0123_0132_1023_1230
Counting sequence:
1, 1, 2, 6, 20, 68, 229, 766, 2567, 8672, 29622, 102389, 357973, 1264690, 4509858, 16214582, 58718850, 213992722, 784234263, 2888302913, 10684557392, 39681589280, 147901022427, 553041455503, 2074068644892, 7799349613298, 29401399322227, 111088198188807, 420614045294846, 1595693110225200, 6064647612049161, 23088689068732430, 88040524797277979, 336211308535024596, 1285727860831134770, 4923308437860356541, 18875722962189447109, 72453398772056074726, 278416554039421149698, 1070994293574789440139, 4123934120322028066385, 15894510092842113088244, 61315945895154103382170, 236740195857875666804491, 914798791770317362249623, 3537676175312437574444038, 13690977782370525181767820, 53022562062873647812080627, 205486674556276592091037795, 796876479492006865800697588, 3092225628833142787485594432, 12006413352255393749871424903, 46645217334853694818024431241, 181318876975452367377421613982, 705199329114463508158434824938, 2744132871801576712013531345353, 10683526493795626089031557014331, 41613350454558670968448018436320, 162163088159136168723177763812508, 632216296948659563829433267014015, 2465852894133141004238978374311337, 9621664412573215311065305088175946, 37558555614025650744968732719291962, 146668737396637320723827327147385766, 572968629841012820299559973124583866, 2239152302891531897567335481447922762, 8753687436403250583381246948629186527, 34233269777448162791705834742874650481, 133921781880579500267185487044899114864, 524077221940786519707532817880119998456, 2051523527632539478605775393186192426267, 8033244221459377956112556394995406999267, 31465522784590396895526047486323636156096, 123283474051196839738317453679350320187634, 483167007892912953049583380047918705330231, 1894126054627857178118737026728162896625047, 7427394948375316266232521033822654888906082, 29132459456428759601465634106407782147940096, 114295163658664681256703559369505848715084629, 448524134461501979729141061872425284763003711, 1760549885860954372961172740918334873442866902, 6912144472672123551593164255072652792290107842, 27144179842577485587246010392145751168893544961, 106619752852215529189104352456437508710776057459, 418883564673329127788694149360066841570785857816, 1646043947219846261429593797627335759590096105912, 6469635619093825492165156111494036318176669723007, 25433516710119842629118435102870856007862446331441, 100004418039807353525283152611059822234770304380814, 393292973491681638071595637039477889747281655931446, 1547018584686457555918203104310467812405006071509957, 6086328583792648615972778390835324531012711960605547, 23949365761691083828365260037993542774374237083829896, 94256148749182767338716790932645468498320336495261164, 371022943533791664017040688593534531481124096452627071, 1460715528474685417260719843968369544456392576634343907, 5751786825111065882333653120728397809169219540147762352, 22652214928911735843445253346981264852669351145978092366, 89225269570435325414125034611182354035741917245659214919, 351506174345263900414543038321901391543403243396542594091, 1384983421894138058551584296554060471935597744863465698202
Generating function in Maple syntax:
1/2*((-2*x^5+2*x^4+3*x^3-6*x^2+4*x-1)*(1-4*x)^(1/2)+6*x^5-6*x^4+x^3+4*x^2-4*x+1)/x/(2*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(-2 x^{5}+2 x^{4}+3 x^{3}-6 x^{2}+4 x -1\right) \sqrt{1-4 x}+6 x^{5}-6 x^{4}+x^{3}+4 x^{2}-4 x +1}{2 x \left(2 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**5 - 3*x**4 + x**3/2 + 2*x**2 - 2*x + sqrt(1 - 4*x)*(-2*x**5 + 2*x**4 + 3*x**3 - 6*x**2 + 4*x - 1)/2 + 1/2)/(x*(x - 1)**3*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^6*F(x)^2-(2*x-1)*(6*x^5-6*x^4+x^3+4*x^2-4*x+1)*(x-1)^3*F(x)+4*x^10-24*x^8+50*x^7-31*x^6-32*x^5+77*x^4-69*x^3+34*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(6 x^{5}-6 x^{4}+x^{3}+4 x^{2}-4 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+4 x^{10}-24 x^{8}+50 x^{7}-31 x^{6}-32 x^{5}+77 x^{4}-69 x^{3}+34 x^{2}-9 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 68
