0123_0132_1230
Counting sequence:
1, 1, 2, 6, 21, 78, 294, 1108, 4165, 15638, 58762, 221324, 836330, 3171916, 12074924, 46131496, 176825773, 679821798, 2620668290, 10126767068, 39215528382, 152150654116, 591331343476, 2301726368280, 8971740956066, 35014119898748, 136805568493284, 535075776576888, 2094787396712820, 8208134360422488, 32188395967081048, 126321826465162832, 496087478021348989, 1949476453204330886, 7665469184657022258, 30158067010081885948, 118712614364072895926, 467525011723157595316, 1842106311484170107684, 7261306005639916898232, 28634810954547440996310, 112964927945759730717972, 445813937864177216647788, 1760013630152367500988904, 6950612852105395599703564, 27457925035432332042293160, 108503378449108028963543144, 428887692476666373537878576, 1695754400171505377102270418, 6706501431760997789518549468, 26530033339949590328002219252, 104974448365257257889026431704, 415459848176643771625754282540, 1644637001691518188695380545256, 6511825237199167406856498987144, 25788344566739217308520060406000, 102147753297106210389975918223780, 404683571349027334057877262304824, 1603543271473455279687967455597320, 6355083628908365836378200338194544, 25190373646482495638142472950245736, 99866107682615195058726892693426096, 395976459075349649737432095111889072, 1570312266841097313354156502916750496, 6228247864378624328272783232090383901, 24706252069038334760081061973283434694, 98018256455332121583901027234435192722, 388923609004844112819326168279002922812, 1543394912193606024047420786049311742310, 6125527901328345673763499310456279473492, 24314314969025506181549881639451615501828, 96523051392881099259835573142532845105144, 383220767889247821946501399664975480867214, 1521649355467952033191060122204070111874980, 6042634416419135024480381909386288155121564, 23998435158450670534905258071648639410979976, 95319803961375011409975758544157514207927708, 378639365017670148505556232666041255333823368, 1504214030177372376108162972423463539613204680, 5976317283894999435258414617953604539579412848, 23746342652364327289682474539806779550465894982, 94362157708367844965072825166367960470786023156, 375004137938297813921668943025169232562715225276, 1490425848990320322837115698912608467230421340360, 5924066081674572241278677659094774647456111484036, 23548526842430051922095404747827156370035040811704, 93614059162400757508975760643464994523399164843032, 372178327895144591867882410296865666820021069171152, 1479765743276676864869361570628637847296887773605020, 5883909528370900906799250847173659154329883448800072, 23397497078140075539329863023202878071833195750781688, 93047028935192647641852837136606091546744147362686864, 370053598248033160716415391704613028903125047697417304, 1471821380830847063586008458140053933246377242488753360, 5854277477535542193835091636244392512933766441810198224, 23287271336162478722611135865243056128497141088699100256, 92638265427700862624831043586347635150446224105034281778, 368542995675519039127221073060898959102543630175307052188, 1466261015953110895719722167834042147116761163604679214740, 5833903685064960784002906338369135181311327644121579629208, 23213014382566017042976421535993446407989703018922820260412
Generating function in Maple syntax:
((-8*x^3+16*x^2-8*x+1)*(1-4*x)^(1/2)+40*x^3-58*x^2+24*x-3)/(32*x^3-40*x^2+16*x-2)
Generating function in latex syntax:
\frac{\left(-8 x^{3}+16 x^{2}-8 x +1\right) \sqrt{1-4 x}+40 x^{3}-58 x^{2}+24 x -3}{32 x^{3}-40 x^{2}+16 x -2}
Generating function in sympy syntax:
(40*x**3 - 58*x**2 + 24*x + sqrt(1 - 4*x)*(-8*x**3 + 16*x**2 - 8*x + 1) - 3)/(32*x**3 - 40*x**2 + 16*x - 2)
Implicit equation for the generating function in Maple syntax:
(4*x-1)*(2*x-1)^4*F(x)^2-(4*x-1)*(10*x^2-12*x+3)*(2*x-1)^2*F(x)+16*x^6+36*x^5-169*x^4+196*x^3-99*x^2+23*x-2 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) \left(2 x -1\right)^{4} F \! \left(x \right)^{2}-\left(4 x -1\right) \left(10 x^{2}-12 x +3\right) \left(2 x -1\right)^{2} F \! \left(x \right)+16 x^{6}+36 x^{5}-169 x^{4}+196 x^{3}-99 x^{2}+23 x -2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
2
a(3) = 6
a(4) = 21
a(5) = 78
a(6) = 294
a(n+6) = -64*(2*n-1)/(n+6)*a(n)+32*(13*n+10)/(n+6)*a(n+1)-16*(32*n+59)/(n+6)*a(n+2)+24*(13*n+37)/(n+6)*a(n+3)-4*(25*n+96)/(n+6)*a(n+4)+2*(8*n+39)/(n+6)*a(n+5), n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 78
a \! \left(6\right) = 294
a \! \left(n +6\right) = -\frac{64 \left(2 n -1\right) a \! \left(n \right)}{n +6}+\frac{32 \left(13 n +10\right) a \! \left(n +1\right)}{n +6}-\frac{16 \left(32 n +59\right) a \! \left(n +2\right)}{n +6}+\frac{24 \left(13 n +37\right) a \! \left(n +3\right)}{n +6}-\frac{4 \left(25 n +96\right) a \! \left(n +4\right)}{n +6}+\frac{2 \left(8 n +39\right) a \! \left(n +5\right)}{n +6}, \quad n \geq 7
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/229/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[320,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[15,x,k[0]]+F[195,x,k[0]]+F[51,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[8,x,k[0]]
F[15,x,k[0]] = F[11,x]*F[16,x,k[0]]
F[16,x,k[0]] = (F[17,x,k[0]]*k[0]-F[17,x,1])/(-1+k[0])
F[17,x,k[0]] = F[1,x]+F[109,x,k[0]]+F[15,x,k[0]]+F[18,x,k[0]]+F[51,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[8,x,k[0]]
F[19,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[20,x,k[0]]+F[22,x,k[0]]
F[20,x,k[0]] = F[11,x]*F[21,x,k[0]]
F[21,x,k[0]] = (F[19,x,k[0]]*k[0]-F[19,x,1])/(-1+k[0])
F[22,x,k[0]] = F[11,x]*F[23,x,k[0]]
F[23,x,k[0]] = F[24,x]+F[34,x,k[0]]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[11,x]*F[25,x]
F[28,x] = F[26,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]+F[33,x]
F[30,x] = 0
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[26,x]+F[29,x]
F[33,x] = F[11,x]*F[28,x]
F[34,x,k[0]] = F[35,x,k[0]]+F[43,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]+F[39,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x,k[0]]
F[38,x,k[0]] = F[1,x]+F[36,x,k[0]]
F[39,x,k[0]] = F[30,x]+F[40,x,k[0]]+F[42,x,k[0]]
F[40,x,k[0]] = F[41,x,k[0]]*F[8,x,k[0]]
F[41,x,k[0]] = F[26,x]+F[39,x,k[0]]
F[42,x,k[0]] = F[11,x]*F[35,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[47,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[11,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[36,x,k[0]]+F[44,x,k[0]]
F[47,x,k[0]] = 2*F[30,x]+F[48,x,k[0]]+F[50,x,k[0]]
F[48,x,k[0]] = F[11,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[39,x,k[0]]+F[47,x,k[0]]
F[50,x,k[0]] = F[11,x]*F[43,x,k[0]]
F[51,x,k[0]] = F[11,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x]+F[90,x,k[0]]
F[53,x] = F[54,x]+F[81,x]
F[54,x] = F[55,x]+F[67,x]
