0132_1023_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 62, 182, 539, 1653, 5291, 17598, 60268, 210752, 748007, 2684072, 9713242, 35393216, 129714131, 477774971, 1767532455, 6564654530, 24467329294, 91484680171, 343063835827, 1289912576731, 4861963239432, 18367386718557, 69533618166084, 263748086187553, 1002242485431282, 3814987039508096, 14544637113835861, 55534067025918103, 212336134709434097, 812944050743241236, 3116285512092931114, 11959798420229484178, 45950804393356222005, 176733862924469893606, 680425372004892885485, 2622127042826311268480, 10113918592737512206319, 39044429914103632916701, 150853479209483666220127, 583300119601793219751872, 2257117854094840960868160, 8740328711568358897214705, 33868773757261417467111565, 131327898242310105937772013, 509552245179898617839074246, 1978261657756723611356185363, 7684785670515442297724196078, 29869166945774877770321404107, 116157871455786937883132810072, 451959718027962478700180879886, 1759414616608836885477257293654, 6852456927844909526486261682763, 26700952856774923962065110695505, 104088460289122448149051830416046, 405944995127577273961610882293062, 1583850964596120619148481805006856, 6182127958584856803410133463373535, 24139737743045629131556972491341228, 94295850558771984399625456113937502, 368479169875816668702387637039315732, 1440418573150919687319244578163991375, 5632681584560312771887421020949188215, 22033725021956517537145556686786001795, 86218923998960285873759638198948594358, 337485502510215975851931771357872611034, 1321422108420282271080238105217966624247, 5175569924646105560599532005104968752867, 20276890389709399865290182117750985886135, 79463489365077377845930604613672927122972, 311496878311103321146981025291063958714217, 1221395654430378811847650189244410257852032, 4790408930363303911366165142369306702059861, 18793142726809884575286919146229914140996606, 73745243611532458459841267587627097588555276, 289450081175264899454586077493338818883435810, 1136359577947336271932237339928947105281300825, 4462290049988320482464450223349164541024571339, 17526585015616776834737558369592773957120621676, 68854441132780194707892887738008411450407565252, 270557451039395118028652134695824678307165703322, 1063353702922273835973056000856750793433717187005, 4180080073556524734514734513797394822059255253290, 16435314834665426797069222332015761675775501404455, 64633260585762914370496792228651772026853538697928, 254224158304000796523953750263852568519394465457119, 1000134600800354781929399869506563287032014546891937, 3935312233584004685417854810703391675221500952750287, 15487357822491889407128329439658426462821091304525900, 60960876535340415751462568532589813573604633253322452, 239993345518077005168915786526997049489483441806275117, 944973797977428207852605890261980245143589376492428017, 3721443204405954385563870580993327948782110129144225281, 14657929356129575437016877925885195327658001399305631666, 57743358069601357782187700766499181446170550301696689711, 227508830794229349661819540712601504148400885320427506450, 896519947090131496687170070707925932753875218121656754255
Generating function in Maple syntax:
1/4*(-2*(x^2+x-1)*(x-1)^5*(x-1/2)*(1-4*x)^(1/2)-4*x^13+14*x^12-10*x^11-14*x^10+26*x^9-12*x^8-15*x^7+16*x^6+10*x^5-37*x^4+43*x^3-26*x^2+8*x-1)/(x^2+x-1)/(x-1)^5/x/(x-1/2)
Generating function in latex syntax:
\frac{-2 \left(x^{2}+x -1\right) \left(x -1\right)^{5} \left(x -\frac{1}{2}\right) \sqrt{1-4 x}-4 x^{13}+14 x^{12}-10 x^{11}-14 x^{10}+26 x^{9}-12 x^{8}-15 x^{7}+16 x^{6}+10 x^{5}-37 x^{4}+43 x^{3}-26 x^{2}+8 x -1}{4 \left(x^{2}+x -1\right) \left(x -1\right)^{5} x \left(x -\frac{1}{2}\right)}
Generating function in sympy syntax:
(-x**13 + 7*x**12/2 - 5*x**11/2 - 7*x**10/2 + 13*x**9/2 - 3*x**8 - 15*x**7/4 + 4*x**6 + 5*x**5/2 - 37*x**4/4 + 43*x**3/4 - 13*x**2/2 + 2*x + sqrt(1 - 4*x)*(x - 1)**5*(x - 1/2)*(-2*x**2 - 2*x + 2)/4 - 1/4)/(x*(x - 1)**5*(x - 1/2)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x^2+x-1)^2*(x-1)^10*F(x)^2+(2*x-1)*(x^2+x-1)*(4*x^13-14*x^12+10*x^11+14*x^10-26*x^9+12*x^8+15*x^7-16*x^6-10*x^5+37*x^4-43*x^3+26*x^2-8*x+1)*(x-1)^5*F(x)+1-16*x+116*x^2-2768*x^5+1424*x^4-501*x^3-288*x^13-830*x^12+1877*x^11-2208*x^10+1206*x^9+984*x^8-3059*x^7+3665*x^6+420*x^17+17*x^16-703*x^15+904*x^14+4*x^25-28*x^24+69*x^23-42*x^22-125*x^21+276*x^20-135*x^19-259*x^18 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{10} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(x^{2}+x -1\right) \left(4 x^{13}-14 x^{12}+10 x^{11}+14 x^{10}-26 x^{9}+12 x^{8}+15 x^{7}-16 x^{6}-10 x^{5}+37 x^{4}-43 x^{3}+26 x^{2}-8 x +1\right) \left(x -1\right)^{5} F \! \left(x \right)+1-16 x +116 x^{2}-2768 x^{5}+1424 x^{4}-501 x^{3}-288 x^{13}-830 x^{12}+1877 x^{11}-2208 x^{10}+1206 x^{9}+984 x^{8}-3059 x^{7}+3665 x^{6}+420 x^{17}+17 x^{16}-703 x^{15}+904 x^{14}+4 x^{25}-28 x^{24}+69 x^{23}-42 x^{22}-125 x^{21}+276 x^{20}-135 x^{19}-259 x^{18} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 182
a(7) = 539
a(8) = 1653
a(9) = 5291
a(10) = 17598
a(11) = 60268
a(12) = 210752
a(13) = 748007
a(14) = 2684072
a(15) = 9713242
a(16) = 35393216
a(17) = 129714131
a(n+7) = 8*(2*n+1)/(n+8)*a(n)+4*(3*n+4)/(n+8)*a(n+1)-2*(24*n+61)/(n+8)*a(n+2)+(16+3*n)/(n+8)*a(n+3)+2*(23*n+104)/(n+8)*a(n+4)-(35*n+198)/(n+8)*a(n+5)+2*(5*n+34)/(n+8)*a(n+6)-1/24*(3*n^5-70*n^4+197*n^3+1990*n^2-4280*n-2640)/(n+8), n >= 18
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) = 62
a \! \left(6\right) = 182
a \! \left(7\right) = 539
a \! \left(8\right) = 1653
a \! \left(9\right) = 5291
a \! \left(10\right) = 17598
a \! \left(11\right) = 60268
a \! \left(12\right) = 210752
a \! \left(13\right) = 748007
a \! \left(14\right) = 2684072
a \! \left(15\right) = 9713242
a \! \left(16\right) = 35393216
a \! \left(17\right) = 129714131
a \! \left(n +7\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +8}+\frac{4 \left(3 n +4\right) a \! \left(n +1\right)}{n +8}-\frac{2 \left(24 n +61\right) a \! \left(n +2\right)}{n +8}+\frac{\left(16+3 n \right) a \! \left(n +3\right)}{n +8}+\frac{2 \left(23 n +104\right) a \! \left(n +4\right)}{n +8}-\frac{\left(35 n +198\right) a \! \left(n +5\right)}{n +8}+\frac{2 \left(5 n +34\right) a \! \left(n +6\right)}{n +8}-\frac{3 n^{5}-70 n^{4}+197 n^{3}+1990 n^{2}-4280 n -2640}{24 \left(n +8\right)}, \quad n \geq 18
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21270/
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[111,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[110,x]+F[48,x]+F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[21,x]+F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[10,x]+F[14,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[12,x]+F[18,x]
F[18,x] = F[15,x]+F[16,x]+F[19,x]
F[19,x] = F[10,x]*F[12,x]
F[20,x] = F[12,x]*F[13,x]
F[21,x] = F[22,x]+F[27,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[15,x]+F[24,x]+F[26,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[10,x]+F[23,x]
F[26,x] = F[12,x]*F[22,x]
F[27,x] = F[23,x]+F[28,x]
F[28,x] = F[15,x]+F[29,x]+F[37,x]+F[47,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[10,x]+F[31,x]
F[34,x] = 2*F[15,x]+F[29,x]+F[35,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[23,x]+F[34,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[12,x]+F[39,x]
F[42,x] = 2*F[15,x]+F[37,x]+F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[19,x]
F[46,x] = F[43,x]
F[47,x] = F[12,x]*F[27,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x,1]
F[50,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[108,x,k[0]]+F[51,x,k[0]]+F[98,x,k[0]]
F[51,x,k[0]] = F[12,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[69,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[62,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[9,x]
F[55,x,k[0]] = F[56,x,k[0]]+F[60,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]*F[59,x,k[0]]
F[58,x,k[0]] = F[1,x]+F[56,x,k[0]]
F[59,x,k[0]] = k[0]*x
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[55,x,k[0]]
F[62,x,k[0]] = F[13,x]+F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[59,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[10,x]+F[64,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[12,x]*F[63,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[81,x,k[0]]