a(6) = 229
a(7) = 766
a(8) = 2567
a(9) = 8672
a(10) = 29622
a(n+7) = -8*(2*n-1)/(n+8)*a(n)+4*(7*n-6)/(n+8)*a(n+1)+2*(5*n+47)/(n+8)*a(n+2)-8*(8*n+33)/(n+8)*a(n+3)+(345+71*n)/(n+8)*a(n+4)-(38*n+223)/(n+8)*a(n+5)+(69+10*n)/(n+8)*a(n+6)+3/2*(n-2)*(n-5)/(n+8), 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) = 68
a \! \left(6\right) = 229
a \! \left(7\right) = 766
a \! \left(8\right) = 2567
a \! \left(9\right) = 8672
a \! \left(10\right) = 29622
a \! \left(n +7\right) = -\frac{8 \left(2 n -1\right) a \! \left(n \right)}{n +8}+\frac{4 \left(7 n -6\right) a \! \left(n +1\right)}{n +8}+\frac{2 \left(5 n +47\right) a \! \left(n +2\right)}{n +8}-\frac{8 \left(8 n +33\right) a \! \left(n +3\right)}{n +8}+\frac{\left(345+71 n \right) a \! \left(n +4\right)}{n +8}-\frac{\left(38 n +223\right) a \! \left(n +5\right)}{n +8}+\frac{\left(69+10 n \right) a \! \left(n +6\right)}{n +8}+\frac{3 \left(n -2\right) \left(n -5\right)}{2 \left(n +8\right)}, \quad n \geq 11
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21134/
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[4,x]+F[97,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[38,x]+F[6,x]
F[6,x] = F[21,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[12,x]
F[10,x] = F[11,x]+F[13,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = x
F[13,x] = F[14,x]+F[8,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[12,x]
F[19,x] = F[14,x]
F[20,x] = F[12,x]*F[8,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[1,x]+F[22,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[22,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[22,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = 2*F[15,x]+F[33,x]+F[37,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]
F[36,x] = F[32,x]
F[37,x] = F[12,x]*F[25,x]
F[38,x] = F[39,x]+F[82,x]
F[39,x] = F[40,x]+F[46,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[24,x]+F[43,x]
F[43,x] = F[40,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[43,x]
F[46,x] = F[15,x]+F[47,x]+F[64,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[53,x]
F[49,x] = F[22,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[52,x]
F[52,x] = F[22,x]+F[50,x]
F[53,x] = F[54,x]+F[60,x]
F[54,x] = F[15,x]+F[47,x]+F[55,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[22,x]+F[57,x]
F[57,x] = F[15,x]+F[55,x]+F[58,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[22,x]+F[57,x]
F[60,x] = F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[50,x]+F[63,x]
F[63,x] = F[61,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[22,x]+F[67,x]
F[67,x] = F[15,x]+F[30,x]+F[68,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[12,x]+F[67,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[15,x]+F[58,x]+F[64,x]
F[72,x] = F[15,x]+F[73,x]+F[77,x]+F[81,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[29,x]+F[75,x]
F[75,x] = 2*F[15,x]+F[73,x]+F[76,x]
F[76,x] = F[12,x]*F[57,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[67,x]
F[80,x] = F[72,x]
F[81,x] = F[12,x]*F[71,x]
F[82,x] = F[44,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[50,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[50,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[84,x]
F[91,x] = 3*F[15,x]+F[92,x]+F[96,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[87,x]
F[95,x] = F[91,x]
F[96,x] = F[12,x]*F[90,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[99,x,1]
F[99,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[102,x,k[0]]+F[104,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]*F[99,x,k[0]]
F[101,x,k[0]] = k[0]*x
F[102,x,k[0]] = F[103,x,k[0]]*F[12,x]
F[103,x,k[0]] = (F[99,x,k[0]]*k[0]-F[99,x,1])/(-1+k[0])
F[104,x,k[0]] = F[105,x,k[0]]*F[12,x]