F[55,x] = F[1,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[11,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[1,x]+F[11,x]
F[60,x] = F[56,x]+F[61,x]
F[61,x] = F[30,x]+F[62,x]+F[66,x]
F[62,x] = F[11,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[11,x]
F[65,x] = F[61,x]
F[66,x] = F[11,x]*F[56,x]
F[67,x] = F[26,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[11,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[26,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[11,x]*F[26,x]
F[74,x] = F[68,x]+F[75,x]
F[75,x] = 2*F[30,x]+F[76,x]+F[80,x]
F[76,x] = F[11,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[72,x]
F[79,x] = F[75,x]
F[80,x] = F[11,x]*F[68,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[26,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[11,x]*F[85,x]
F[85,x] = F[56,x]+F[83,x]
F[86,x] = F[29,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[11,x]*F[89,x]
F[89,x] = F[68,x]+F[87,x]
F[90,x,k[0]] = F[100,x,k[0]]+F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[96,x,k[0]]
F[92,x,k[0]] = F[36,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[94,x,k[0]] = F[8,x,k[0]]*F[95,x,k[0]]
F[95,x,k[0]] = F[56,x]+F[93,x,k[0]]
F[96,x,k[0]] = F[39,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[8,x,k[0]]*F[99,x,k[0]]
F[99,x,k[0]] = F[68,x]+F[97,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]+F[105,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]+F[44,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[11,x]
F[104,x,k[0]] = F[102,x,k[0]]+F[93,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[47,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[11,x]
F[108,x,k[0]] = F[106,x,k[0]]+F[97,x,k[0]]
F[109,x,k[0]] = F[11,x]*F[110,x,k[0]]
F[110,x,k[0]] = F[111,x]+F[174,x,k[0]]
F[111,x] = F[112,x]+F[54,x]
F[112,x] = F[113,x]+F[147,x]
F[113,x] = F[114,x]+F[26,x]
F[114,x] = F[115,x]+F[117,x]+F[30,x]
F[115,x] = F[11,x]*F[116,x]
F[116,x] = F[114,x]+F[56,x]
F[117,x] = F[11,x]*F[118,x]
F[118,x] = F[119,x]+F[123,x]
F[119,x] = F[120,x]+F[26,x]
F[120,x] = F[121,x]+F[30,x]+F[73,x]
F[121,x] = F[11,x]*F[122,x]
F[122,x] = F[11,x]+F[120,x]
F[123,x] = F[124,x]+F[138,x]
F[124,x] = F[125,x]+F[30,x]+F[31,x]
F[125,x] = F[11,x]*F[126,x]
F[126,x] = F[119,x]+F[127,x]
F[127,x] = F[124,x]+F[128,x]
F[128,x] = F[129,x]+F[133,x]+F[137,x]+F[30,x]
F[129,x] = F[11,x]*F[130,x]
F[130,x] = F[131,x]+F[72,x]
F[131,x] = 2*F[30,x]+F[129,x]+F[132,x]
F[132,x] = F[11,x]*F[29,x]
F[133,x] = F[11,x]*F[134,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[120,x]
F[136,x] = F[128,x]
F[137,x] = F[11,x]*F[124,x]
F[138,x] = F[137,x]+F[139,x]+F[144,x]+F[30,x]
F[139,x] = F[11,x]*F[140,x]
F[140,x] = F[120,x]+F[141,x]
F[141,x] = F[132,x]+F[139,x]+F[142,x]+F[30,x]
F[142,x] = F[11,x]*F[143,x]
F[143,x] = F[120,x]+F[141,x]
F[144,x] = F[11,x]*F[145,x]
F[145,x] = F[135,x]+F[146,x]
F[146,x] = F[138,x]
F[147,x] = F[148,x]+F[29,x]
F[148,x] = 2*F[30,x]+F[149,x]+F[151,x]
F[149,x] = F[11,x]*F[150,x]
F[150,x] = F[148,x]+F[68,x]
F[151,x] = F[11,x]*F[152,x]
F[152,x] = F[153,x]+F[159,x]
F[153,x] = F[154,x]+F[157,x]
F[154,x] = F[155,x]
F[155,x] = F[11,x]*F[156,x]
F[156,x] = F[154,x]+F[26,x]
F[157,x] = F[158,x]
F[158,x] = F[11,x]*F[154,x]
F[159,x] = F[160,x]+F[170,x]
F[160,x] = F[161,x]
F[161,x] = F[11,x]*F[162,x]
F[162,x] = F[153,x]+F[163,x]
F[163,x] = F[160,x]+F[164,x]
F[164,x] = 3*F[30,x]+F[165,x]+F[169,x]
F[165,x] = F[11,x]*F[166,x]
F[166,x] = F[167,x]+F[168,x]
F[167,x] = F[157,x]
F[168,x] = F[164,x]
F[169,x] = F[11,x]*F[160,x]
F[170,x] = 3*F[30,x]+F[169,x]+F[171,x]
F[171,x] = F[11,x]*F[172,x]
F[172,x] = F[167,x]+F[173,x]
F[173,x] = F[170,x]
F[174,x,k[0]] = F[175,x,k[0]]+F[183,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]+F[92,x,k[0]]
F[176,x,k[0]] = F[177,x,k[0]]+F[180,x,k[0]]
F[177,x,k[0]] = F[178,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]*F[8,x,k[0]]
F[179,x,k[0]] = F[177,x,k[0]]+F[26,x]
F[180,x,k[0]] = F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]*F[8,x,k[0]]
F[182,x,k[0]] = F[180,x,k[0]]+F[68,x]
F[183,x,k[0]] = F[184,x,k[0]]+F[188,x,k[0]]
F[184,x,k[0]] = F[185,x,k[0]]+F[44,x,k[0]]
F[185,x,k[0]] = F[186,x,k[0]]
F[186,x,k[0]] = F[11,x]*F[187,x,k[0]]
F[187,x,k[0]] = F[185,x,k[0]]+F[93,x,k[0]]
F[188,x,k[0]] = F[189,x,k[0]]+F[192,x,k[0]]
F[189,x,k[0]] = F[190,x,k[0]]
F[190,x,k[0]] = F[11,x]*F[191,x,k[0]]
F[191,x,k[0]] = F[177,x,k[0]]+F[189,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]
F[193,x,k[0]] = F[11,x]*F[194,x,k[0]]
F[194,x,k[0]] = F[180,x,k[0]]+F[192,x,k[0]]
F[195,x,k[0]] = F[11,x]*F[196,x,k[0]]
F[196,x,k[0]] = F[111,x]+F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]+F[258,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]+F[234,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[36,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[203,x,k[0]]+F[30,x]
F[201,x,k[0]] = F[202,x,k[0]]*F[8,x,k[0]]
F[202,x,k[0]] = F[200,x,k[0]]+F[56,x]
F[203,x,k[0]] = F[11,x]*F[204,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]+F[210,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]+F[36,x,k[0]]
F[206,x,k[0]] = F[207,x,k[0]]+F[209,x,k[0]]+F[30,x]
F[207,x,k[0]] = F[208,x,k[0]]*F[8,x,k[0]]
F[208,x,k[0]] = F[11,x]+F[206,x,k[0]]
F[209,x,k[0]] = F[11,x]*F[36,x,k[0]]
F[210,x,k[0]] = F[211,x,k[0]]+F[225,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]+F[30,x]+F[40,x,k[0]]
F[212,x,k[0]] = F[11,x]*F[213,x,k[0]]
F[213,x,k[0]] = F[205,x,k[0]]+F[214,x,k[0]]
F[214,x,k[0]] = F[211,x,k[0]]+F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]+F[220,x,k[0]]+F[224,x,k[0]]+F[30,x]
F[216,x,k[0]] = F[217,x,k[0]]*F[8,x,k[0]]
F[217,x,k[0]] = F[218,x,k[0]]+F[72,x]
F[218,x,k[0]] = 2*F[30,x]+F[216,x,k[0]]+F[219,x,k[0]]
F[219,x,k[0]] = F[11,x]*F[39,x,k[0]]
F[220,x,k[0]] = F[11,x]*F[221,x,k[0]]
F[221,x,k[0]] = F[222,x,k[0]]+F[223,x,k[0]]
F[222,x,k[0]] = F[206,x,k[0]]
F[223,x,k[0]] = F[215,x,k[0]]
F[224,x,k[0]] = F[11,x]*F[211,x,k[0]]
F[225,x,k[0]] = F[224,x,k[0]]+F[226,x,k[0]]+F[231,x,k[0]]+F[30,x]
F[226,x,k[0]] = F[227,x,k[0]]*F[8,x,k[0]]
F[227,x,k[0]] = F[120,x]+F[228,x,k[0]]
F[228,x,k[0]] = F[219,x,k[0]]+F[226,x,k[0]]+F[229,x,k[0]]+F[30,x]
F[229,x,k[0]] = F[11,x]*F[230,x,k[0]]
F[230,x,k[0]] = F[206,x,k[0]]+F[228,x,k[0]]
F[231,x,k[0]] = F[11,x]*F[232,x,k[0]]
F[232,x,k[0]] = F[222,x,k[0]]+F[233,x,k[0]]
F[233,x,k[0]] = F[225,x,k[0]]
F[234,x,k[0]] = F[235,x,k[0]]+F[39,x,k[0]]
F[235,x,k[0]] = 2*F[30,x]+F[236,x,k[0]]+F[238,x,k[0]]
F[236,x,k[0]] = F[237,x,k[0]]*F[8,x,k[0]]
F[237,x,k[0]] = F[235,x,k[0]]+F[68,x]
F[238,x,k[0]] = F[11,x]*F[239,x,k[0]]
F[239,x,k[0]] = F[240,x,k[0]]+F[243,x,k[0]]
F[240,x,k[0]] = F[241,x,k[0]]+F[44,x,k[0]]