F[70,x,k[0]] = F[22,x]+F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]+F[77,x,k[0]]
F[72,x,k[0]] = F[15,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[12,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[56,x,k[0]]+F[72,x,k[0]]
F[75,x,k[0]] = F[59,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[10,x]+F[72,x,k[0]]
F[77,x,k[0]] = 2*F[15,x]+F[78,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[12,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[60,x,k[0]]+F[77,x,k[0]]
F[80,x,k[0]] = F[12,x]*F[71,x,k[0]]
F[81,x,k[0]] = F[27,x]+F[82,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]+F[88,x,k[0]]
F[83,x,k[0]] = 2*F[15,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[12,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[64,x,k[0]]+F[83,x,k[0]]
F[86,x,k[0]] = F[59,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[23,x]+F[83,x,k[0]]
F[88,x,k[0]] = 3*F[15,x]+F[89,x,k[0]]+F[97,x,k[0]]
F[89,x,k[0]] = F[12,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]+F[94,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[12,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[64,x,k[0]]+F[91,x,k[0]]
F[94,x,k[0]] = 3*F[15,x]+F[89,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[12,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[83,x,k[0]]+F[94,x,k[0]]
F[97,x,k[0]] = F[12,x]*F[82,x,k[0]]
F[98,x,k[0]] = F[12,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[50,x,k[0]]*k[0]-F[50,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[59,x,k[0]]
F[101,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[102,x,k[0]]+F[106,x,k[0]]
F[102,x,k[0]] = F[103,x,k[0]]*F[12,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[105,x,k[0]]
F[104,x,k[0]] = F[58,x,k[0]]+F[66,x,k[0]]
F[105,x,k[0]] = F[76,x,k[0]]+F[87,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]*F[12,x]
F[107,x,k[0]] = 1/(-1+k[0])*(F[101,x,k[0]]*k[0]-F[101,x,1])
F[108,x,k[0]] = F[109,x,k[0]]*F[12,x]
F[109,x,k[0]] = 1/(-1+k[0])*(F[101,x,k[0]]*k[0]-F[101,x,1])
F[110,x] = F[100,x,1]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[113,x]+F[155,x]
F[113,x] = F[114,x]+F[126,x]
F[114,x] = F[1,x]+F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[12,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[1,x]+F[12,x]
F[119,x] = F[115,x]+F[120,x]
F[120,x] = F[121,x]+F[125,x]+F[15,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[12,x]
F[124,x] = F[120,x]
F[125,x] = F[115,x]*F[12,x]
F[126,x] = F[127,x]+F[143,x]
F[127,x] = F[128,x]
F[128,x] = F[12,x]*F[129,x]
F[129,x] = F[130,x]+F[133,x]
F[130,x] = F[1,x]+F[131,x]
F[131,x] = F[132,x]
F[132,x] = F[12,x]*F[130,x]
F[133,x] = F[134,x]+F[140,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[118,x]+F[137,x]
F[137,x] = F[134,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[12,x]*F[134,x]
F[140,x] = F[141,x]
F[141,x] = F[12,x]*F[142,x]
F[142,x] = F[134,x]
F[143,x] = F[144,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[10,x]+F[45,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[144,x]
F[149,x] = 2*F[15,x]+F[150,x]+F[154,x]
F[150,x] = F[12,x]*F[151,x]
F[151,x] = F[152,x]+F[153,x]
F[152,x] = F[45,x]
F[153,x] = F[149,x]
F[154,x] = F[12,x]*F[148,x]
F[155,x] = F[156,x]+F[183,x]
F[156,x] = F[157,x]+F[163,x]
F[157,x] = F[158,x]
F[158,x] = F[12,x]*F[159,x]
F[159,x] = F[160,x]+F[9,x]
F[160,x] = F[157,x]+F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[12,x]*F[160,x]
F[163,x] = F[15,x]+F[164,x]+F[173,x]
F[164,x] = F[12,x]*F[165,x]
F[165,x] = F[166,x]+F[167,x]
F[166,x] = F[10,x]+F[31,x]
F[167,x] = F[168,x]+F[169,x]
F[168,x] = F[15,x]+F[164,x]+F[26,x]
F[169,x] = F[170,x]
F[170,x] = F[12,x]*F[171,x]
F[171,x] = F[172,x]+F[31,x]
F[172,x] = F[170,x]
F[173,x] = F[12,x]*F[174,x]
F[174,x] = F[175,x]+F[176,x]
F[175,x] = F[10,x]+F[39,x]
F[176,x] = F[177,x]+F[178,x]
F[177,x] = F[15,x]+F[173,x]+F[24,x]
F[178,x] = 2*F[15,x]+F[179,x]+F[43,x]
F[179,x] = F[12,x]*F[180,x]