F[105,x,k[0]] = F[106,x,k[0]]+F[5,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[153,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]+F[136,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]+F[112,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[101,x,k[0]]*F[111,x,k[0]]
F[111,x,k[0]] = F[1,x]+F[109,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[118,x,k[0]]+F[15,x]
F[113,x,k[0]] = F[101,x,k[0]]*F[114,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[22,x]
F[115,x,k[0]] = F[113,x,k[0]]+F[116,x,k[0]]+F[15,x]
F[116,x,k[0]] = F[117,x,k[0]]*F[12,x]
F[117,x,k[0]] = F[109,x,k[0]]+F[115,x,k[0]]
F[118,x,k[0]] = F[119,x,k[0]]*F[12,x]
F[119,x,k[0]] = F[120,x,k[0]]+F[125,x,k[0]]
F[120,x,k[0]] = F[109,x,k[0]]+F[121,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]+F[124,x,k[0]]+F[15,x]
F[122,x,k[0]] = F[101,x,k[0]]*F[123,x,k[0]]
F[123,x,k[0]] = F[12,x]+F[121,x,k[0]]
F[124,x,k[0]] = F[109,x,k[0]]*F[12,x]
F[125,x,k[0]] = F[112,x,k[0]]+F[126,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]+F[131,x,k[0]]+F[135,x,k[0]]+F[15,x]
F[127,x,k[0]] = F[101,x,k[0]]*F[128,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[29,x]
F[129,x,k[0]] = 2*F[15,x]+F[127,x,k[0]]+F[130,x,k[0]]
F[130,x,k[0]] = F[115,x,k[0]]*F[12,x]
F[131,x,k[0]] = F[12,x]*F[132,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[134,x,k[0]]
F[133,x,k[0]] = F[121,x,k[0]]
F[134,x,k[0]] = F[126,x,k[0]]
F[135,x,k[0]] = F[112,x,k[0]]*F[12,x]
F[136,x,k[0]] = F[137,x,k[0]]+F[140,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]
F[138,x,k[0]] = F[12,x]*F[139,x,k[0]]
F[139,x,k[0]] = F[109,x,k[0]]+F[137,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[12,x]*F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]+F[146,x,k[0]]
F[143,x,k[0]] = F[137,x,k[0]]+F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[12,x]*F[137,x,k[0]]
F[146,x,k[0]] = F[140,x,k[0]]+F[147,x,k[0]]
F[147,x,k[0]] = 3*F[15,x]+F[148,x,k[0]]+F[152,x,k[0]]
F[148,x,k[0]] = F[12,x]*F[149,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]+F[151,x,k[0]]
F[150,x,k[0]] = F[144,x,k[0]]
F[151,x,k[0]] = F[147,x,k[0]]
F[152,x,k[0]] = F[12,x]*F[140,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[204,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[163,x,k[0]]
F[155,x,k[0]] = F[15,x]+F[156,x,k[0]]+F[158,x,k[0]]
F[156,x,k[0]] = F[101,x,k[0]]*F[157,x,k[0]]
F[157,x,k[0]] = F[137,x,k[0]]+F[22,x]
F[158,x,k[0]] = F[12,x]*F[159,x,k[0]]
F[159,x,k[0]] = F[139,x,k[0]]+F[160,x,k[0]]
F[160,x,k[0]] = F[155,x,k[0]]+F[161,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[12,x]*F[160,x,k[0]]
F[163,x,k[0]] = F[15,x]+F[164,x,k[0]]+F[169,x,k[0]]+F[186,x,k[0]]
F[164,x,k[0]] = F[101,x,k[0]]*F[165,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[50,x]
F[166,x,k[0]] = F[167,x,k[0]]
F[167,x,k[0]] = F[12,x]*F[168,x,k[0]]
F[168,x,k[0]] = F[137,x,k[0]]+F[166,x,k[0]]
F[169,x,k[0]] = F[12,x]*F[170,x,k[0]]
F[170,x,k[0]] = F[171,x,k[0]]+F[172,x,k[0]]
F[171,x,k[0]] = F[115,x,k[0]]+F[166,x,k[0]]
F[172,x,k[0]] = F[173,x,k[0]]+F[179,x,k[0]]
F[173,x,k[0]] = F[15,x]+F[164,x,k[0]]+F[169,x,k[0]]+F[174,x,k[0]]
F[174,x,k[0]] = F[12,x]*F[175,x,k[0]]
F[175,x,k[0]] = F[137,x,k[0]]+F[176,x,k[0]]
F[176,x,k[0]] = 2*F[15,x]+F[174,x,k[0]]+F[177,x,k[0]]
F[177,x,k[0]] = F[12,x]*F[178,x,k[0]]
F[178,x,k[0]] = F[115,x,k[0]]+F[176,x,k[0]]
F[179,x,k[0]] = F[180,x,k[0]]
F[180,x,k[0]] = F[12,x]*F[181,x,k[0]]
F[181,x,k[0]] = F[182,x,k[0]]+F[185,x,k[0]]
F[182,x,k[0]] = F[183,x,k[0]]
F[183,x,k[0]] = F[12,x]*F[184,x,k[0]]
F[184,x,k[0]] = F[137,x,k[0]]+F[182,x,k[0]]
F[185,x,k[0]] = F[180,x,k[0]]
F[186,x,k[0]] = F[12,x]*F[187,x,k[0]]
F[187,x,k[0]] = F[188,x,k[0]]+F[192,x,k[0]]
F[188,x,k[0]] = F[137,x,k[0]]+F[189,x,k[0]]
F[189,x,k[0]] = 2*F[15,x]+F[145,x,k[0]]+F[190,x,k[0]]
F[190,x,k[0]] = F[12,x]*F[191,x,k[0]]
F[191,x,k[0]] = F[121,x,k[0]]+F[189,x,k[0]]
F[192,x,k[0]] = F[193,x,k[0]]+F[194,x,k[0]]
F[193,x,k[0]] = 2*F[15,x]+F[177,x,k[0]]+F[186,x,k[0]]