F[241,x,k[0]] = F[242,x,k[0]]
F[242,x,k[0]] = F[11,x]*F[44,x,k[0]]
F[243,x,k[0]] = F[244,x,k[0]]+F[254,x,k[0]]
F[244,x,k[0]] = F[245,x,k[0]]
F[245,x,k[0]] = F[11,x]*F[246,x,k[0]]
F[246,x,k[0]] = F[240,x,k[0]]+F[247,x,k[0]]
F[247,x,k[0]] = F[244,x,k[0]]+F[248,x,k[0]]
F[248,x,k[0]] = 3*F[30,x]+F[249,x,k[0]]+F[253,x,k[0]]
F[249,x,k[0]] = F[11,x]*F[250,x,k[0]]
F[250,x,k[0]] = F[251,x,k[0]]+F[252,x,k[0]]
F[251,x,k[0]] = F[241,x,k[0]]
F[252,x,k[0]] = F[248,x,k[0]]
F[253,x,k[0]] = F[11,x]*F[244,x,k[0]]
F[254,x,k[0]] = 3*F[30,x]+F[253,x,k[0]]+F[255,x,k[0]]
F[255,x,k[0]] = F[11,x]*F[256,x,k[0]]
F[256,x,k[0]] = F[251,x,k[0]]+F[257,x,k[0]]
F[257,x,k[0]] = F[254,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[293,x,k[0]]
F[259,x,k[0]] = F[260,x,k[0]]+F[44,x,k[0]]
F[260,x,k[0]] = 2*F[30,x]+F[261,x,k[0]]+F[263,x,k[0]]
F[261,x,k[0]] = F[11,x]*F[262,x,k[0]]
F[262,x,k[0]] = F[200,x,k[0]]+F[260,x,k[0]]
F[263,x,k[0]] = F[11,x]*F[264,x,k[0]]
F[264,x,k[0]] = F[265,x,k[0]]+F[269,x,k[0]]
F[265,x,k[0]] = F[266,x,k[0]]+F[44,x,k[0]]
F[266,x,k[0]] = 2*F[30,x]+F[242,x,k[0]]+F[267,x,k[0]]
F[267,x,k[0]] = F[11,x]*F[268,x,k[0]]
F[268,x,k[0]] = F[206,x,k[0]]+F[266,x,k[0]]
F[269,x,k[0]] = F[270,x,k[0]]+F[284,x,k[0]]
F[270,x,k[0]] = 2*F[30,x]+F[271,x,k[0]]+F[48,x,k[0]]
F[271,x,k[0]] = F[11,x]*F[272,x,k[0]]
F[272,x,k[0]] = F[265,x,k[0]]+F[273,x,k[0]]
F[273,x,k[0]] = F[270,x,k[0]]+F[274,x,k[0]]
F[274,x,k[0]] = 2*F[30,x]+F[275,x,k[0]]+F[279,x,k[0]]+F[283,x,k[0]]
F[275,x,k[0]] = F[11,x]*F[276,x,k[0]]
F[276,x,k[0]] = F[218,x,k[0]]+F[277,x,k[0]]
F[277,x,k[0]] = 3*F[30,x]+F[275,x,k[0]]+F[278,x,k[0]]
F[278,x,k[0]] = F[11,x]*F[47,x,k[0]]
F[279,x,k[0]] = F[11,x]*F[280,x,k[0]]
F[280,x,k[0]] = F[281,x,k[0]]+F[282,x,k[0]]
F[281,x,k[0]] = F[266,x,k[0]]
F[282,x,k[0]] = F[274,x,k[0]]
F[283,x,k[0]] = F[11,x]*F[270,x,k[0]]
F[284,x,k[0]] = 2*F[30,x]+F[283,x,k[0]]+F[285,x,k[0]]+F[290,x,k[0]]
F[285,x,k[0]] = F[11,x]*F[286,x,k[0]]
F[286,x,k[0]] = F[228,x,k[0]]+F[287,x,k[0]]
F[287,x,k[0]] = 2*F[30,x]+F[278,x,k[0]]+F[285,x,k[0]]+F[288,x,k[0]]
F[288,x,k[0]] = F[11,x]*F[289,x,k[0]]
F[289,x,k[0]] = F[266,x,k[0]]+F[287,x,k[0]]
F[290,x,k[0]] = F[11,x]*F[291,x,k[0]]
F[291,x,k[0]] = F[281,x,k[0]]+F[292,x,k[0]]
F[292,x,k[0]] = F[284,x,k[0]]
F[293,x,k[0]] = F[294,x,k[0]]+F[47,x,k[0]]
F[294,x,k[0]] = 3*F[30,x]+F[295,x,k[0]]+F[297,x,k[0]]
F[295,x,k[0]] = F[11,x]*F[296,x,k[0]]
F[296,x,k[0]] = F[235,x,k[0]]+F[294,x,k[0]]
F[297,x,k[0]] = F[11,x]*F[298,x,k[0]]
F[298,x,k[0]] = F[299,x,k[0]]+F[305,x,k[0]]
F[299,x,k[0]] = F[300,x,k[0]]+F[303,x,k[0]]
F[300,x,k[0]] = F[301,x,k[0]]
F[301,x,k[0]] = F[11,x]*F[302,x,k[0]]
F[302,x,k[0]] = F[300,x,k[0]]+F[44,x,k[0]]
F[303,x,k[0]] = F[304,x,k[0]]
F[304,x,k[0]] = F[11,x]*F[300,x,k[0]]
F[305,x,k[0]] = F[306,x,k[0]]+F[316,x,k[0]]
F[306,x,k[0]] = F[307,x,k[0]]
F[307,x,k[0]] = F[11,x]*F[308,x,k[0]]
F[308,x,k[0]] = F[299,x,k[0]]+F[309,x,k[0]]
F[309,x,k[0]] = F[306,x,k[0]]+F[310,x,k[0]]
F[310,x,k[0]] = 4*F[30,x]+F[311,x,k[0]]+F[315,x,k[0]]
F[311,x,k[0]] = F[11,x]*F[312,x,k[0]]
F[312,x,k[0]] = F[313,x,k[0]]+F[314,x,k[0]]
F[313,x,k[0]] = F[303,x,k[0]]
F[314,x,k[0]] = F[310,x,k[0]]
F[315,x,k[0]] = F[11,x]*F[306,x,k[0]]
F[316,x,k[0]] = 4*F[30,x]+F[315,x,k[0]]+F[317,x,k[0]]
F[317,x,k[0]] = F[11,x]*F[318,x,k[0]]
F[318,x,k[0]] = F[313,x,k[0]]+F[319,x,k[0]]
F[319,x,k[0]] = F[316,x,k[0]]
F[320,x] = F[11,x]*F[321,x]
F[321,x] = F[322,x,1]
F[322,x,k[0]] = F[1,x]+F[323,x,k[0]]+F[325,x,k[0]]+F[329,x,k[0]]
F[323,x,k[0]] = F[11,x]*F[324,x,k[0]]
F[324,x,k[0]] = 1/(-1+k[0])*(F[322,x,k[0]]*k[0]-F[322,x,1])
F[325,x,k[0]] = F[326,x,k[0]]*F[8,x,k[0]]
F[326,x,k[0]] = F[1,x]+F[325,x,k[0]]+F[327,x,k[0]]
F[327,x,k[0]] = F[11,x]*F[328,x,k[0]]
F[328,x,k[0]] = 1/(-1+k[0])*(F[326,x,k[0]]*k[0]-F[326,x,1])
F[329,x,k[0]] = F[11,x]*F[330,x,k[0]]
F[330,x,k[0]] = F[331,x,k[0]]+F[344,x,k[0]]
F[331,x,k[0]] = F[332,x,k[0]]+F[58,x]
F[332,x,k[0]] = F[333,x,k[0]]+F[335,x,k[0]]
F[333,x,k[0]] = F[334,x,k[0]]+F[36,x,k[0]]
F[334,x,k[0]] = F[209,x,k[0]]
F[335,x,k[0]] = F[336,x,k[0]]+F[338,x,k[0]]
F[336,x,k[0]] = F[337,x,k[0]]
F[337,x,k[0]] = F[11,x]*F[332,x,k[0]]
F[338,x,k[0]] = 2*F[30,x]+F[339,x,k[0]]+F[343,x,k[0]]
F[339,x,k[0]] = F[11,x]*F[340,x,k[0]]
F[340,x,k[0]] = F[341,x,k[0]]+F[342,x,k[0]]
F[341,x,k[0]] = F[334,x,k[0]]
F[342,x,k[0]] = F[338,x,k[0]]
F[343,x,k[0]] = F[11,x]*F[336,x,k[0]]
F[344,x,k[0]] = F[118,x]+F[345,x,k[0]]
F[345,x,k[0]] = F[346,x,k[0]]+F[352,x,k[0]]
F[346,x,k[0]] = F[347,x,k[0]]+F[350,x,k[0]]
F[347,x,k[0]] = F[348,x,k[0]]
F[348,x,k[0]] = F[349,x,k[0]]*F[8,x,k[0]]
F[349,x,k[0]] = F[26,x]+F[347,x,k[0]]
F[350,x,k[0]] = F[351,x,k[0]]
F[351,x,k[0]] = F[11,x]*F[347,x,k[0]]
F[352,x,k[0]] = F[353,x,k[0]]+F[363,x,k[0]]
F[353,x,k[0]] = F[354,x,k[0]]
F[354,x,k[0]] = F[11,x]*F[355,x,k[0]]
F[355,x,k[0]] = F[346,x,k[0]]+F[356,x,k[0]]
F[356,x,k[0]] = F[353,x,k[0]]+F[357,x,k[0]]
F[357,x,k[0]] = 3*F[30,x]+F[358,x,k[0]]+F[362,x,k[0]]
F[358,x,k[0]] = F[11,x]*F[359,x,k[0]]
F[359,x,k[0]] = F[360,x,k[0]]+F[361,x,k[0]]
F[360,x,k[0]] = F[350,x,k[0]]
F[361,x,k[0]] = F[357,x,k[0]]
F[362,x,k[0]] = F[11,x]*F[353,x,k[0]]
F[363,x,k[0]] = 3*F[30,x]+F[362,x,k[0]]+F[364,x,k[0]]
F[364,x,k[0]] = F[11,x]*F[365,x,k[0]]
F[365,x,k[0]] = F[360,x,k[0]]+F[366,x,k[0]]
F[366,x,k[0]] = F[363,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{320}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{195}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{109}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{28}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{35}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x \right)+F_{90}\! \left(x , y\right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{81}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{67}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{11}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{60}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{30}\! \left(x \right)+F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{56}\! \left(x \right)
