F_{118}\! \left(x \right)+F_{72}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{19}\! \left(x \right)
F_{122}\! \left(x \right) = F_{107}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{121}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{19}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{127}\! \left(x \right)
F_{126}\! \left(x \right) = F_{42}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{19}\! \left(x \right)
F_{130}\! \left(x \right) = F_{128}\! \left(x \right)+F_{45}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = 2 F_{38}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{72}\! \left(x \right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = 3 F_{38}\! \left(x \right)+F_{143}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{144}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{146}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = 3 F_{38}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = 3 F_{38}\! \left(x \right)+F_{148}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{152}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{155}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{157}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{158}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{164}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{165}\! \left(x , y\right) = -\frac{-y F_{159}\! \left(x , y\right)+F_{159}\! \left(x , 1\right)}{-1+y}
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{167}\! \left(x , y\right) = -\frac{-y F_{159}\! \left(x , y\right)+F_{159}\! \left(x , 1\right)}{-1+y}
F_{168}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x \right)+F_{175}\! \left(x , y\right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{76}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{22}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{172}\! \left(x \right) F_{19}\! \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_{51}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{176}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{19}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{185}\! \left(x \right)
F_{184}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \left(x \right)
F_{185}\! \left(x \right) = F_{100}\! \left(x \right)+F_{66}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{19}\! \left(x \right)
F_{187}\! \left(x \right) = F_{1}\! \left(x \right)+F_{182}\! \left(x \right)+F_{186}\! \left(x \right)+F_{188}\! \left(x \right)+F_{263}\! \left(x \right)+F_{8}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right) F_{19}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{220}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{217}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{204}\! \left(x \right)
F_{192}\! \left(x \right) = F_{1}\! \left(x \right)+F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{19}\! \left(x \right) F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{197}\! \left(x \right) = F_{193}\! \left(x \right)+F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)+F_{203}\! \left(x \right)+F_{38}\! \left(x \right)
F_{199}\! \left(x \right) = F_{19}\! \left(x \right) F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{202}\! \left(x \right)
F_{201}\! \left(x \right) = F_{19}\! \left(x \right)
F_{202}\! \left(x \right) = F_{198}\! \left(x \right)
F_{203}\! \left(x \right) = F_{19}\! \left(x \right) F_{193}\! \left(x \right)
F_{204}\! \left(x \right) = F_{193}\! \left(x \right)+F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)
F_{206}\! \left(x \right) = F_{19}\! \left(x \right) F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{208}\! \left(x \right)+F_{209}\! \left(x \right)
F_{208}\! \left(x \right) = F_{126}\! \left(x \right)+F_{17}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{211}\! \left(x \right)