F[194,x,k[0]] = 2*F[15,x]+F[195,x,k[0]]+F[199,x,k[0]]+F[203,x,k[0]]
F[195,x,k[0]] = F[12,x]*F[196,x,k[0]]
F[196,x,k[0]] = F[129,x,k[0]]+F[197,x,k[0]]
F[197,x,k[0]] = 3*F[15,x]+F[195,x,k[0]]+F[198,x,k[0]]
F[198,x,k[0]] = F[12,x]*F[176,x,k[0]]
F[199,x,k[0]] = F[12,x]*F[200,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]+F[202,x,k[0]]
F[201,x,k[0]] = F[189,x,k[0]]
F[202,x,k[0]] = F[194,x,k[0]]
F[203,x,k[0]] = F[12,x]*F[193,x,k[0]]
F[204,x,k[0]] = F[161,x,k[0]]+F[205,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[12,x]*F[207,x,k[0]]
F[207,x,k[0]] = F[208,x,k[0]]+F[211,x,k[0]]
F[208,x,k[0]] = F[182,x,k[0]]+F[209,x,k[0]]
F[209,x,k[0]] = F[210,x,k[0]]
F[210,x,k[0]] = F[12,x]*F[182,x,k[0]]
F[211,x,k[0]] = F[212,x,k[0]]+F[213,x,k[0]]
F[212,x,k[0]] = F[206,x,k[0]]
F[213,x,k[0]] = 4*F[15,x]+F[214,x,k[0]]+F[218,x,k[0]]
F[214,x,k[0]] = F[12,x]*F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]+F[217,x,k[0]]
F[216,x,k[0]] = F[209,x,k[0]]
F[217,x,k[0]] = F[213,x,k[0]]
F[218,x,k[0]] = F[12,x]*F[212,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{97}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{22}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \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_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{82}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{24}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)+F_{64}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{22}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{54}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{22}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right)+F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{22}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{67}\! \left(x \right)
F_{80}\! \left(x \right) = F_{72}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{82}\! \left(x \right) = F_{44}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{50}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{84}\! \left(x \right)
F_{91}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{87}\! \left(x \right)
F_{95}\! \left(x \right) = F_{91}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x , 1\right)
F_{99}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = y x
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_{99}\! \left(x , y\right)+F_{99}\! \left(x , 1\right)}{-1+y}
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{109}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{22}\! \left(x \right)
F_{115}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{116}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{125}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)+F_{124}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{123}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{121}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)+F_{131}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{15}\! \left(x \right)
F_{127}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{29}\! \left(x \right)
F_{129}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{127}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{131}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{132}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{121}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{126}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{140}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{137}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{137}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{148}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{149}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{151}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{140}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{163}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{156}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{157}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{22}\! \left(x \right)