F_{67}\! \left(x \right) = F_{26}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{11}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{26}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{74}\! \left(x \right) = F_{68}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{11}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{72}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right) F_{68}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{26}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{11}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{56}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{29}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{68}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{36}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{56}\! \left(x \right)+F_{93}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{68}\! \left(x \right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x \right)+F_{174}\! \left(x , y\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{54}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{147}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{26}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)+F_{30}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right) F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{56}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{26}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{30}\! \left(x \right)+F_{73}\! \left(x \right)
F_{121}\! \left(x \right) = F_{11}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{11}\! \left(x \right)+F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{138}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{125}\! \left(x \right) = F_{11}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{119}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{124}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{133}\! \left(x \right)+F_{137}\! \left(x \right)+F_{30}\! \left(x \right)
F_{129}\! \left(x \right) = F_{11}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{72}\! \left(x \right)
F_{131}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{129}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{11}\! \left(x \right) F_{29}\! \left(x \right)
F_{133}\! \left(x \right) = F_{11}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{120}\! \left(x \right)
F_{136}\! \left(x \right) = F_{128}\! \left(x \right)
F_{137}\! \left(x \right) = F_{11}\! \left(x \right) F_{124}\! \left(x \right)
F_{138}\! \left(x \right) = F_{137}\! \left(x \right)+F_{139}\! \left(x \right)+F_{144}\! \left(x \right)+F_{30}\! \left(x \right)
F_{139}\! \left(x \right) = F_{11}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{120}\! \left(x \right)+F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{132}\! \left(x \right)+F_{139}\! \left(x \right)+F_{142}\! \left(x \right)+F_{30}\! \left(x \right)
F_{142}\! \left(x \right) = F_{11}\! \left(x \right) F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{120}\! \left(x \right)+F_{141}\! \left(x \right)
F_{144}\! \left(x \right) = F_{11}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{135}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{138}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{29}\! \left(x \right)
F_{148}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{149}\! \left(x \right)+F_{151}\! \left(x \right)
F_{149}\! \left(x \right) = F_{11}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{148}\! \left(x \right)+F_{68}\! \left(x \right)
F_{151}\! \left(x \right) = F_{11}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{159}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{157}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{11}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{154}\! \left(x \right)+F_{26}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{11}\! \left(x \right) F_{154}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{170}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{11}\! \left(x \right) F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{153}\! \left(x \right)+F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{160}\! \left(x \right)+F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = 3 F_{30}\! \left(x \right)+F_{165}\! \left(x \right)+F_{169}\! \left(x \right)
F_{165}\! \left(x \right) = F_{11}\! \left(x \right) F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{168}\! \left(x \right)
F_{167}\! \left(x \right) = F_{157}\! \left(x \right)
F_{168}\! \left(x \right) = F_{164}\! \left(x \right)
F_{169}\! \left(x \right) = F_{11}\! \left(x \right) F_{160}\! \left(x \right)
F_{170}\! \left(x \right) = 3 F_{30}\! \left(x \right)+F_{169}\! \left(x \right)+F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{11}\! \left(x \right) F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{167}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{170}\! \left(x \right)
F_{174}\! \left(x , y\right) = F_{175}\! \left(x , y\right)+F_{183}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{26}\! \left(x \right)
F_{180}\! \left(x , y\right) = F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{68}\! \left(x \right)
F_{183}\! \left(x , y\right) = F_{184}\! \left(x , y\right)+F_{188}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{186}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{185}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{189}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{177}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{194}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{111}\! \left(x \right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{258}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{234}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{203}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{203}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{204}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{210}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{207}\! \left(x , y\right)+F_{209}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{11}\! \left(x \right)+F_{206}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{30}\! \left(x \right)+F_{40}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{211}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{220}\! \left(x , y\right)+F_{224}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{72}\! \left(x \right)
F_{218}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{216}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{221}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{215}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{211}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{224}\! \left(x , y\right)+F_{226}\! \left(x , y\right)+F_{231}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{120}\! \left(x \right)+F_{228}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{226}\! \left(x , y\right)+F_{229}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{230}\! \left(x , y\right)
F_{230}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{231}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{232}\! \left(x , y\right)