F_{210}\! \left(x \right) = F_{206}\! \left(x \right)
F_{211}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{212}\! \left(x \right)+F_{216}\! \left(x \right)
F_{212}\! \left(x \right) = F_{19}\! \left(x \right) F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right)+F_{215}\! \left(x \right)
F_{214}\! \left(x \right) = F_{126}\! \left(x \right)
F_{215}\! \left(x \right) = F_{211}\! \left(x \right)
F_{216}\! \left(x \right) = F_{19}\! \left(x \right) F_{210}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)+F_{219}\! \left(x \right)
F_{218}\! \left(x \right) = F_{17}\! \left(x \right)
F_{219}\! \left(x \right) = F_{210}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)+F_{250}\! \left(x \right)
F_{221}\! \left(x \right) = F_{222}\! \left(x \right)+F_{226}\! \left(x \right)
F_{222}\! \left(x \right) = F_{17}\! \left(x \right)+F_{223}\! \left(x \right)
F_{223}\! \left(x \right) = F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{19}\! \left(x \right) F_{225}\! \left(x \right)
F_{225}\! \left(x \right) = F_{193}\! \left(x \right)+F_{223}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)+F_{247}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right)+F_{230}\! \left(x \right)+F_{38}\! \left(x \right)
F_{228}\! \left(x \right) = F_{19}\! \left(x \right) F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{193}\! \left(x \right)+F_{227}\! \left(x \right)
F_{230}\! \left(x \right) = F_{19}\! \left(x \right) F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)+F_{233}\! \left(x \right)
F_{232}\! \left(x \right) = F_{107}\! \left(x \right)+F_{17}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{243}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right)+F_{38}\! \left(x \right)+F_{73}\! \left(x \right)
F_{235}\! \left(x \right) = F_{19}\! \left(x \right) F_{236}\! \left(x \right)
F_{236}\! \left(x \right) = F_{232}\! \left(x \right)+F_{237}\! \left(x \right)
F_{237}\! \left(x \right) = F_{234}\! \left(x \right)+F_{238}\! \left(x \right)
F_{238}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{124}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{19}\! \left(x \right) F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)+F_{242}\! \left(x \right)
F_{241}\! \left(x \right) = F_{107}\! \left(x \right)
F_{242}\! \left(x \right) = F_{238}\! \left(x \right)
F_{243}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{111}\! \left(x \right)+F_{244}\! \left(x \right)
F_{244}\! \left(x \right) = F_{19}\! \left(x \right) F_{245}\! \left(x \right)
F_{245}\! \left(x \right) = F_{241}\! \left(x \right)+F_{246}\! \left(x \right)
F_{246}\! \left(x \right) = F_{243}\! \left(x \right)
F_{247}\! \left(x \right) = F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{19}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{205}\! \left(x \right)+F_{247}\! \left(x \right)
F_{250}\! \left(x \right) = F_{251}\! \left(x \right)+F_{252}\! \left(x \right)
F_{251}\! \left(x \right) = F_{72}\! \left(x \right)
F_{252}\! \left(x \right) = F_{253}\! \left(x \right)
F_{253}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{254}\! \left(x \right)+F_{256}\! \left(x \right)
F_{254}\! \left(x \right) = F_{19}\! \left(x \right) F_{255}\! \left(x \right)
F_{255}\! \left(x \right) = F_{210}\! \left(x \right)+F_{253}\! \left(x \right)
F_{256}\! \left(x \right) = F_{19}\! \left(x \right) F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right)+F_{259}\! \left(x \right)
F_{258}\! \left(x \right) = F_{22}\! \left(x \right)
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = F_{19}\! \left(x \right) F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = F_{258}\! \left(x \right)+F_{262}\! \left(x \right)
F_{262}\! \left(x \right) = F_{260}\! \left(x \right)
