0123_0213_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 65, 200, 599, 1810, 5650, 18352, 61769, 213646, 753497, 2694436, 9732861, 35430622, 129786096, 477914680, 1767805851, 6565193010, 24468395119, 91486797324, 343068051800, 1289920986224, 4861980031964, 18367420274044, 69533685246583, 263748220321714, 1002242753684825, 3814987576027324, 14544638186938841, 55534069172283766, 212336139002491356, 812944059329964904, 3116285529267462367, 11959798454580417818, 45950804462061255979, 176733863061885249404, 680425372279732345320, 2622127043376004567424, 10113918593836922330768, 39044429916302491533308, 150853479213881445879899, 583300119610588880476634, 2257117854112432446848021, 8740328711603542135905836, 33868773757331784376659178, 131327898242450840456786628, 509552245180180088010341998, 1978261657757286553533176740, 7684785670516568185047329337, 29869166945777129549772906214, 116157871455791441449812018675, 451959718027971485846122761508, 1759414616608854899789502974466, 6852456927844945555143700918812, 26700952856774996019433301716288, 104088460289122592263874475923508, 405944995127577562191395752674611, 1583850964596121195608277392288314, 6182127958584857956330090067867033, 24139737743045631437397476981209964, 94295850558771989011307421809336273, 368479169875816677925753116431952038, 1440418573150919705765978041672538740, 5632681584560312808780892000697684040, 22033725021956517610932505203744505447, 86218923998960286021333545843065937002, 337485502510215976147079603813777191395, 1321422108420282271670533797907654729948, 5175569924646105561780123435429903229080, 20276890389709399867651365051124302228736, 79463489365077377850652970598088576446744, 311496878311103321156425757450287733227068, 1221395654430378811866539653870919312123203, 4790408930363303911403944072120778805413994, 18793142726809884575362477006539373862479373, 73745243611532458459992383309550986556899852, 289450081175264899454888308939298081877208598, 1136359577947336271932841802824282085869440972, 4462290049988320482465659149145362441877930686, 17526585015616776834739976221194114153125753716, 68854441132780194707897723441225564176415473097, 270557451039395118028661806102282400487501214822, 1063353702922273835973075343669704126856730754299, 4180080073556524734514773199423362794695971480484, 16435314834665426797069299703267796815901994080946, 64633260585762914370496946971156002807750303771676, 254224158304000796523954059748861289776684867865864, 1000134600800354781929400488476581149742736038017012, 3935312233584004685417856048643428080534581530000379, 15487357822491889407128331915538500373535030778972170, 60960876535340415751462573484349963175011928158112593, 239993345518077005168915796430517351572365225935072972, 944973797977428207852605910069020853969399555071048222, 3721443204405954385563870620607409173973844290990269548, 14657929356129575437016878005113357790241630138058883842, 57743358069601357782187700924955506391078081999007395476, 227508830794229349661819541029514154070156383349971544877, 896519947090131496687170071341751232649066923035532082766
Generating function in Maple syntax:
1/2*(-2*(x-1/2)*(x-1)^6*(1-4*x)^(1/2)-4*x^8+10*x^7-17*x^6+40*x^5-57*x^4+50*x^3-27*x^2+8*x-1)/x/(2*x-1)/(x-1)^6
Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(x -1\right)^{6} \sqrt{1-4 x}-4 x^{8}+10 x^{7}-17 x^{6}+40 x^{5}-57 x^{4}+50 x^{3}-27 x^{2}+8 x -1}{2 x \left(2 x -1\right) \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-2*x**8 + 5*x**7 - 17*x**6/2 + 20*x**5 - 57*x**4/2 + 25*x**3 - 27*x**2/2 + 4*x + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**6/2 - 1/2)/(x*(x - 1)**6*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^12*F(x)^2+(2*x-1)*(4*x^8-10*x^7+17*x^6-40*x^5+57*x^4-50*x^3+27*x^2-8*x+1)*(x-1)^6*F(x)+4*x^15-16*x^14+6*x^13+161*x^12-848*x^11+2490*x^10-4911*x^9+6985*x^8-7412*x^7+5948*x^6-3607*x^5+1629*x^4-531*x^3+118*x^2-16*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{12} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(4 x^{8}-10 x^{7}+17 x^{6}-40 x^{5}+57 x^{4}-50 x^{3}+27 x^{2}-8 x +1\right) \left(x -1\right)^{6} F \! \left(x \right)+4 x^{15}-16 x^{14}+6 x^{13}+161 x^{12}-848 x^{11}+2490 x^{10}-4911 x^{9}+6985 x^{8}-7412 x^{7}+5948 x^{6}-3607 x^{5}+1629 x^{4}-531 x^{3}+118 x^{2}-16 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 200