F[180,x] = F[181,x]+F[182,x]
F[181,x] = F[39,x]
F[182,x] = F[178,x]
F[183,x] = F[184,x]+F[193,x]
F[184,x] = F[185,x]
F[185,x] = F[12,x]*F[186,x]
F[186,x] = F[187,x]+F[188,x]
F[187,x] = F[157,x]
F[188,x] = F[189,x]
F[189,x] = F[12,x]*F[190,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[157,x]
F[192,x] = F[189,x]
F[193,x] = F[194,x]
F[194,x] = F[12,x]*F[195,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[31,x]
F[197,x] = F[194,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{111}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{110}\! \left(x \right)+F_{48}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{21}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \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_{12}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{27}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{37}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right)
F_{46}\! \left(x \right) = F_{43}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x , 1\right)
F_{50}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = y x
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{63}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = 2 F_{15}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = 3 F_{15}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{50}\! \left(x , y\right)+F_{50}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{106}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{107}\! \left(x , y\right) = -\frac{-y F_{101}\! \left(x , y\right)+F_{101}\! \left(x , 1\right)}{-1+y}
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{109}\! \left(x , y\right) = -\frac{-y F_{101}\! \left(x , y\right)+F_{101}\! \left(x , 1\right)}{-1+y}
F_{110}\! \left(x \right) = F_{100}\! \left(x , 1\right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{155}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{126}\! \left(x \right)
F_{114}\! \left(x \right) = F_{1}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{125}\! \left(x \right)+F_{15}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{12}\! \left(x \right)
F_{124}\! \left(x \right) = F_{120}\! \left(x \right)
F_{125}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{143}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{133}\! \left(x \right)
F_{130}\! \left(x \right) = F_{1}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{140}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{118}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{134}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{134}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{144}\! \left(x \right)
F_{149}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{150}\! \left(x \right)+F_{154}\! \left(x \right)
F_{150}\! \left(x \right) = F_{12}\! \left(x \right) F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)+F_{153}\! \left(x \right)
F_{152}\! \left(x \right) = F_{45}\! \left(x \right)
F_{153}\! \left(x \right) = F_{149}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{148}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{183}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{163}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{12}\! \left(x \right) F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{9}\! \left(x \right)
F_{160}\! \left(x \right) = F_{157}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{160}\! \left(x \right)
F_{163}\! \left(x \right) = F_{15}\! \left(x \right)+F_{164}\! \left(x \right)+F_{173}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{167}\! \left(x \right)
F_{166}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{15}\! \left(x \right)+F_{164}\! \left(x \right)+F_{26}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{12}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{31}\! \left(x \right)
F_{172}\! \left(x \right) = F_{170}\! \left(x \right)
F_{173}\! \left(x \right) = F_{12}\! \left(x \right) F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{176}\! \left(x \right)