F_{263}\! \left(x \right) = F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{16} \left(x \right)^{2} F_{19}\! \left(x \right) F_{192}\! \left(x \right)
F_{265}\! \left(x \right) = F_{19}\! \left(x \right) F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)+F_{269}\! \left(x \right)
F_{267}\! \left(x \right) = F_{192}\! \left(x \right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{17}\! \left(x \right)+F_{210}\! \left(x \right)
F_{269}\! \left(x \right) = F_{270}\! \left(x \right)+F_{271}\! \left(x \right)
F_{270}\! \left(x \right) = F_{17}\! \left(x \right)+F_{227}\! \left(x \right)
F_{271}\! \left(x \right) = F_{253}\! \left(x \right)+F_{72}\! \left(x \right)
F_{272}\! \left(x \right) = F_{19}\! \left(x \right) F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{1}\! \left(x \right)+F_{274}\! \left(x \right)+F_{276}\! \left(x \right)+F_{280}\! \left(x \right)
F_{274}\! \left(x \right) = F_{275}\! \left(x , 1\right)
F_{275}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{19}\! \left(x \right)
F_{276}\! \left(x \right) = F_{19}\! \left(x \right) F_{277}\! \left(x \right)
F_{277}\! \left(x \right) = F_{278}\! \left(x \right)+F_{279}\! \left(x \right)
F_{278}\! \left(x \right) = F_{195}\! \left(x \right)+F_{207}\! \left(x \right)
F_{279}\! \left(x \right) = F_{231}\! \left(x \right)+F_{257}\! \left(x \right)
F_{280}\! \left(x \right) = F_{19}\! \left(x \right) F_{273}\! \left(x \right)
F_{281}\! \left(x \right) = F_{19}\! \left(x \right) F_{277}\! \left(x \right)
F_{282}\! \left(x \right) = F_{19}\! \left(x \right) F_{283}\! \left(x \right)
F_{283}\! \left(x \right) = F_{1}\! \left(x \right)+F_{284}\! \left(x \right)+F_{289}\! \left(x \right)+F_{306}\! \left(x \right)
F_{284}\! \left(x \right) = F_{19}\! \left(x \right) F_{285}\! \left(x \right)
F_{285}\! \left(x \right) = F_{286}\! \left(x \right)+F_{287}\! \left(x \right)
F_{286}\! \left(x \right) = F_{16}\! \left(x \right)+F_{44}\! \left(x \right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)+F_{76}\! \left(x \right)
F_{288}\! \left(x \right) = F_{102}\! \left(x \right)+F_{72}\! \left(x \right)
F_{289}\! \left(x \right) = F_{19}\! \left(x \right) F_{290}\! \left(x \right)
F_{290}\! \left(x \right) = F_{1}\! \left(x \right)+F_{291}\! \left(x \right)+F_{301}\! \left(x \right)+F_{306}\! \left(x \right)+F_{308}\! \left(x \right)
F_{291}\! \left(x \right) = F_{19}\! \left(x \right) F_{292}\! \left(x \right)
F_{292}\! \left(x \right) = F_{293}\! \left(x , 1\right)
F_{293}\! \left(x , y\right) = F_{294}\! \left(x , y\right)+F_{297}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = F_{295}\! \left(x , y\right)+F_{296}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{298}\! \left(x , y\right)+F_{299}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{76}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{288}\! \left(x \right)+F_{300}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{301}\! \left(x \right) = F_{302}\! \left(x , 1\right)
F_{302}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{303}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = -\frac{-F_{304}\! \left(x , y\right) y +F_{304}\! \left(x , 1\right)}{-1+y}
F_{304}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{158}\! \left(x , y\right)+F_{166}\! \left(x , y\right)+F_{302}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{293}\! \left(x , y\right)
F_{306}\! \left(x \right) = F_{19}\! \left(x \right) F_{307}\! \left(x \right)
F_{307}\! \left(x \right) = F_{159}\! \left(x , 1\right)
F_{308}\! \left(x \right) = F_{166}\! \left(x , 1\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_19(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_282(x) + F_4(x))
Eq(F_4(x), F_19(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_272(x) + F_281(x) + F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_1(x) + F_182(x) + F_186(x) + F_265(x) + F_8(x))