F_{232}\! \left(x , y\right) = F_{222}\! \left(x , y\right)+F_{233}\! \left(x , y\right)
F_{233}\! \left(x , y\right) = F_{225}\! \left(x , y\right)
F_{234}\! \left(x , y\right) = F_{235}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{235}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{236}\! \left(x , y\right)+F_{238}\! \left(x , y\right)
F_{236}\! \left(x , y\right) = F_{237}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{237}\! \left(x , y\right) = F_{235}\! \left(x , y\right)+F_{68}\! \left(x \right)
F_{238}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{239}\! \left(x , y\right)
F_{239}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{243}\! \left(x , y\right)
F_{240}\! \left(x , y\right) = F_{241}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{241}\! \left(x , y\right) = F_{242}\! \left(x , y\right)
F_{242}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{243}\! \left(x , y\right) = F_{244}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{244}\! \left(x , y\right) = F_{245}\! \left(x , y\right)
F_{245}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{246}\! \left(x , y\right)
F_{246}\! \left(x , y\right) = F_{240}\! \left(x , y\right)+F_{247}\! \left(x , y\right)
F_{247}\! \left(x , y\right) = F_{244}\! \left(x , y\right)+F_{248}\! \left(x , y\right)
F_{248}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{249}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{249}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{250}\! \left(x , y\right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{252}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{241}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{248}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{244}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{253}\! \left(x , y\right)+F_{255}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{256}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{257}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{254}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{293}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{261}\! \left(x , y\right)+F_{263}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{263}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{264}\! \left(x , y\right)
F_{264}\! \left(x , y\right) = F_{265}\! \left(x , y\right)+F_{269}\! \left(x , y\right)
F_{265}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{266}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{242}\! \left(x , y\right)+F_{267}\! \left(x , y\right)
F_{267}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{268}\! \left(x , y\right)
F_{268}\! \left(x , y\right) = F_{206}\! \left(x , y\right)+F_{266}\! \left(x , y\right)
F_{269}\! \left(x , y\right) = F_{270}\! \left(x , y\right)+F_{284}\! \left(x , y\right)
F_{270}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{271}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{271}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{272}\! \left(x , y\right)
F_{272}\! \left(x , y\right) = F_{265}\! \left(x , y\right)+F_{273}\! \left(x , y\right)
F_{273}\! \left(x , y\right) = F_{270}\! \left(x , y\right)+F_{274}\! \left(x , y\right)
F_{274}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{275}\! \left(x , y\right)+F_{279}\! \left(x , y\right)+F_{283}\! \left(x , y\right)
F_{275}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{276}\! \left(x , y\right)
F_{276}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{277}\! \left(x , y\right)
F_{277}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{275}\! \left(x , y\right)+F_{278}\! \left(x , y\right)
F_{278}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{279}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{280}\! \left(x , y\right)
F_{280}\! \left(x , y\right) = F_{281}\! \left(x , y\right)+F_{282}\! \left(x , y\right)
F_{281}\! \left(x , y\right) = F_{266}\! \left(x , y\right)
F_{282}\! \left(x , y\right) = F_{274}\! \left(x , y\right)
F_{283}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{270}\! \left(x , y\right)
F_{284}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{283}\! \left(x , y\right)+F_{285}\! \left(x , y\right)+F_{290}\! \left(x , y\right)
F_{285}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{286}\! \left(x , y\right)
F_{286}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{287}\! \left(x , y\right)
F_{287}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{278}\! \left(x , y\right)+F_{285}\! \left(x , y\right)+F_{288}\! \left(x , y\right)
F_{288}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{289}\! \left(x , y\right)
F_{289}\! \left(x , y\right) = F_{266}\! \left(x , y\right)+F_{287}\! \left(x , y\right)
F_{290}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{291}\! \left(x , y\right)
F_{291}\! \left(x , y\right) = F_{281}\! \left(x , y\right)+F_{292}\! \left(x , y\right)
F_{292}\! \left(x , y\right) = F_{284}\! \left(x , y\right)
F_{293}\! \left(x , y\right) = F_{294}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{294}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{295}\! \left(x , y\right)+F_{297}\! \left(x , y\right)
F_{295}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{296}\! \left(x , y\right)
F_{296}\! \left(x , y\right) = F_{235}\! \left(x , y\right)+F_{294}\! \left(x , y\right)
F_{297}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{298}\! \left(x , y\right)
F_{298}\! \left(x , y\right) = F_{299}\! \left(x , y\right)+F_{305}\! \left(x , y\right)
F_{299}\! \left(x , y\right) = F_{300}\! \left(x , y\right)+F_{303}\! \left(x , y\right)
F_{300}\! \left(x , y\right) = F_{301}\! \left(x , y\right)
F_{301}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{302}\! \left(x , y\right)
F_{302}\! \left(x , y\right) = F_{300}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{303}\! \left(x , y\right) = F_{304}\! \left(x , y\right)
F_{304}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{300}\! \left(x , y\right)
F_{305}\! \left(x , y\right) = F_{306}\! \left(x , y\right)+F_{316}\! \left(x , y\right)
F_{306}\! \left(x , y\right) = F_{307}\! \left(x , y\right)
F_{307}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{308}\! \left(x , y\right)
F_{308}\! \left(x , y\right) = F_{299}\! \left(x , y\right)+F_{309}\! \left(x , y\right)
F_{309}\! \left(x , y\right) = F_{306}\! \left(x , y\right)+F_{310}\! \left(x , y\right)
F_{310}\! \left(x , y\right) = 4 F_{30}\! \left(x \right)+F_{311}\! \left(x , y\right)+F_{315}\! \left(x , y\right)
F_{311}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{312}\! \left(x , y\right)