a(7) = 599
a(8) = 1810
a(9) = 5650
a(10) = 18352
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(1+n)+2*(4*n+11)/(n+4)*a(n+2)-1/120*(n-1)*(3*n^5-38*n^4-143*n^3+1802*n^2-1456*n-480)/(n+4), 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) = 20
a \! \left(5\right) = 65
a \! \left(6\right) = 200
a \! \left(7\right) = 599
a \! \left(8\right) = 1810
a \! \left(9\right) = 5650
a \! \left(10\right) = 18352
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(1+n \right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}-\frac{\left(n -1\right) \left(3 n^{5}-38 n^{4}-143 n^{3}+1802 n^{2}-1456 n -480\right)}{120 \left(n +4\right)}, \quad n \geq 11
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21148/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[115,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[114,x]+F[49,x]+F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[23,x]+F[8,x]
F[8,x] = F[14,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = k[0]*x
F[14,x] = F[10,x]+F[15,x]
F[15,x] = F[16,x]+F[17,x]+F[22,x]
F[16,x] = 0
F[17,x] = F[12,x]*F[18,x]
F[18,x] = F[10,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[10,x]+F[19,x]
F[22,x] = F[12,x]*F[14,x]
F[23,x] = F[24,x]+F[29,x]
F[24,x] = F[10,x]+F[25,x]
F[25,x] = F[16,x]+F[26,x]+F[28,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[10,x]+F[25,x]
F[28,x] = F[12,x]*F[24,x]
F[29,x] = F[25,x]+F[30,x]
F[30,x] = F[16,x]+F[31,x]+F[33,x]+F[41,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[15,x]+F[30,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[10,x]+F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[19,x]+F[38,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[25,x]+F[43,x]
F[43,x] = F[16,x]+F[33,x]+F[41,x]+F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[19,x]+F[46,x]
F[46,x] = 2*F[16,x]+F[44,x]+F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[25,x]+F[46,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x,1]
F[51,x,k[0]] = F[1,x]+F[102,x,k[0]]+F[104,x,k[0]]+F[112,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[12,x]*F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[69,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[62,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[9,x]
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[13,x,k[0]]*F[59,x,k[0]]
F[59,x,k[0]] = F[1,x]+F[57,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[56,x,k[0]]
F[62,x,k[0]] = F[14,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[13,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[10,x]+F[64,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[12,x]*F[63,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[81,x,k[0]]
F[70,x,k[0]] = F[24,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[77,x,k[0]]
F[72,x,k[0]] = F[16,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[12,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[57,x,k[0]]+F[72,x,k[0]]
F[75,x,k[0]] = F[13,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[10,x]+F[72,x,k[0]]
F[77,x,k[0]] = 2*F[16,x]+F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[12,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[60,x,k[0]]+F[77,x,k[0]]
F[80,x,k[0]] = F[12,x]*F[71,x,k[0]]
F[81,x,k[0]] = F[29,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = 2*F[16,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[12,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[64,x,k[0]]+F[83,x,k[0]]
F[86,x,k[0]] = F[13,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[25,x]+F[83,x,k[0]]
F[88,x,k[0]] = 3*F[16,x]+F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[12,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[67,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[12,x]*F[92,x,k[0]]