F_{158}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{139}\! \left(x , y\right)+F_{160}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{160}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{169}\! \left(x , y\right)+F_{186}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{50}\! \left(x \right)
F_{166}\! \left(x , y\right) = F_{167}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{168}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{170}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{171}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)+F_{179}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{164}\! \left(x , y\right)+F_{169}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{174}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{174}\! \left(x , y\right)+F_{177}\! \left(x , y\right)
F_{177}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{178}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{176}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{180}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{185}\! \left(x , y\right)
F_{182}\! \left(x , y\right) = F_{183}\! \left(x , y\right)
F_{183}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{184}\! \left(x , y\right)
F_{184}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{182}\! \left(x , y\right)
F_{185}\! \left(x , y\right) = F_{180}\! \left(x , y\right)
F_{186}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{187}\! \left(x , y\right)
F_{187}\! \left(x , y\right) = F_{188}\! \left(x , y\right)+F_{192}\! \left(x , y\right)
F_{188}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{189}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{145}\! \left(x , y\right)+F_{190}\! \left(x , y\right)
F_{190}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{191}\! \left(x , y\right)
F_{191}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{189}\! \left(x , y\right)
F_{192}\! \left(x , y\right) = F_{193}\! \left(x , y\right)+F_{194}\! \left(x , y\right)
F_{193}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{177}\! \left(x , y\right)+F_{186}\! \left(x , y\right)
F_{194}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{199}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{195}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{195}\! \left(x , y\right)+F_{198}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{176}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{189}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = F_{194}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{193}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{207}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = F_{208}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{208}\! \left(x , y\right) = F_{182}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{182}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = F_{212}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = 4 F_{15}\! \left(x \right)+F_{214}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{209}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{218}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{212}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_97(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_38(x) + F_6(x))
Eq(F_6(x), F_21(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_12(x))
Eq(F_10(x), F_11(x) + F_13(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_8(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_12(x))
Eq(F_19(x), F_14(x))