Eq(F_8(x), F_19(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_156(x, k_0) + F_158(x, k_0) + F_166(x, k_0) + F_168(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_19(x))
Eq(F_12(x, k_0), F_13(x, k_0) + F_64(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_34(x, k_0))
Eq(F_14(x, k_0), F_15(x) + F_24(x, k_0))
Eq(F_15(x), F_16(x) + F_21(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_19(x))
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x), F_17(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_19(x)*F_21(x))
Eq(F_24(x, k_0), F_25(x, k_0) + F_31(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_29(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_20(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_19(x)*F_25(x, k_0))
Eq(F_31(x, k_0), F_29(x, k_0) + F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_19(x)*F_31(x, k_0))
Eq(F_34(x, k_0), F_35(x) + F_49(x, k_0))
Eq(F_35(x), F_21(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_45(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_43(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_19(x)*F_40(x))
Eq(F_40(x), F_19(x) + F_41(x))
Eq(F_41(x), F_38(x) + F_39(x) + F_42(x))
Eq(F_42(x), F_17(x)*F_19(x))
Eq(F_43(x), F_19(x)*F_44(x))
Eq(F_44(x), F_17(x) + F_37(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_19(x)*F_47(x))
Eq(F_47(x), F_22(x) + F_48(x))
Eq(F_48(x), F_46(x))
Eq(F_49(x, k_0), F_50(x, k_0) + F_56(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_54(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_20(x, k_0)*F_53(x, k_0))
Eq(F_53(x, k_0), F_17(x) + F_51(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_19(x)*F_50(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_19(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_51(x, k_0) + F_57(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_19(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_54(x, k_0) + F_63(x, k_0))
Eq(F_63(x, k_0), F_61(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_99(x, k_0))
Eq(F_65(x, k_0), F_66(x) + F_80(x, k_0))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_17(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_17(x) + F_68(x))
Eq(F_71(x), F_72(x) + F_77(x))
Eq(F_72(x), F_38(x) + F_73(x) + F_75(x))
Eq(F_73(x), F_19(x)*F_74(x))
Eq(F_74(x), F_17(x) + F_72(x))
Eq(F_75(x), F_19(x)*F_76(x))
Eq(F_76(x), F_17(x) + F_72(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_19(x)*F_79(x))
Eq(F_79(x), F_22(x) + F_77(x))
Eq(F_80(x, k_0), F_81(x, k_0) + F_90(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_87(x, k_0))
Eq(F_82(x, k_0), F_38(x) + F_83(x, k_0) + F_85(x, k_0))
Eq(F_83(x, k_0), F_19(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_26(x, k_0) + F_82(x, k_0))
Eq(F_85(x, k_0), F_20(x, k_0)*F_86(x, k_0))
Eq(F_86(x, k_0), F_17(x) + F_82(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_19(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_29(x, k_0) + F_87(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0) + F_96(x, k_0))
Eq(F_91(x, k_0), 2*F_38(x) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_92(x, k_0), F_19(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_29(x, k_0) + F_91(x, k_0))
Eq(F_94(x, k_0), F_19(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_82(x, k_0) + F_91(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_19(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_32(x, k_0) + F_96(x, k_0))
Eq(F_99(x, k_0), F_100(x) + F_131(x, k_0))
Eq(F_100(x), F_101(x) + F_71(x))
Eq(F_101(x), F_102(x) + F_128(x))
Eq(F_102(x), F_103(x) + F_105(x) + F_113(x) + F_38(x))
Eq(F_103(x), F_104(x)*F_19(x))
Eq(F_104(x), F_102(x) + F_37(x))
Eq(F_105(x), F_106(x)*F_19(x))
Eq(F_106(x), F_107(x) + F_110(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_19(x))
Eq(F_109(x), F_107(x) + F_19(x))