F[92,x,k[0]] = F[83,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = 3*F[16,x]+F[91,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[12,x]*F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]+F[99,x,k[0]]
F[96,x,k[0]] = F[97,x,k[0]]
F[97,x,k[0]] = F[12,x]*F[98,x,k[0]]
F[98,x,k[0]] = F[64,x,k[0]]+F[96,x,k[0]]
F[99,x,k[0]] = 3*F[16,x]+F[100,x,k[0]]+F[94,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[12,x]
F[101,x,k[0]] = F[83,x,k[0]]+F[99,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[12,x]
F[103,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[104,x,k[0]] = F[105,x,k[0]]*F[13,x,k[0]]
F[105,x,k[0]] = F[1,x]+F[104,x,k[0]]+F[106,x,k[0]]+F[110,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[12,x]
F[107,x,k[0]] = F[108,x,k[0]]+F[109,x,k[0]]
F[108,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[109,x,k[0]] = F[76,x,k[0]]+F[87,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[12,x]
F[111,x,k[0]] = 1/(-1+k[0])*(F[105,x,k[0]]*k[0]-F[105,x,1])
F[112,x,k[0]] = F[113,x,k[0]]*F[12,x]
F[113,x,k[0]] = 1/(-1+k[0])*(F[105,x,k[0]]*k[0]-F[105,x,1])
F[114,x] = F[104,x,1]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[136,x]
F[117,x] = F[118,x]+F[125,x]
F[118,x] = F[1,x]+F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[122,x]+F[9,x]
F[122,x] = F[119,x]+F[123,x]
F[123,x] = F[124,x]
F[124,x] = F[12,x]*F[122,x]
F[125,x] = F[12,x]+F[126,x]
F[126,x] = F[127,x]+F[128,x]+F[16,x]
F[127,x] = F[10,x]*F[12,x]
F[128,x] = F[12,x]*F[129,x]
F[129,x] = F[130,x]+F[133,x]
F[130,x] = F[12,x]+F[131,x]
F[131,x] = F[132,x]
F[132,x] = F[12,x]*F[130,x]
F[133,x] = F[126,x]+F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[133,x]
F[136,x] = F[137,x]+F[189,x]
F[137,x] = F[138,x]+F[149,x]
F[138,x] = F[139,x]
F[139,x] = F[12,x]*F[140,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[1,x]+F[12,x]
F[142,x] = F[138,x]+F[143,x]
F[143,x] = F[144,x]+F[148,x]+F[16,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[12,x]
F[147,x] = F[143,x]
F[148,x] = F[12,x]*F[138,x]
F[149,x] = F[150,x]+F[16,x]+F[183,x]
F[150,x] = F[12,x]*F[151,x]
F[151,x] = F[152,x]+F[158,x]
F[152,x] = F[119,x]+F[153,x]
F[153,x] = F[127,x]+F[154,x]+F[16,x]
F[154,x] = F[12,x]*F[155,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[12,x]
F[157,x] = F[153,x]
F[158,x] = F[149,x]+F[159,x]
F[159,x] = F[16,x]+F[160,x]+F[164,x]+F[176,x]
F[160,x] = F[12,x]*F[161,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[153,x]
F[163,x] = F[159,x]
F[164,x] = F[12,x]*F[165,x]
F[165,x] = F[166,x]
F[166,x] = F[12,x]*F[167,x]
F[167,x] = F[168,x]+F[170,x]
F[168,x] = F[10,x]+F[169,x]
F[169,x] = F[127,x]
F[170,x] = F[165,x]+F[171,x]
F[171,x] = 2*F[16,x]+F[164,x]+F[172,x]
F[172,x] = F[12,x]*F[173,x]
F[173,x] = F[174,x]+F[175,x]
F[174,x] = F[169,x]
F[175,x] = F[171,x]
F[176,x] = F[12,x]*F[177,x]
F[177,x] = F[178,x]+F[180,x]
F[178,x] = F[179,x]
F[179,x] = F[10,x]*F[12,x]
F[180,x] = F[181,x]
F[181,x] = 2*F[16,x]+F[176,x]+F[182,x]
F[182,x] = F[12,x]*F[35,x]
F[183,x] = F[12,x]*F[184,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[10,x]+F[35,x]
F[186,x] = F[187,x]+F[188,x]
F[187,x] = F[16,x]+F[183,x]+F[26,x]
F[188,x] = F[39,x]
F[189,x] = F[143,x]+F[190,x]
F[190,x] = F[16,x]+F[164,x]+F[191,x]+F[195,x]
F[191,x] = F[12,x]*F[192,x]
F[192,x] = F[193,x]+F[194,x]
F[193,x] = F[126,x]
F[194,x] = F[190,x]
F[195,x] = F[12,x]*F[196,x]
F[196,x] = F[197,x]+F[198,x]
F[197,x] = F[179,x]
F[198,x] = F[199,x]
F[199,x] = 2*F[16,x]+F[182,x]+F[195,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{114}\! \left(x \right)+F_{49}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{22}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{10}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)+F_{41}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{10}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right)+F_{33}\! \left(x \right)+F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{25}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x , 1\right)