Eq(F_20(x), F_12(x)*F_8(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_1(x) + F_22(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_22(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_22(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), 2*F_15(x) + F_33(x) + F_37(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_12(x)*F_25(x))
Eq(F_38(x), F_39(x) + F_82(x))
Eq(F_39(x), F_40(x) + F_46(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_24(x) + F_43(x))
Eq(F_43(x), F_40(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_43(x))
Eq(F_46(x), F_15(x) + F_47(x) + F_64(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_53(x))
Eq(F_49(x), F_22(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_52(x))
Eq(F_52(x), F_22(x) + F_50(x))
Eq(F_53(x), F_54(x) + F_60(x))
Eq(F_54(x), F_15(x) + F_47(x) + F_55(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_22(x) + F_57(x))
Eq(F_57(x), F_15(x) + F_55(x) + F_58(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_22(x) + F_57(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_50(x) + F_63(x))
Eq(F_63(x), F_61(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_22(x) + F_67(x))
Eq(F_67(x), F_15(x) + F_30(x) + F_68(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_12(x) + F_67(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_15(x) + F_58(x) + F_64(x))
Eq(F_72(x), F_15(x) + F_73(x) + F_77(x) + F_81(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_29(x) + F_75(x))
Eq(F_75(x), 2*F_15(x) + F_73(x) + F_76(x))
Eq(F_76(x), F_12(x)*F_57(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_67(x))
Eq(F_80(x), F_72(x))
Eq(F_81(x), F_12(x)*F_71(x))
Eq(F_82(x), F_44(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_50(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_50(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_84(x))
Eq(F_91(x), 3*F_15(x) + F_92(x) + F_96(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_87(x))
Eq(F_95(x), F_91(x))
Eq(F_96(x), F_12(x)*F_90(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_99(x, 1))
Eq(F_99(x, k_0), F_1(x) + F_100(x, k_0) + F_102(x, k_0) + F_104(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0)*F_99(x, k_0))
Eq(F_101(x, k_0), k_0*x)
Eq(F_102(x, k_0), F_103(x, k_0)*F_12(x))
Eq(F_103(x, k_0), (-k_0*F_99(x, k_0) + F_99(x, 1))/(1 - k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_12(x))
Eq(F_105(x, k_0), F_106(x, k_0) + F_5(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_153(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0) + F_136(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0) + F_112(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_101(x, k_0)*F_111(x, k_0))
Eq(F_111(x, k_0), F_1(x) + F_109(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_118(x, k_0) + F_15(x))
Eq(F_113(x, k_0), F_101(x, k_0)*F_114(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_22(x))
Eq(F_115(x, k_0), F_113(x, k_0) + F_116(x, k_0) + F_15(x))
Eq(F_116(x, k_0), F_117(x, k_0)*F_12(x))
Eq(F_117(x, k_0), F_109(x, k_0) + F_115(x, k_0))
Eq(F_118(x, k_0), F_119(x, k_0)*F_12(x))
Eq(F_119(x, k_0), F_120(x, k_0) + F_125(x, k_0))
Eq(F_120(x, k_0), F_109(x, k_0) + F_121(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0) + F_124(x, k_0) + F_15(x))
Eq(F_122(x, k_0), F_101(x, k_0)*F_123(x, k_0))
Eq(F_123(x, k_0), F_12(x) + F_121(x, k_0))
Eq(F_124(x, k_0), F_109(x, k_0)*F_12(x))
Eq(F_125(x, k_0), F_112(x, k_0) + F_126(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0) + F_131(x, k_0) + F_135(x, k_0) + F_15(x))
Eq(F_127(x, k_0), F_101(x, k_0)*F_128(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_29(x))
Eq(F_129(x, k_0), F_127(x, k_0) + F_130(x, k_0) + 2*F_15(x))
Eq(F_130(x, k_0), F_115(x, k_0)*F_12(x))
Eq(F_131(x, k_0), F_12(x)*F_132(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_134(x, k_0))
Eq(F_133(x, k_0), F_121(x, k_0))
Eq(F_134(x, k_0), F_126(x, k_0))
Eq(F_135(x, k_0), F_112(x, k_0)*F_12(x))
Eq(F_136(x, k_0), F_137(x, k_0) + F_140(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0))