Eq(F_110(x), F_105(x) + F_111(x) + 2*F_38(x))
Eq(F_111(x), F_112(x)*F_19(x))
Eq(F_112(x), F_110(x) + F_41(x))
Eq(F_113(x), F_114(x)*F_19(x))
Eq(F_114(x), F_115(x) + F_72(x))
Eq(F_115(x), F_113(x) + F_116(x) + F_121(x) + F_38(x))
Eq(F_116(x), F_117(x)*F_19(x))
Eq(F_117(x), F_118(x) + F_22(x))
Eq(F_118(x), F_116(x) + F_119(x) + 2*F_38(x))
Eq(F_119(x), F_120(x)*F_19(x))
Eq(F_120(x), F_118(x) + F_72(x))
Eq(F_121(x), F_122(x)*F_19(x))
Eq(F_122(x), F_107(x) + F_123(x))
Eq(F_123(x), F_121(x) + F_124(x) + 2*F_38(x))
Eq(F_124(x), F_125(x)*F_19(x))
Eq(F_125(x), F_126(x) + F_127(x))
Eq(F_126(x), F_42(x))
Eq(F_127(x), F_124(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_19(x))
Eq(F_130(x), F_128(x) + F_45(x))
Eq(F_131(x, k_0), F_132(x, k_0) + F_141(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_138(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_136(x, k_0) + 2*F_38(x))
Eq(F_134(x, k_0), F_135(x, k_0)*F_19(x))
Eq(F_135(x, k_0), F_133(x, k_0) + F_51(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_20(x, k_0))
Eq(F_137(x, k_0), F_133(x, k_0) + F_72(x))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_19(x))
Eq(F_140(x, k_0), F_138(x, k_0) + F_54(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0) + F_153(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_145(x, k_0) + 3*F_38(x))
Eq(F_143(x, k_0), F_144(x, k_0)*F_19(x))
Eq(F_144(x, k_0), F_142(x, k_0) + F_57(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0)*F_19(x))
Eq(F_146(x, k_0), F_133(x, k_0) + F_147(x, k_0))
Eq(F_147(x, k_0), F_145(x, k_0) + F_148(x, k_0) + 3*F_38(x))
Eq(F_148(x, k_0), F_149(x, k_0)*F_19(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_54(x, k_0))
Eq(F_150(x, k_0), F_148(x, k_0) + F_151(x, k_0) + 3*F_38(x))
Eq(F_151(x, k_0), F_152(x, k_0)*F_19(x))
Eq(F_152(x, k_0), F_133(x, k_0) + F_150(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0)*F_19(x))
Eq(F_155(x, k_0), F_153(x, k_0) + F_60(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0)*F_19(x))
Eq(F_157(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_158(x, k_0), F_159(x, k_0)*F_20(x, k_0))
Eq(F_159(x, k_0), F_1(x) + F_158(x, k_0) + F_160(x, k_0) + F_164(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0)*F_19(x))
Eq(F_161(x, k_0), F_162(x, k_0) + F_163(x, k_0))
Eq(F_162(x, k_0), F_28(x, k_0) + F_53(x, k_0))
Eq(F_163(x, k_0), F_137(x, k_0) + F_86(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0)*F_19(x))
Eq(F_165(x, k_0), (k_0*F_159(x, k_0) - F_159(x, 1))/(k_0 - 1))
Eq(F_166(x, k_0), F_167(x, k_0)*F_19(x))
Eq(F_167(x, k_0), (-k_0*F_159(x, k_0) + F_159(x, 1))/(1 - k_0))
Eq(F_168(x, k_0), F_169(x, k_0)*F_19(x))
Eq(F_169(x, k_0), F_14(x, k_0) + F_170(x, k_0))
Eq(F_170(x, k_0), F_171(x) + F_175(x, k_0))
Eq(F_171(x), F_172(x) + F_76(x))
Eq(F_172(x), F_173(x) + F_22(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_172(x)*F_19(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_51(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_176(x, k_0)*F_19(x))
Eq(F_179(x, k_0), F_180(x, k_0) + F_54(x, k_0))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_179(x, k_0)*F_19(x))
Eq(F_182(x), F_183(x)*F_19(x))
Eq(F_183(x), F_184(x) + F_185(x))
Eq(F_184(x), F_15(x) + F_35(x))
Eq(F_185(x), F_100(x) + F_66(x))
Eq(F_186(x), F_187(x)*F_19(x))
Eq(F_187(x), F_1(x) + F_182(x) + F_186(x) + F_188(x) + F_263(x) + F_8(x))
Eq(F_188(x), F_189(x)*F_19(x))
Eq(F_189(x), F_190(x) + F_220(x))
Eq(F_190(x), F_191(x) + F_217(x))
Eq(F_191(x), F_192(x) + F_204(x))
Eq(F_192(x), F_1(x) + F_193(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_19(x)*F_195(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_1(x) + F_19(x))
Eq(F_197(x), F_193(x) + F_198(x))
Eq(F_198(x), F_199(x) + F_203(x) + F_38(x))
Eq(F_199(x), F_19(x)*F_200(x))
Eq(F_200(x), F_201(x) + F_202(x))
Eq(F_201(x), F_19(x))