F_{51}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{102}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{9}\! \left(x \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_{13}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{1}\! \left(x \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_{12}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = 2 F_{16}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = 2 F_{16}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 3 F_{16}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = 3 F_{16}\! \left(x \right)+F_{91}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = 3 F_{16}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{101}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{103}\! \left(x , y\right) = -\frac{-y F_{51}\! \left(x , y\right)+F_{51}\! \left(x , 1\right)}{-1+y}
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{13}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{104}\! \left(x , y\right)+F_{106}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{111}\! \left(x , y\right) = -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{113}\! \left(x , y\right) = -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}
F_{114}\! \left(x \right) = F_{104}\! \left(x , 1\right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{136}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{125}\! \left(x \right)
F_{118}\! \left(x \right) = F_{1}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{9}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)+F_{16}\! \left(x \right)
F_{127}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{133}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{133}\! \left(x \right) = F_{126}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{189}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{149}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{142}\! \left(x \right) = F_{138}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{148}\! \left(x \right)+F_{16}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right)
F_{147}\! \left(x \right) = F_{143}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{16}\! \left(x \right)+F_{183}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{158}\! \left(x \right)
F_{152}\! \left(x \right) = F_{119}\! \left(x \right)+F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{127}\! \left(x \right)+F_{154}\! \left(x \right)+F_{16}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12}\! \left(x \right)
F_{157}\! \left(x \right) = F_{153}\! \left(x \right)
F_{158}\! \left(x \right) = F_{149}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{16}\! \left(x \right)+F_{160}\! \left(x \right)+F_{164}\! \left(x \right)+F_{176}\! \left(x \right)
F_{160}\! \left(x \right) = F_{12}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{153}\! \left(x \right)
F_{163}\! \left(x \right) = F_{159}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{12}\! \left(x \right) F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{170}\! \left(x \right)
F_{168}\! \left(x \right) = F_{10}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{127}\! \left(x \right)
F_{170}\! \left(x \right) = F_{165}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{164}\! \left(x \right)+F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{12}\! \left(x \right) F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{175}\! \left(x \right)
F_{174}\! \left(x \right) = F_{169}\! \left(x \right)
F_{175}\! \left(x \right) = F_{171}\! \left(x \right)
F_{176}\! \left(x \right) = F_{12}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{180}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{176}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{183}\! \left(x \right) = F_{12}\! \left(x \right) F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{10}\! \left(x \right)+F_{35}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{188}\! \left(x \right)
F_{187}\! \left(x \right) = F_{16}\! \left(x \right)+F_{183}\! \left(x \right)+F_{26}\! \left(x \right)
F_{188}\! \left(x \right) = F_{39}\! \left(x \right)