F_{175}\! \left(x \right) = F_{10}\! \left(x \right)+F_{39}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{178}\! \left(x \right)
F_{177}\! \left(x \right) = F_{15}\! \left(x \right)+F_{173}\! \left(x \right)+F_{24}\! \left(x \right)
F_{178}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{179}\! \left(x \right)+F_{43}\! \left(x \right)
F_{179}\! \left(x \right) = F_{12}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{182}\! \left(x \right)
F_{181}\! \left(x \right) = F_{39}\! \left(x \right)
F_{182}\! \left(x \right) = F_{178}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{193}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = F_{12}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{188}\! \left(x \right)
F_{187}\! \left(x \right) = F_{157}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = F_{12}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{157}\! \left(x \right)
F_{192}\! \left(x \right) = F_{189}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{12}\! \left(x \right) F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{31}\! \left(x \right)
F_{197}\! \left(x \right) = F_{194}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_111(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_110(x) + F_48(x) + F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_21(x) + F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_10(x) + F_14(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_12(x) + F_18(x))
Eq(F_18(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_19(x), F_10(x)*F_12(x))
Eq(F_20(x), F_12(x)*F_13(x))
Eq(F_21(x), F_22(x) + F_27(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_15(x) + F_24(x) + F_26(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_10(x) + F_23(x))
Eq(F_26(x), F_12(x)*F_22(x))
Eq(F_27(x), F_23(x) + F_28(x))
Eq(F_28(x), F_15(x) + F_29(x) + F_37(x) + F_47(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_10(x) + F_31(x))
Eq(F_34(x), 2*F_15(x) + F_29(x) + F_35(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_23(x) + F_34(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_12(x) + F_39(x))
Eq(F_42(x), 2*F_15(x) + F_37(x) + F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_19(x))
Eq(F_46(x), F_43(x))
Eq(F_47(x), F_12(x)*F_27(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_50(x, 1))
Eq(F_50(x, k_0), F_1(x) + F_100(x, k_0) + F_108(x, k_0) + F_51(x, k_0) + F_98(x, k_0))
Eq(F_51(x, k_0), F_12(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_69(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_62(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_9(x))
Eq(F_55(x, k_0), F_56(x, k_0) + F_60(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0)*F_59(x, k_0))
Eq(F_58(x, k_0), F_1(x) + F_56(x, k_0))
Eq(F_59(x, k_0), k_0*x)
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_55(x, k_0))
Eq(F_62(x, k_0), F_13(x) + F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_59(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_10(x) + F_64(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_12(x)*F_63(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_81(x, k_0))
Eq(F_70(x, k_0), F_22(x) + F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0) + F_77(x, k_0))
Eq(F_72(x, k_0), F_15(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_12(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_56(x, k_0) + F_72(x, k_0))
Eq(F_75(x, k_0), F_59(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_10(x) + F_72(x, k_0))
Eq(F_77(x, k_0), 2*F_15(x) + F_78(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_12(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_60(x, k_0) + F_77(x, k_0))
Eq(F_80(x, k_0), F_12(x)*F_71(x, k_0))
Eq(F_81(x, k_0), F_27(x) + F_82(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0) + F_88(x, k_0))
Eq(F_83(x, k_0), 2*F_15(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_12(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_64(x, k_0) + F_83(x, k_0))
Eq(F_86(x, k_0), F_59(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_23(x) + F_83(x, k_0))