Eq(F_202(x), F_198(x))
Eq(F_203(x), F_19(x)*F_193(x))
Eq(F_204(x), F_193(x) + F_205(x))
Eq(F_205(x), F_206(x))
Eq(F_206(x), F_19(x)*F_207(x))
Eq(F_207(x), F_208(x) + F_209(x))
Eq(F_208(x), F_126(x) + F_17(x))
Eq(F_209(x), F_210(x) + F_211(x))
Eq(F_210(x), F_206(x))
Eq(F_211(x), F_212(x) + F_216(x) + 2*F_38(x))
Eq(F_212(x), F_19(x)*F_213(x))
Eq(F_213(x), F_214(x) + F_215(x))
Eq(F_214(x), F_126(x))
Eq(F_215(x), F_211(x))
Eq(F_216(x), F_19(x)*F_210(x))
Eq(F_217(x), F_218(x) + F_219(x))
Eq(F_218(x), F_17(x))
Eq(F_219(x), F_210(x))
Eq(F_220(x), F_221(x) + F_250(x))
Eq(F_221(x), F_222(x) + F_226(x))
Eq(F_222(x), F_17(x) + F_223(x))
Eq(F_223(x), F_224(x))
Eq(F_224(x), F_19(x)*F_225(x))
Eq(F_225(x), F_193(x) + F_223(x))
Eq(F_226(x), F_227(x) + F_247(x))
Eq(F_227(x), F_228(x) + F_230(x) + F_38(x))
Eq(F_228(x), F_19(x)*F_229(x))
Eq(F_229(x), F_193(x) + F_227(x))
Eq(F_230(x), F_19(x)*F_231(x))
Eq(F_231(x), F_232(x) + F_233(x))
Eq(F_232(x), F_107(x) + F_17(x))
Eq(F_233(x), F_234(x) + F_243(x))
Eq(F_234(x), F_235(x) + F_38(x) + F_73(x))
Eq(F_235(x), F_19(x)*F_236(x))
Eq(F_236(x), F_232(x) + F_237(x))
Eq(F_237(x), F_234(x) + F_238(x))
Eq(F_238(x), F_124(x) + F_239(x) + 2*F_38(x))
Eq(F_239(x), F_19(x)*F_240(x))
Eq(F_240(x), F_241(x) + F_242(x))
Eq(F_241(x), F_107(x))
Eq(F_242(x), F_238(x))
Eq(F_243(x), F_111(x) + F_244(x) + 2*F_38(x))
Eq(F_244(x), F_19(x)*F_245(x))
Eq(F_245(x), F_241(x) + F_246(x))
Eq(F_246(x), F_243(x))
Eq(F_247(x), F_248(x))
Eq(F_248(x), F_19(x)*F_249(x))
Eq(F_249(x), F_205(x) + F_247(x))
Eq(F_250(x), F_251(x) + F_252(x))
Eq(F_251(x), F_72(x))
Eq(F_252(x), F_253(x))
Eq(F_253(x), F_254(x) + F_256(x) + 2*F_38(x))
Eq(F_254(x), F_19(x)*F_255(x))
Eq(F_255(x), F_210(x) + F_253(x))
Eq(F_256(x), F_19(x)*F_257(x))
Eq(F_257(x), F_258(x) + F_259(x))
Eq(F_258(x), F_22(x))
Eq(F_259(x), F_260(x))
Eq(F_260(x), F_19(x)*F_261(x))
Eq(F_261(x), F_258(x) + F_262(x))
Eq(F_262(x), F_260(x))
Eq(F_263(x), F_264(x))
Eq(F_264(x), F_16(x)**2*F_19(x)*F_192(x))
Eq(F_265(x), F_19(x)*F_266(x))
Eq(F_266(x), F_267(x) + F_269(x))
Eq(F_267(x), F_192(x) + F_268(x))
Eq(F_268(x), F_17(x) + F_210(x))
Eq(F_269(x), F_270(x) + F_271(x))
Eq(F_270(x), F_17(x) + F_227(x))
Eq(F_271(x), F_253(x) + F_72(x))
Eq(F_272(x), F_19(x)*F_273(x))
Eq(F_273(x), F_1(x) + F_274(x) + F_276(x) + F_280(x))
Eq(F_274(x), F_275(x, 1))
Eq(F_275(x, k_0), F_159(x, k_0)*F_19(x))
Eq(F_276(x), F_19(x)*F_277(x))
Eq(F_277(x), F_278(x) + F_279(x))
Eq(F_278(x), F_195(x) + F_207(x))
Eq(F_279(x), F_231(x) + F_257(x))
Eq(F_280(x), F_19(x)*F_273(x))
Eq(F_281(x), F_19(x)*F_277(x))
Eq(F_282(x), F_19(x)*F_283(x))
Eq(F_283(x), F_1(x) + F_284(x) + F_289(x) + F_306(x))
Eq(F_284(x), F_19(x)*F_285(x))
Eq(F_285(x), F_286(x) + F_287(x))
Eq(F_286(x), F_16(x) + F_44(x))
Eq(F_287(x), F_288(x) + F_76(x))
Eq(F_288(x), F_102(x) + F_72(x))
Eq(F_289(x), F_19(x)*F_290(x))
Eq(F_290(x), F_1(x) + F_291(x) + F_301(x) + F_306(x) + F_308(x))
Eq(F_291(x), F_19(x)*F_292(x))
Eq(F_292(x), F_293(x, 1))
Eq(F_293(x, k_0), F_294(x, k_0) + F_297(x, k_0))
Eq(F_294(x, k_0), F_295(x, k_0) + F_296(x, k_0))
Eq(F_295(x, k_0), F_16(x) + F_25(x, k_0))
Eq(F_296(x, k_0), F_44(x) + F_59(x, k_0))
Eq(F_297(x, k_0), F_298(x, k_0) + F_299(x, k_0))
Eq(F_298(x, k_0), F_76(x) + F_95(x, k_0))
Eq(F_299(x, k_0), F_288(x) + F_300(x, k_0))
Eq(F_300(x, k_0), F_133(x, k_0) + F_142(x, k_0))
Eq(F_301(x), F_302(x, 1))
Eq(F_302(x, k_0), F_19(x)*F_303(x, k_0))
Eq(F_303(x, k_0), (k_0*F_304(x, k_0) - F_304(x, 1))/(k_0 - 1))
Eq(F_304(x, k_0), F_1(x) + F_158(x, k_0) + F_166(x, k_0) + F_302(x, k_0) + F_305(x, k_0))
Eq(F_305(x, k_0), F_19(x)*F_293(x, k_0))
Eq(F_306(x), F_19(x)*F_307(x))
Eq(F_307(x), F_159(x, 1))
Eq(F_308(x), F_166(x, 1))
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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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