F_{189}\! \left(x \right) = F_{143}\! \left(x \right)+F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{16}\! \left(x \right)+F_{164}\! \left(x \right)+F_{191}\! \left(x \right)+F_{195}\! \left(x \right)
F_{191}\! \left(x \right) = F_{12}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{194}\! \left(x \right)
F_{193}\! \left(x \right) = F_{126}\! \left(x \right)
F_{194}\! \left(x \right) = F_{190}\! \left(x \right)
F_{195}\! \left(x \right) = F_{12}\! \left(x \right) F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{198}\! \left(x \right)
F_{197}\! \left(x \right) = F_{179}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right)
F_{199}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{182}\! \left(x \right)+F_{195}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_115(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_114(x) + F_49(x) + F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_23(x) + F_8(x))
Eq(F_8(x), F_14(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x), F_10(x) + F_15(x))
Eq(F_15(x), F_16(x) + F_17(x) + F_22(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_12(x)*F_18(x))
Eq(F_18(x), F_10(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_10(x) + F_19(x))
Eq(F_22(x), F_12(x)*F_14(x))
Eq(F_23(x), F_24(x) + F_29(x))
Eq(F_24(x), F_10(x) + F_25(x))
Eq(F_25(x), F_16(x) + F_26(x) + F_28(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_10(x) + F_25(x))
Eq(F_28(x), F_12(x)*F_24(x))
Eq(F_29(x), F_25(x) + F_30(x))
Eq(F_30(x), F_16(x) + F_31(x) + F_33(x) + F_41(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_15(x) + F_30(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_10(x) + F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_19(x) + F_38(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_25(x) + F_43(x))
Eq(F_43(x), F_16(x) + F_33(x) + F_41(x) + F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_19(x) + F_46(x))
Eq(F_46(x), 2*F_16(x) + F_44(x) + F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_25(x) + F_46(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x, 1))
Eq(F_51(x, k_0), F_1(x) + F_102(x, k_0) + F_104(x, k_0) + F_112(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_12(x)*F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_69(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_62(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_9(x))
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_13(x, k_0)*F_59(x, k_0))
Eq(F_59(x, k_0), F_1(x) + F_57(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_56(x, k_0))
Eq(F_62(x, k_0), F_14(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_13(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_10(x) + F_64(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_12(x)*F_63(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_81(x, k_0))
Eq(F_70(x, k_0), F_24(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_77(x, k_0))
Eq(F_72(x, k_0), F_16(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_12(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_57(x, k_0) + F_72(x, k_0))
Eq(F_75(x, k_0), F_13(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_10(x) + F_72(x, k_0))
Eq(F_77(x, k_0), 2*F_16(x) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_12(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_60(x, k_0) + F_77(x, k_0))
Eq(F_80(x, k_0), F_12(x)*F_71(x, k_0))
Eq(F_81(x, k_0), F_29(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), 2*F_16(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_12(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_64(x, k_0) + F_83(x, k_0))
Eq(F_86(x, k_0), F_13(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_25(x) + F_83(x, k_0))
Eq(F_88(x, k_0), 3*F_16(x) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_12(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_67(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_12(x)*F_92(x, k_0))