F_{312}\! \left(x , y\right) = F_{313}\! \left(x , y\right)+F_{314}\! \left(x , y\right)
F_{313}\! \left(x , y\right) = F_{303}\! \left(x , y\right)
F_{314}\! \left(x , y\right) = F_{310}\! \left(x , y\right)
F_{315}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{306}\! \left(x , y\right)
F_{316}\! \left(x , y\right) = 4 F_{30}\! \left(x \right)+F_{315}\! \left(x , y\right)+F_{317}\! \left(x , y\right)
F_{317}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{318}\! \left(x , y\right)
F_{318}\! \left(x , y\right) = F_{313}\! \left(x , y\right)+F_{319}\! \left(x , y\right)
F_{319}\! \left(x , y\right) = F_{316}\! \left(x , y\right)
F_{320}\! \left(x \right) = F_{11}\! \left(x \right) F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x , 1\right)
F_{322}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{323}\! \left(x , y\right)+F_{325}\! \left(x , y\right)+F_{329}\! \left(x , y\right)
F_{323}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{324}\! \left(x , y\right)
F_{324}\! \left(x , y\right) = -\frac{-y F_{322}\! \left(x , y\right)+F_{322}\! \left(x , 1\right)}{-1+y}
F_{325}\! \left(x , y\right) = F_{326}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{326}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{325}\! \left(x , y\right)+F_{327}\! \left(x , y\right)
F_{327}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{328}\! \left(x , y\right)
F_{328}\! \left(x , y\right) = -\frac{-y F_{326}\! \left(x , y\right)+F_{326}\! \left(x , 1\right)}{-1+y}
F_{329}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{330}\! \left(x , y\right)
F_{330}\! \left(x , y\right) = F_{331}\! \left(x , y\right)+F_{344}\! \left(x , y\right)
F_{331}\! \left(x , y\right) = F_{332}\! \left(x , y\right)+F_{58}\! \left(x \right)
F_{332}\! \left(x , y\right) = F_{333}\! \left(x , y\right)+F_{335}\! \left(x , y\right)
F_{333}\! \left(x , y\right) = F_{334}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{334}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{335}\! \left(x , y\right) = F_{336}\! \left(x , y\right)+F_{338}\! \left(x , y\right)
F_{336}\! \left(x , y\right) = F_{337}\! \left(x , y\right)
F_{337}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{332}\! \left(x , y\right)
F_{338}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{339}\! \left(x , y\right)+F_{343}\! \left(x , y\right)
F_{339}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{340}\! \left(x , y\right)
F_{340}\! \left(x , y\right) = F_{341}\! \left(x , y\right)+F_{342}\! \left(x , y\right)
F_{341}\! \left(x , y\right) = F_{334}\! \left(x , y\right)
F_{342}\! \left(x , y\right) = F_{338}\! \left(x , y\right)
F_{343}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{336}\! \left(x , y\right)
F_{344}\! \left(x , y\right) = F_{118}\! \left(x \right)+F_{345}\! \left(x , y\right)
F_{345}\! \left(x , y\right) = F_{346}\! \left(x , y\right)+F_{352}\! \left(x , y\right)
F_{346}\! \left(x , y\right) = F_{347}\! \left(x , y\right)+F_{350}\! \left(x , y\right)
F_{347}\! \left(x , y\right) = F_{348}\! \left(x , y\right)
F_{348}\! \left(x , y\right) = F_{349}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{349}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{347}\! \left(x , y\right)
F_{350}\! \left(x , y\right) = F_{351}\! \left(x , y\right)
F_{351}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{347}\! \left(x , y\right)
F_{352}\! \left(x , y\right) = F_{353}\! \left(x , y\right)+F_{363}\! \left(x , y\right)
F_{353}\! \left(x , y\right) = F_{354}\! \left(x , y\right)
F_{354}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{355}\! \left(x , y\right)
F_{355}\! \left(x , y\right) = F_{346}\! \left(x , y\right)+F_{356}\! \left(x , y\right)
F_{356}\! \left(x , y\right) = F_{353}\! \left(x , y\right)+F_{357}\! \left(x , y\right)
F_{357}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{358}\! \left(x , y\right)+F_{362}\! \left(x , y\right)
F_{358}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{359}\! \left(x , y\right)
F_{359}\! \left(x , y\right) = F_{360}\! \left(x , y\right)+F_{361}\! \left(x , y\right)
F_{360}\! \left(x , y\right) = F_{350}\! \left(x , y\right)
F_{361}\! \left(x , y\right) = F_{357}\! \left(x , y\right)
F_{362}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{353}\! \left(x , y\right)
F_{363}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{362}\! \left(x , y\right)+F_{364}\! \left(x , y\right)
F_{364}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{365}\! \left(x , y\right)
F_{365}\! \left(x , y\right) = F_{360}\! \left(x , y\right)+F_{366}\! \left(x , y\right)
F_{366}\! \left(x , y\right) = F_{363}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_320(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0) + F_15(x, k_0) + F_195(x, k_0) + F_51(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_8(x, k_0))
Eq(F_15(x, k_0), F_11(x)*F_16(x, k_0))
Eq(F_16(x, k_0), (-k_0*F_17(x, k_0) + F_17(x, 1))/(1 - k_0))
Eq(F_17(x, k_0), F_1(x) + F_109(x, k_0) + F_15(x, k_0) + F_18(x, k_0) + F_51(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_8(x, k_0))
Eq(F_19(x, k_0), F_1(x) + F_18(x, k_0) + F_20(x, k_0) + F_22(x, k_0))
Eq(F_20(x, k_0), F_11(x)*F_21(x, k_0))
Eq(F_21(x, k_0), (-k_0*F_19(x, k_0) + F_19(x, 1))/(1 - k_0))
Eq(F_22(x, k_0), F_11(x)*F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x) + F_34(x, k_0))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_11(x)*F_25(x))
Eq(F_28(x), F_26(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_33(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_26(x) + F_29(x))
Eq(F_33(x), F_11(x)*F_28(x))
Eq(F_34(x, k_0), F_35(x, k_0) + F_43(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0) + F_39(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x, k_0))
Eq(F_38(x, k_0), F_1(x) + F_36(x, k_0))
Eq(F_39(x, k_0), F_30(x) + F_40(x, k_0) + F_42(x, k_0))
Eq(F_40(x, k_0), F_41(x, k_0)*F_8(x, k_0))
Eq(F_41(x, k_0), F_26(x) + F_39(x, k_0))
Eq(F_42(x, k_0), F_11(x)*F_35(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_47(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_11(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_36(x, k_0) + F_44(x, k_0))
Eq(F_47(x, k_0), 2*F_30(x) + F_48(x, k_0) + F_50(x, k_0))
Eq(F_48(x, k_0), F_11(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_39(x, k_0) + F_47(x, k_0))
Eq(F_50(x, k_0), F_11(x)*F_43(x, k_0))
Eq(F_51(x, k_0), F_11(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x) + F_90(x, k_0))
Eq(F_53(x), F_54(x) + F_81(x))
Eq(F_54(x), F_55(x) + F_67(x))