Eq(F_88(x, k_0), 3*F_15(x) + F_89(x, k_0) + F_97(x, k_0))
Eq(F_89(x, k_0), F_12(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0) + F_94(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_12(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_64(x, k_0) + F_91(x, k_0))
Eq(F_94(x, k_0), 3*F_15(x) + F_89(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_12(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_83(x, k_0) + F_94(x, k_0))
Eq(F_97(x, k_0), F_12(x)*F_82(x, k_0))
Eq(F_98(x, k_0), F_12(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_50(x, k_0) - F_50(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_59(x, k_0))
Eq(F_101(x, k_0), F_1(x) + F_100(x, k_0) + F_102(x, k_0) + F_106(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_12(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_105(x, k_0))
Eq(F_104(x, k_0), F_58(x, k_0) + F_66(x, k_0))
Eq(F_105(x, k_0), F_76(x, k_0) + F_87(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0)*F_12(x))
Eq(F_107(x, k_0), (k_0*F_101(x, k_0) - F_101(x, 1))/(k_0 - 1))
Eq(F_108(x, k_0), F_109(x, k_0)*F_12(x))
Eq(F_109(x, k_0), (-k_0*F_101(x, k_0) + F_101(x, 1))/(1 - k_0))
Eq(F_110(x), F_100(x, 1))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_155(x))
Eq(F_113(x), F_114(x) + F_126(x))
Eq(F_114(x), F_1(x) + F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_12(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_1(x) + F_12(x))
Eq(F_119(x), F_115(x) + F_120(x))
Eq(F_120(x), F_121(x) + F_125(x) + F_15(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_12(x))
Eq(F_124(x), F_120(x))
Eq(F_125(x), F_115(x)*F_12(x))
Eq(F_126(x), F_127(x) + F_143(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_12(x)*F_129(x))
Eq(F_129(x), F_130(x) + F_133(x))
Eq(F_130(x), F_1(x) + F_131(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_12(x)*F_130(x))
Eq(F_133(x), F_134(x) + F_140(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_118(x) + F_137(x))
Eq(F_137(x), F_134(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_12(x)*F_134(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_12(x)*F_142(x))
Eq(F_142(x), F_134(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_10(x) + F_45(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_144(x))
Eq(F_149(x), 2*F_15(x) + F_150(x) + F_154(x))
Eq(F_150(x), F_12(x)*F_151(x))
Eq(F_151(x), F_152(x) + F_153(x))
Eq(F_152(x), F_45(x))
Eq(F_153(x), F_149(x))
Eq(F_154(x), F_12(x)*F_148(x))
Eq(F_155(x), F_156(x) + F_183(x))
Eq(F_156(x), F_157(x) + F_163(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_12(x)*F_159(x))
Eq(F_159(x), F_160(x) + F_9(x))
Eq(F_160(x), F_157(x) + F_161(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_12(x)*F_160(x))
Eq(F_163(x), F_15(x) + F_164(x) + F_173(x))
Eq(F_164(x), F_12(x)*F_165(x))
Eq(F_165(x), F_166(x) + F_167(x))
Eq(F_166(x), F_10(x) + F_31(x))
Eq(F_167(x), F_168(x) + F_169(x))
Eq(F_168(x), F_15(x) + F_164(x) + F_26(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_12(x)*F_171(x))
Eq(F_171(x), F_172(x) + F_31(x))
Eq(F_172(x), F_170(x))
Eq(F_173(x), F_12(x)*F_174(x))
Eq(F_174(x), F_175(x) + F_176(x))
Eq(F_175(x), F_10(x) + F_39(x))
Eq(F_176(x), F_177(x) + F_178(x))
Eq(F_177(x), F_15(x) + F_173(x) + F_24(x))
Eq(F_178(x), 2*F_15(x) + F_179(x) + F_43(x))
Eq(F_179(x), F_12(x)*F_180(x))
Eq(F_180(x), F_181(x) + F_182(x))
Eq(F_181(x), F_39(x))
Eq(F_182(x), F_178(x))
Eq(F_183(x), F_184(x) + F_193(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_12(x)*F_186(x))
Eq(F_186(x), F_187(x) + F_188(x))
Eq(F_187(x), F_157(x))
Eq(F_188(x), F_189(x))
Eq(F_189(x), F_12(x)*F_190(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_157(x))
Eq(F_192(x), F_189(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_12(x)*F_195(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_31(x))
Eq(F_197(x), F_194(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 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]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": 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