Eq(F_92(x, k_0), F_83(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), 3*F_16(x) + F_91(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_12(x)*F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0) + F_99(x, k_0))
Eq(F_96(x, k_0), F_97(x, k_0))
Eq(F_97(x, k_0), F_12(x)*F_98(x, k_0))
Eq(F_98(x, k_0), F_64(x, k_0) + F_96(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0) + 3*F_16(x) + F_94(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_12(x))
Eq(F_101(x, k_0), F_83(x, k_0) + F_99(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_12(x))
Eq(F_103(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_104(x, k_0), F_105(x, k_0)*F_13(x, k_0))
Eq(F_105(x, k_0), F_1(x) + F_104(x, k_0) + F_106(x, k_0) + F_110(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_12(x))
Eq(F_107(x, k_0), F_108(x, k_0) + F_109(x, k_0))
Eq(F_108(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_109(x, k_0), F_76(x, k_0) + F_87(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_12(x))
Eq(F_111(x, k_0), (k_0*F_105(x, k_0) - F_105(x, 1))/(k_0 - 1))
Eq(F_112(x, k_0), F_113(x, k_0)*F_12(x))
Eq(F_113(x, k_0), (-k_0*F_105(x, k_0) + F_105(x, 1))/(1 - k_0))
Eq(F_114(x), F_104(x, 1))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_136(x))
Eq(F_117(x), F_118(x) + F_125(x))
Eq(F_118(x), F_1(x) + F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_122(x) + F_9(x))
Eq(F_122(x), F_119(x) + F_123(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_12(x)*F_122(x))
Eq(F_125(x), F_12(x) + F_126(x))
Eq(F_126(x), F_127(x) + F_128(x) + F_16(x))
Eq(F_127(x), F_10(x)*F_12(x))
Eq(F_128(x), F_12(x)*F_129(x))
Eq(F_129(x), F_130(x) + F_133(x))
Eq(F_130(x), F_12(x) + F_131(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_12(x)*F_130(x))
Eq(F_133(x), F_126(x) + F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_133(x))
Eq(F_136(x), F_137(x) + F_189(x))
Eq(F_137(x), F_138(x) + F_149(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_12(x)*F_140(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_1(x) + F_12(x))
Eq(F_142(x), F_138(x) + F_143(x))
Eq(F_143(x), F_144(x) + F_148(x) + F_16(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_12(x))
Eq(F_147(x), F_143(x))
Eq(F_148(x), F_12(x)*F_138(x))
Eq(F_149(x), F_150(x) + F_16(x) + F_183(x))
Eq(F_150(x), F_12(x)*F_151(x))
Eq(F_151(x), F_152(x) + F_158(x))
Eq(F_152(x), F_119(x) + F_153(x))
Eq(F_153(x), F_127(x) + F_154(x) + F_16(x))
Eq(F_154(x), F_12(x)*F_155(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_12(x))
Eq(F_157(x), F_153(x))
Eq(F_158(x), F_149(x) + F_159(x))
Eq(F_159(x), F_16(x) + F_160(x) + F_164(x) + F_176(x))
Eq(F_160(x), F_12(x)*F_161(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_153(x))
Eq(F_163(x), F_159(x))
Eq(F_164(x), F_12(x)*F_165(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_12(x)*F_167(x))
Eq(F_167(x), F_168(x) + F_170(x))
Eq(F_168(x), F_10(x) + F_169(x))
Eq(F_169(x), F_127(x))
Eq(F_170(x), F_165(x) + F_171(x))
Eq(F_171(x), 2*F_16(x) + F_164(x) + F_172(x))
Eq(F_172(x), F_12(x)*F_173(x))
Eq(F_173(x), F_174(x) + F_175(x))
Eq(F_174(x), F_169(x))
Eq(F_175(x), F_171(x))
Eq(F_176(x), F_12(x)*F_177(x))
Eq(F_177(x), F_178(x) + F_180(x))
Eq(F_178(x), F_179(x))
Eq(F_179(x), F_10(x)*F_12(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), 2*F_16(x) + F_176(x) + F_182(x))
Eq(F_182(x), F_12(x)*F_35(x))
Eq(F_183(x), F_12(x)*F_184(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_10(x) + F_35(x))
Eq(F_186(x), F_187(x) + F_188(x))
Eq(F_187(x), F_16(x) + F_183(x) + F_26(x))
Eq(F_188(x), F_39(x))
Eq(F_189(x), F_143(x) + F_190(x))
Eq(F_190(x), F_16(x) + F_164(x) + F_191(x) + F_195(x))
Eq(F_191(x), F_12(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_194(x))
Eq(F_193(x), F_126(x))
Eq(F_194(x), F_190(x))
Eq(F_195(x), F_12(x)*F_196(x))
Eq(F_196(x), F_197(x) + F_198(x))
Eq(F_197(x), F_179(x))
Eq(F_198(x), F_199(x))
Eq(F_199(x), 2*F_16(x) + F_182(x) + F_195(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": [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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 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