Eq(F_55(x), F_1(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_11(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_1(x) + F_11(x))
Eq(F_60(x), F_56(x) + F_61(x))
Eq(F_61(x), F_30(x) + F_62(x) + F_66(x))
Eq(F_62(x), F_11(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_11(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_11(x)*F_56(x))
Eq(F_67(x), F_26(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_11(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_26(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_11(x)*F_26(x))
Eq(F_74(x), F_68(x) + F_75(x))
Eq(F_75(x), 2*F_30(x) + F_76(x) + F_80(x))
Eq(F_76(x), F_11(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_72(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_11(x)*F_68(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_26(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_11(x)*F_85(x))
Eq(F_85(x), F_56(x) + F_83(x))
Eq(F_86(x), F_29(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_11(x)*F_89(x))
Eq(F_89(x), F_68(x) + F_87(x))
Eq(F_90(x, k_0), F_100(x, k_0) + F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_96(x, k_0))
Eq(F_92(x, k_0), F_36(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_94(x, k_0), F_8(x, k_0)*F_95(x, k_0))
Eq(F_95(x, k_0), F_56(x) + F_93(x, k_0))
Eq(F_96(x, k_0), F_39(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_8(x, k_0)*F_99(x, k_0))
Eq(F_99(x, k_0), F_68(x) + F_97(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_105(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0) + F_44(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0))
Eq(F_103(x, k_0), F_104(x, k_0)*F_11(x))
Eq(F_104(x, k_0), F_102(x, k_0) + F_93(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_47(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_11(x))
Eq(F_108(x, k_0), F_106(x, k_0) + F_97(x, k_0))
Eq(F_109(x, k_0), F_11(x)*F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x) + F_174(x, k_0))
Eq(F_111(x), F_112(x) + F_54(x))
Eq(F_112(x), F_113(x) + F_147(x))
Eq(F_113(x), F_114(x) + F_26(x))
Eq(F_114(x), F_115(x) + F_117(x) + F_30(x))
Eq(F_115(x), F_11(x)*F_116(x))
Eq(F_116(x), F_114(x) + F_56(x))
Eq(F_117(x), F_11(x)*F_118(x))
Eq(F_118(x), F_119(x) + F_123(x))
Eq(F_119(x), F_120(x) + F_26(x))
Eq(F_120(x), F_121(x) + F_30(x) + F_73(x))
Eq(F_121(x), F_11(x)*F_122(x))
Eq(F_122(x), F_11(x) + F_120(x))
Eq(F_123(x), F_124(x) + F_138(x))
Eq(F_124(x), F_125(x) + F_30(x) + F_31(x))
Eq(F_125(x), F_11(x)*F_126(x))
Eq(F_126(x), F_119(x) + F_127(x))
Eq(F_127(x), F_124(x) + F_128(x))
Eq(F_128(x), F_129(x) + F_133(x) + F_137(x) + F_30(x))
Eq(F_129(x), F_11(x)*F_130(x))
Eq(F_130(x), F_131(x) + F_72(x))
Eq(F_131(x), F_129(x) + F_132(x) + 2*F_30(x))
Eq(F_132(x), F_11(x)*F_29(x))
Eq(F_133(x), F_11(x)*F_134(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_120(x))
Eq(F_136(x), F_128(x))
Eq(F_137(x), F_11(x)*F_124(x))
Eq(F_138(x), F_137(x) + F_139(x) + F_144(x) + F_30(x))
Eq(F_139(x), F_11(x)*F_140(x))
Eq(F_140(x), F_120(x) + F_141(x))
Eq(F_141(x), F_132(x) + F_139(x) + F_142(x) + F_30(x))
Eq(F_142(x), F_11(x)*F_143(x))
Eq(F_143(x), F_120(x) + F_141(x))
Eq(F_144(x), F_11(x)*F_145(x))
Eq(F_145(x), F_135(x) + F_146(x))
Eq(F_146(x), F_138(x))
Eq(F_147(x), F_148(x) + F_29(x))
Eq(F_148(x), F_149(x) + F_151(x) + 2*F_30(x))
Eq(F_149(x), F_11(x)*F_150(x))
Eq(F_150(x), F_148(x) + F_68(x))
Eq(F_151(x), F_11(x)*F_152(x))
Eq(F_152(x), F_153(x) + F_159(x))
Eq(F_153(x), F_154(x) + F_157(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_11(x)*F_156(x))
Eq(F_156(x), F_154(x) + F_26(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_11(x)*F_154(x))
Eq(F_159(x), F_160(x) + F_170(x))
Eq(F_160(x), F_161(x))
Eq(F_161(x), F_11(x)*F_162(x))
Eq(F_162(x), F_153(x) + F_163(x))
Eq(F_163(x), F_160(x) + F_164(x))
Eq(F_164(x), F_165(x) + F_169(x) + 3*F_30(x))
Eq(F_165(x), F_11(x)*F_166(x))
Eq(F_166(x), F_167(x) + F_168(x))
Eq(F_167(x), F_157(x))
Eq(F_168(x), F_164(x))
Eq(F_169(x), F_11(x)*F_160(x))
Eq(F_170(x), F_169(x) + F_171(x) + 3*F_30(x))
Eq(F_171(x), F_11(x)*F_172(x))
Eq(F_172(x), F_167(x) + F_173(x))
Eq(F_173(x), F_170(x))
Eq(F_174(x, k_0), F_175(x, k_0) + F_183(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0) + F_92(x, k_0))
Eq(F_176(x, k_0), F_177(x, k_0) + F_180(x, k_0))
Eq(F_177(x, k_0), F_178(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0)*F_8(x, k_0))
Eq(F_179(x, k_0), F_177(x, k_0) + F_26(x))
Eq(F_180(x, k_0), F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0)*F_8(x, k_0))
Eq(F_182(x, k_0), F_180(x, k_0) + F_68(x))
Eq(F_183(x, k_0), F_184(x, k_0) + F_188(x, k_0))
Eq(F_184(x, k_0), F_185(x, k_0) + F_44(x, k_0))
Eq(F_185(x, k_0), F_186(x, k_0))
Eq(F_186(x, k_0), F_11(x)*F_187(x, k_0))
Eq(F_187(x, k_0), F_185(x, k_0) + F_93(x, k_0))
Eq(F_188(x, k_0), F_189(x, k_0) + F_192(x, k_0))
Eq(F_189(x, k_0), F_190(x, k_0))
Eq(F_190(x, k_0), F_11(x)*F_191(x, k_0))
Eq(F_191(x, k_0), F_177(x, k_0) + F_189(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0))
Eq(F_193(x, k_0), F_11(x)*F_194(x, k_0))
Eq(F_194(x, k_0), F_180(x, k_0) + F_192(x, k_0))
Eq(F_195(x, k_0), F_11(x)*F_196(x, k_0))
Eq(F_196(x, k_0), F_111(x) + F_197(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0) + F_258(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_234(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_36(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_203(x, k_0) + F_30(x))
Eq(F_201(x, k_0), F_202(x, k_0)*F_8(x, k_0))
Eq(F_202(x, k_0), F_200(x, k_0) + F_56(x))
Eq(F_203(x, k_0), F_11(x)*F_204(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0) + F_210(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0) + F_36(x, k_0))
Eq(F_206(x, k_0), F_207(x, k_0) + F_209(x, k_0) + F_30(x))
Eq(F_207(x, k_0), F_208(x, k_0)*F_8(x, k_0))
Eq(F_208(x, k_0), F_11(x) + F_206(x, k_0))
Eq(F_209(x, k_0), F_11(x)*F_36(x, k_0))
Eq(F_210(x, k_0), F_211(x, k_0) + F_225(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0) + F_30(x) + F_40(x, k_0))
Eq(F_212(x, k_0), F_11(x)*F_213(x, k_0))
Eq(F_213(x, k_0), F_205(x, k_0) + F_214(x, k_0))
Eq(F_214(x, k_0), F_211(x, k_0) + F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0) + F_220(x, k_0) + F_224(x, k_0) + F_30(x))
Eq(F_216(x, k_0), F_217(x, k_0)*F_8(x, k_0))
Eq(F_217(x, k_0), F_218(x, k_0) + F_72(x))
Eq(F_218(x, k_0), F_216(x, k_0) + F_219(x, k_0) + 2*F_30(x))
Eq(F_219(x, k_0), F_11(x)*F_39(x, k_0))
Eq(F_220(x, k_0), F_11(x)*F_221(x, k_0))
Eq(F_221(x, k_0), F_222(x, k_0) + F_223(x, k_0))
Eq(F_222(x, k_0), F_206(x, k_0))
Eq(F_223(x, k_0), F_215(x, k_0))
Eq(F_224(x, k_0), F_11(x)*F_211(x, k_0))
Eq(F_225(x, k_0), F_224(x, k_0) + F_226(x, k_0) + F_231(x, k_0) + F_30(x))