Eq(F_138(x, k_0), F_12(x)*F_139(x, k_0))
Eq(F_139(x, k_0), F_109(x, k_0) + F_137(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_12(x)*F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0) + F_146(x, k_0))
Eq(F_143(x, k_0), F_137(x, k_0) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_12(x)*F_137(x, k_0))
Eq(F_146(x, k_0), F_140(x, k_0) + F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0) + 3*F_15(x) + F_152(x, k_0))
Eq(F_148(x, k_0), F_12(x)*F_149(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_151(x, k_0))
Eq(F_150(x, k_0), F_144(x, k_0))
Eq(F_151(x, k_0), F_147(x, k_0))
Eq(F_152(x, k_0), F_12(x)*F_140(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_204(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_163(x, k_0))
Eq(F_155(x, k_0), F_15(x) + F_156(x, k_0) + F_158(x, k_0))
Eq(F_156(x, k_0), F_101(x, k_0)*F_157(x, k_0))
Eq(F_157(x, k_0), F_137(x, k_0) + F_22(x))
Eq(F_158(x, k_0), F_12(x)*F_159(x, k_0))
Eq(F_159(x, k_0), F_139(x, k_0) + F_160(x, k_0))
Eq(F_160(x, k_0), F_155(x, k_0) + F_161(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_12(x)*F_160(x, k_0))
Eq(F_163(x, k_0), F_15(x) + F_164(x, k_0) + F_169(x, k_0) + F_186(x, k_0))
Eq(F_164(x, k_0), F_101(x, k_0)*F_165(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_50(x))
Eq(F_166(x, k_0), F_167(x, k_0))
Eq(F_167(x, k_0), F_12(x)*F_168(x, k_0))
Eq(F_168(x, k_0), F_137(x, k_0) + F_166(x, k_0))
Eq(F_169(x, k_0), F_12(x)*F_170(x, k_0))
Eq(F_170(x, k_0), F_171(x, k_0) + F_172(x, k_0))
Eq(F_171(x, k_0), F_115(x, k_0) + F_166(x, k_0))
Eq(F_172(x, k_0), F_173(x, k_0) + F_179(x, k_0))
Eq(F_173(x, k_0), F_15(x) + F_164(x, k_0) + F_169(x, k_0) + F_174(x, k_0))
Eq(F_174(x, k_0), F_12(x)*F_175(x, k_0))
Eq(F_175(x, k_0), F_137(x, k_0) + F_176(x, k_0))
Eq(F_176(x, k_0), 2*F_15(x) + F_174(x, k_0) + F_177(x, k_0))
Eq(F_177(x, k_0), F_12(x)*F_178(x, k_0))
Eq(F_178(x, k_0), F_115(x, k_0) + F_176(x, k_0))
Eq(F_179(x, k_0), F_180(x, k_0))
Eq(F_180(x, k_0), F_12(x)*F_181(x, k_0))
Eq(F_181(x, k_0), F_182(x, k_0) + F_185(x, k_0))
Eq(F_182(x, k_0), F_183(x, k_0))
Eq(F_183(x, k_0), F_12(x)*F_184(x, k_0))
Eq(F_184(x, k_0), F_137(x, k_0) + F_182(x, k_0))
Eq(F_185(x, k_0), F_180(x, k_0))
Eq(F_186(x, k_0), F_12(x)*F_187(x, k_0))
Eq(F_187(x, k_0), F_188(x, k_0) + F_192(x, k_0))
Eq(F_188(x, k_0), F_137(x, k_0) + F_189(x, k_0))
Eq(F_189(x, k_0), F_145(x, k_0) + 2*F_15(x) + F_190(x, k_0))
Eq(F_190(x, k_0), F_12(x)*F_191(x, k_0))
Eq(F_191(x, k_0), F_121(x, k_0) + F_189(x, k_0))
Eq(F_192(x, k_0), F_193(x, k_0) + F_194(x, k_0))
Eq(F_193(x, k_0), 2*F_15(x) + F_177(x, k_0) + F_186(x, k_0))
Eq(F_194(x, k_0), 2*F_15(x) + F_195(x, k_0) + F_199(x, k_0) + F_203(x, k_0))
Eq(F_195(x, k_0), F_12(x)*F_196(x, k_0))
Eq(F_196(x, k_0), F_129(x, k_0) + F_197(x, k_0))
Eq(F_197(x, k_0), 3*F_15(x) + F_195(x, k_0) + F_198(x, k_0))
Eq(F_198(x, k_0), F_12(x)*F_176(x, k_0))
Eq(F_199(x, k_0), F_12(x)*F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0) + F_202(x, k_0))
Eq(F_201(x, k_0), F_189(x, k_0))
Eq(F_202(x, k_0), F_194(x, k_0))
Eq(F_203(x, k_0), F_12(x)*F_193(x, k_0))
Eq(F_204(x, k_0), F_161(x, k_0) + F_205(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_12(x)*F_207(x, k_0))
Eq(F_207(x, k_0), F_208(x, k_0) + F_211(x, k_0))
Eq(F_208(x, k_0), F_182(x, k_0) + F_209(x, k_0))
Eq(F_209(x, k_0), F_210(x, k_0))
Eq(F_210(x, k_0), F_12(x)*F_182(x, k_0))
Eq(F_211(x, k_0), F_212(x, k_0) + F_213(x, k_0))
Eq(F_212(x, k_0), F_206(x, k_0))
Eq(F_213(x, k_0), 4*F_15(x) + F_214(x, k_0) + F_218(x, k_0))
Eq(F_214(x, k_0), F_12(x)*F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0) + F_217(x, k_0))
Eq(F_216(x, k_0), F_209(x, k_0))
Eq(F_217(x, k_0), F_213(x, k_0))
Eq(F_218(x, k_0), F_12(x)*F_212(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, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, 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