Eq(F_226(x, k_0), F_227(x, k_0)*F_8(x, k_0))
Eq(F_227(x, k_0), F_120(x) + F_228(x, k_0))
Eq(F_228(x, k_0), F_219(x, k_0) + F_226(x, k_0) + F_229(x, k_0) + F_30(x))
Eq(F_229(x, k_0), F_11(x)*F_230(x, k_0))
Eq(F_230(x, k_0), F_206(x, k_0) + F_228(x, k_0))
Eq(F_231(x, k_0), F_11(x)*F_232(x, k_0))
Eq(F_232(x, k_0), F_222(x, k_0) + F_233(x, k_0))
Eq(F_233(x, k_0), F_225(x, k_0))
Eq(F_234(x, k_0), F_235(x, k_0) + F_39(x, k_0))
Eq(F_235(x, k_0), F_236(x, k_0) + F_238(x, k_0) + 2*F_30(x))
Eq(F_236(x, k_0), F_237(x, k_0)*F_8(x, k_0))
Eq(F_237(x, k_0), F_235(x, k_0) + F_68(x))
Eq(F_238(x, k_0), F_11(x)*F_239(x, k_0))
Eq(F_239(x, k_0), F_240(x, k_0) + F_243(x, k_0))
Eq(F_240(x, k_0), F_241(x, k_0) + F_44(x, k_0))
Eq(F_241(x, k_0), F_242(x, k_0))
Eq(F_242(x, k_0), F_11(x)*F_44(x, k_0))
Eq(F_243(x, k_0), F_244(x, k_0) + F_254(x, k_0))
Eq(F_244(x, k_0), F_245(x, k_0))
Eq(F_245(x, k_0), F_11(x)*F_246(x, k_0))
Eq(F_246(x, k_0), F_240(x, k_0) + F_247(x, k_0))
Eq(F_247(x, k_0), F_244(x, k_0) + F_248(x, k_0))
Eq(F_248(x, k_0), F_249(x, k_0) + F_253(x, k_0) + 3*F_30(x))
Eq(F_249(x, k_0), F_11(x)*F_250(x, k_0))
Eq(F_250(x, k_0), F_251(x, k_0) + F_252(x, k_0))
Eq(F_251(x, k_0), F_241(x, k_0))
Eq(F_252(x, k_0), F_248(x, k_0))
Eq(F_253(x, k_0), F_11(x)*F_244(x, k_0))
Eq(F_254(x, k_0), F_253(x, k_0) + F_255(x, k_0) + 3*F_30(x))
Eq(F_255(x, k_0), F_11(x)*F_256(x, k_0))
Eq(F_256(x, k_0), F_251(x, k_0) + F_257(x, k_0))
Eq(F_257(x, k_0), F_254(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_293(x, k_0))
Eq(F_259(x, k_0), F_260(x, k_0) + F_44(x, k_0))
Eq(F_260(x, k_0), F_261(x, k_0) + F_263(x, k_0) + 2*F_30(x))
Eq(F_261(x, k_0), F_11(x)*F_262(x, k_0))
Eq(F_262(x, k_0), F_200(x, k_0) + F_260(x, k_0))
Eq(F_263(x, k_0), F_11(x)*F_264(x, k_0))
Eq(F_264(x, k_0), F_265(x, k_0) + F_269(x, k_0))
Eq(F_265(x, k_0), F_266(x, k_0) + F_44(x, k_0))
Eq(F_266(x, k_0), F_242(x, k_0) + F_267(x, k_0) + 2*F_30(x))
Eq(F_267(x, k_0), F_11(x)*F_268(x, k_0))
Eq(F_268(x, k_0), F_206(x, k_0) + F_266(x, k_0))
Eq(F_269(x, k_0), F_270(x, k_0) + F_284(x, k_0))
Eq(F_270(x, k_0), F_271(x, k_0) + 2*F_30(x) + F_48(x, k_0))
Eq(F_271(x, k_0), F_11(x)*F_272(x, k_0))
Eq(F_272(x, k_0), F_265(x, k_0) + F_273(x, k_0))
Eq(F_273(x, k_0), F_270(x, k_0) + F_274(x, k_0))
Eq(F_274(x, k_0), F_275(x, k_0) + F_279(x, k_0) + F_283(x, k_0) + 2*F_30(x))
Eq(F_275(x, k_0), F_11(x)*F_276(x, k_0))
Eq(F_276(x, k_0), F_218(x, k_0) + F_277(x, k_0))
Eq(F_277(x, k_0), F_275(x, k_0) + F_278(x, k_0) + 3*F_30(x))
Eq(F_278(x, k_0), F_11(x)*F_47(x, k_0))
Eq(F_279(x, k_0), F_11(x)*F_280(x, k_0))
Eq(F_280(x, k_0), F_281(x, k_0) + F_282(x, k_0))
Eq(F_281(x, k_0), F_266(x, k_0))
Eq(F_282(x, k_0), F_274(x, k_0))
Eq(F_283(x, k_0), F_11(x)*F_270(x, k_0))
Eq(F_284(x, k_0), F_283(x, k_0) + F_285(x, k_0) + F_290(x, k_0) + 2*F_30(x))
Eq(F_285(x, k_0), F_11(x)*F_286(x, k_0))
Eq(F_286(x, k_0), F_228(x, k_0) + F_287(x, k_0))
Eq(F_287(x, k_0), F_278(x, k_0) + F_285(x, k_0) + F_288(x, k_0) + 2*F_30(x))
Eq(F_288(x, k_0), F_11(x)*F_289(x, k_0))
Eq(F_289(x, k_0), F_266(x, k_0) + F_287(x, k_0))
Eq(F_290(x, k_0), F_11(x)*F_291(x, k_0))
Eq(F_291(x, k_0), F_281(x, k_0) + F_292(x, k_0))
Eq(F_292(x, k_0), F_284(x, k_0))
Eq(F_293(x, k_0), F_294(x, k_0) + F_47(x, k_0))
Eq(F_294(x, k_0), F_295(x, k_0) + F_297(x, k_0) + 3*F_30(x))
Eq(F_295(x, k_0), F_11(x)*F_296(x, k_0))
Eq(F_296(x, k_0), F_235(x, k_0) + F_294(x, k_0))
Eq(F_297(x, k_0), F_11(x)*F_298(x, k_0))
Eq(F_298(x, k_0), F_299(x, k_0) + F_305(x, k_0))
Eq(F_299(x, k_0), F_300(x, k_0) + F_303(x, k_0))
Eq(F_300(x, k_0), F_301(x, k_0))
Eq(F_301(x, k_0), F_11(x)*F_302(x, k_0))
Eq(F_302(x, k_0), F_300(x, k_0) + F_44(x, k_0))
Eq(F_303(x, k_0), F_304(x, k_0))
Eq(F_304(x, k_0), F_11(x)*F_300(x, k_0))
Eq(F_305(x, k_0), F_306(x, k_0) + F_316(x, k_0))
Eq(F_306(x, k_0), F_307(x, k_0))
Eq(F_307(x, k_0), F_11(x)*F_308(x, k_0))
Eq(F_308(x, k_0), F_299(x, k_0) + F_309(x, k_0))
Eq(F_309(x, k_0), F_306(x, k_0) + F_310(x, k_0))
Eq(F_310(x, k_0), 4*F_30(x) + F_311(x, k_0) + F_315(x, k_0))
Eq(F_311(x, k_0), F_11(x)*F_312(x, k_0))
Eq(F_312(x, k_0), F_313(x, k_0) + F_314(x, k_0))
Eq(F_313(x, k_0), F_303(x, k_0))
Eq(F_314(x, k_0), F_310(x, k_0))
Eq(F_315(x, k_0), F_11(x)*F_306(x, k_0))
Eq(F_316(x, k_0), 4*F_30(x) + F_315(x, k_0) + F_317(x, k_0))
Eq(F_317(x, k_0), F_11(x)*F_318(x, k_0))
Eq(F_318(x, k_0), F_313(x, k_0) + F_319(x, k_0))
Eq(F_319(x, k_0), F_316(x, k_0))
Eq(F_320(x), F_11(x)*F_321(x))
Eq(F_321(x), F_322(x, 1))
Eq(F_322(x, k_0), F_1(x) + F_323(x, k_0) + F_325(x, k_0) + F_329(x, k_0))
Eq(F_323(x, k_0), F_11(x)*F_324(x, k_0))
Eq(F_324(x, k_0), (k_0*F_322(x, k_0) - F_322(x, 1))/(k_0 - 1))
Eq(F_325(x, k_0), F_326(x, k_0)*F_8(x, k_0))
Eq(F_326(x, k_0), F_1(x) + F_325(x, k_0) + F_327(x, k_0))
Eq(F_327(x, k_0), F_11(x)*F_328(x, k_0))
Eq(F_328(x, k_0), (k_0*F_326(x, k_0) - F_326(x, 1))/(k_0 - 1))
Eq(F_329(x, k_0), F_11(x)*F_330(x, k_0))
Eq(F_330(x, k_0), F_331(x, k_0) + F_344(x, k_0))
Eq(F_331(x, k_0), F_332(x, k_0) + F_58(x))
Eq(F_332(x, k_0), F_333(x, k_0) + F_335(x, k_0))
Eq(F_333(x, k_0), F_334(x, k_0) + F_36(x, k_0))
Eq(F_334(x, k_0), F_209(x, k_0))
Eq(F_335(x, k_0), F_336(x, k_0) + F_338(x, k_0))
Eq(F_336(x, k_0), F_337(x, k_0))
Eq(F_337(x, k_0), F_11(x)*F_332(x, k_0))
Eq(F_338(x, k_0), 2*F_30(x) + F_339(x, k_0) + F_343(x, k_0))
Eq(F_339(x, k_0), F_11(x)*F_340(x, k_0))
Eq(F_340(x, k_0), F_341(x, k_0) + F_342(x, k_0))
Eq(F_341(x, k_0), F_334(x, k_0))
Eq(F_342(x, k_0), F_338(x, k_0))
Eq(F_343(x, k_0), F_11(x)*F_336(x, k_0))
Eq(F_344(x, k_0), F_118(x) + F_345(x, k_0))
Eq(F_345(x, k_0), F_346(x, k_0) + F_352(x, k_0))
Eq(F_346(x, k_0), F_347(x, k_0) + F_350(x, k_0))
Eq(F_347(x, k_0), F_348(x, k_0))
Eq(F_348(x, k_0), F_349(x, k_0)*F_8(x, k_0))
Eq(F_349(x, k_0), F_26(x) + F_347(x, k_0))
Eq(F_350(x, k_0), F_351(x, k_0))
Eq(F_351(x, k_0), F_11(x)*F_347(x, k_0))
Eq(F_352(x, k_0), F_353(x, k_0) + F_363(x, k_0))
Eq(F_353(x, k_0), F_354(x, k_0))
Eq(F_354(x, k_0), F_11(x)*F_355(x, k_0))
Eq(F_355(x, k_0), F_346(x, k_0) + F_356(x, k_0))
Eq(F_356(x, k_0), F_353(x, k_0) + F_357(x, k_0))
Eq(F_357(x, k_0), 3*F_30(x) + F_358(x, k_0) + F_362(x, k_0))
Eq(F_358(x, k_0), F_11(x)*F_359(x, k_0))
Eq(F_359(x, k_0), F_360(x, k_0) + F_361(x, k_0))
Eq(F_360(x, k_0), F_350(x, k_0))
Eq(F_361(x, k_0), F_357(x, k_0))
Eq(F_362(x, k_0), F_11(x)*F_353(x, k_0))
Eq(F_363(x, k_0), 3*F_30(x) + F_362(x, k_0) + F_364(x, k_0))
Eq(F_364(x, k_0), F_11(x)*F_365(x, k_0))
Eq(F_365(x, k_0), F_360(x, k_0) + F_366(x, k_0))
Eq(F_366(x, k_0), F_363(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, 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